Following are 15 white papers written by Dr. Robert Nelson. Bob Nelson taught this course for many years prior to his passing in 2013 was regarded an expert in the field of satellites and satellite communications. Chris DeBoy now teaches Satellite Communications Design & Technology and continues the same level of knowledge and teaching dedication.

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Via Satellite, July, 1998

A Primer onSatelliteCommunicationsby Robert A. Nelson

In 1945 Arthur C. Clarke wrote an articleentitled "The Future of WorldCommunications" for the magazineWireless World. This article, which theeditors renamed "Extra-TerrestrialRelays", was published in the Octoberissue. In it Clarke described the propertiesof the geostationary orbit, a circular orbitin the equatorial plane of the earth suchthat a satellite appears to hover over afixed point on the equator. The period ofrevolution is equal to the period ofrotation of the earth with respect to thestars, or 23 hours 56 minutes 4.1 seconds,and thus by Kepler's third law the orbitalradius is 42,164 km. Taking into accountthe radius of the earth, the height of asatellite above the equator is 35,786 km. Clarke observed that only three satelliteswould be required to providecommunications over the inhabited earth.

As a primary application of sucha satellite system, Clarke proposed thatsatellites in geostationary orbit mightprovide direct broadcast television servicesimilar to DBS systems like DirecTV -- aremarkable idea at a time when televisionwas still in its infancy and it was not yetknown whether radio signals couldpenetrate the ionosphere. He worked out asimple link budget, assuming a downlinkfrequency of 3 GHz, and estimated that therequired transmitter output power forbroadcast service to small parabolicantenna receivers would be about 50 watts. Electric power would be provided bysteam generators heated by solar mirrors,but advances in technology might make itpossible to replace them by arrays ofphotoelectric cells. Batteries would beused to provide uninterrupted serviceduring eclipses, which occur in twoseasons centered about the equinoxes.

Clarke also estimated the mass ratio of amultistage launch vehicle necessary todeploy the satellite. However, he imaginedthe geostationary satellites to be outpostsinhabited by astronauts to whom supplieswould be ferried up on a regular basis,much like the Mir space station and theinternational space station now underconstruction. Twenty years later, in his book Voicesfrom the Sky, Clarke wrote a chapterentitled "A Short Pre-History of Comsats,Or: How I Lost a Billion Dollars in MySpare Time". For he did not patent theidea of a geostationary orbit and, believe itor not, orbits can and have been patented. (Recall the recent patent controversybetween Odyssey and ICO.) However,despite the tongue-in-cheek subtitle, thefamous author would not have profitedfrom his idea for two reasons. First,arguably, prior art existed in the literature. In 1929 the Austrian engineerH. Noordwig observed that a satellite at analtitude of 35,786 km in the equatorialplane would appear motionless whenviewed from earth (as cited by BrunoPattan in Satellite Systems: Principles andTechnologies). Second, had Clarkeobtained a patent in 1945, it would haveexpired in 1962, 17 years after the conceptwas first disclosed and two years beforethe first geostationary satellite, Syncom III,was successfully launched. Nevertheless,Clarke can rightfully claim credit for thefirst detailed technical exposition ofsatellite communications with specificreference to the geostationary orbit. Hisvision was realized through the pioneeringefforts of such scientists as John Pierce ofthe Bell Telephone Laboratories, head ofthe Telstar program and co-inventor of thetraveling wave tube amplifier, and HaroldRosen of the Hughes Aircraft Company,who was the driving force behind theSyncom program. Since 1964, approximately 265satellites have been launched intogeostationary orbit, of whichapproximately 185 are operational. Another 67 GEO satellites are presently onorder. The majority of these satellites havebeen used for the traditional fixed satelliteservice in C- and Ku-band, but also includesatellites in the direct broadcast service,

digital audio radio service, and mobilesatellite service. In addition, numerousnongeostationary systems are in theprocess of deployment or have beenproposed for a variety of consumerservices, including mobile telephony, datagathering and messaging, and broadbandapplications. In May, 1997, 73 new GEOsatellites were licensed for broadbandservices at Ka-band and last Septemberapplications for a dozen more systemswere submitted to the FederalCommunications Commission (FCC) forgeostationary, nongeostationary, andhybrid satellite systems to providebroadband services at V-band. The totalnumber of planned new satellites exceeds1300. The design of a satellitecommunications system presents manyinteresting alternatives and tradeoffs. Thecharacteristics include the choice of orbit,the method of multiple access, the methodsof modulation and coding, and the tradeoffbetween power and bandwidth. In thisarticle, these choices will be brieflydescribed and hopefully a sense of whysatellite engineers find this field ofendeavor so fascinating will be conveyed.

ORBIT

The system design begins with the choiceof orbit. The orbital altitude regimes havebeen conveniently classified as Low EarthOrbit (LEO), Medium Earth Orbit (MEO),and geostationary orbit (GEO). Thealtitude of LEO is about 1000 km, orabove the atmosphere but below the firstVan Allen radiation belt. The altitude ofMEO is ten times greater, that is 10,000km, which lies between the first andsecond Van Allen belts. The altitude ofGEO is uniquely 35,786 km as statedabove. A fourth category is High EarthOrbit (HEO), which is at about 20,000 kmand is above the second Van Allen belt butbelow GEO. (The acronym HEO has alsobeen used to mean "highly elliptical orbit"; can we find a new term for this category? The progression LEO, MEO, HEO, GEOis quite appealing.) Besides altitude, two other importantorbital parameters are inclination andeccentricity. The inclination may beselected on the basis of maximizing the

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level of multiple satellite coverage. Elliptical orbits may be used witheccentricities designed to maximize thedwell time over a particular region. The appropriate orbit is often suggestedby the nature of the service, the businessplan, or the constraints of thecommunications link. These properties arewell illustrated by the variety of satellitemobile telephony systems underconstruction. Iridium is designed forcontinuous global coverage. This is a LEOconstellation of 66 satellites in polar orbitsat an altitude of 780 km. The choice ofLEO was dictated by the desire tominimize power in both the satellite andthe mobile handset, minimize the satelliteantenna size, minimize the time delay, orlatency, for a two-way signal, andmaximize the angle of elevation. Theorbital period is 100 minutes and a givensatellite is in view for only ten minutesbefore handover of a call to a followingsatellite. An Iridium satellite has extensiveonboard processing and a telephone call isrouted through the constellation viaintersatellite links. Globalstar employs a constellation of48 satellites in orbits inclined at 52° at analtitude of 1406 km. This systemconcentrates coverage over the temperateregions of the earth from 70° S to 70° Nlatitude. A technique called spatialdiversity is used, wherein signals receivedsimultaneously from two satellites arecombined in the receiver to mitigate lossesdue to blockage and multipath effects. Thus an inclined, nonpolar orbitconstellation was chosen to ensure that atleast two satellites are visible at all times. The Globalstar system uses nonprocessing,or “bent pipe” satellites. The third major mobile telephonysatellite entry is ICO. This system willconsist of 10 operational satellites in MEOat an altitude of 10,355 km. (The acronymICO derives from the term "intermediatecircular orbit", a synonym for MEO.) MEO is an excellent compromise betweenLEO and GEO. The satellite antenna sizeand power are relatively modest and thelatency is still small. Yet the number ofsatellites required for global coverage issignificantly less than LEO and the dwelltime is considerably longer. The ICO orbit

has a period of revolution of 6 hours andthe time a satellite is in view is on the orderof two hours. Other satellite mobile telephonysystems include ECCO and Ellipso. ECCO is a circular orbit constellation inthe equatorial plane designed forcommunications in tropical regions. Ellipso employs elliptical orbits tomaximize coverage over the northernhemisphere. There is, nevertheless, a validgeostationary alternative for a mobiletelephony satellite. The primary advantageis that the system can be built up on aregional basis. With only one satellite, anentire country or geographical region canbe served. Although the two-way timedelay can be over a half second and isquite perceptible, this is a defect that apopulation may be willing to accept if it isunderserved by a terrestrial telephonysystem. An example is the Asia CellularSatellite system (Aces) that is being builtby Lockheed Martin for service to thePacific Rim. To provide the requiredcellular coverage, the satellite antennas areabout 12 meters across.

MULTIPLE ACCESS

Multiple access refers to the method bywhich many users share a common satelliteresource. There are three primarymethods: Frequency Division MultipleAccess (FDMA), Time Division MultipleAccess (TDMA), and Code DivisionMultiple Access (CDMA). With FDMA the available spectrum isdivided among all of the users. Each userobtains a dedicated portion of thespectrum. FDMA can be used for eitheranalog or digital signals. With TDMA each user is assigned atime slot in a repetitive time frame. Databits are stored in a buffer and are burst tothe satellite during the assigned time slot. The signal occupies the entire transponderbandwidth. Because bits are stored duringthe portion of the time frame not assignedto the user, TDMA is inherently digital. CDMA is a method in which the signalto be transmitted is modulated by apseudorandom noise (PRN) code. Thecode rate is usually several orders ofmagnitude greater than the information bit

rate. Their ratio is called the processinggain. The code spreads the signal over thefull bandwidth available (hence CDMA isalso called "spread spectrum") and allusers share the same spectrum. Thereceiver modulates the signals from allusers simultaneously with a replica PRNcode. The desired signal is obtained byautocorrelation, while all of the undesiredsignals are spread over the full bandwidthand appear as white noise. Frequency Division Multiple Access isrelatively simple both conceptually and interms of the hardware required. However,a transponder is a nonlinear device. Thismeans that the output power is not merelyproportional to the input power, but ratheris represented by a curve that can beapproximated by a third order polynomial. For multiple carriers, this nonlinearitygenerates harmonics that produceintermodulation interference amongneighboring channels. In order to mitigatethis effect, the input power is reduced inorder to operate in the linear portion of thetransponder output vs. input powercharacteristic so that intermodulation isreduced to an acceptable level. The reduction in power is called"backoff". At a typical backoff of 6 dB,the input power is only one fourth themaximum possible value at saturation andthe output power is correspondingly less. Backoff is not required when only onecarrier occupies the transponder, such as atypical FM video channel, a TDMAcarrier, or several channels multiplexedonto a single carrier at the earth station. A major advantage of TDMA is thatbackoff is not required, since at any giventime a single user occupies the fullbandwidth of the transponder. Thus theoutput power of the transponder is muchhigher than with FDMA. Anotheradvantage of TDMA is that it is moreflexible. User allocations can be changedwith relatively simple changes to software. CDMA offers the potential of greatercapacity. However, the theory of CDMAassumes that all users appear to contributeequally to the overall noise. Because usersare at different distances with respect toone another, this assumption implies theneed for dynamic power control. Anotheradvantage is that the population of users

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need not be known in advance. As usersare added to the system, the signal qualitydegrades slowly. Other advantages arethat CDMA mitigates interference andenhances data security. The mobile telephony satellite systemsillustrate these alternatives. Both Iridiumand ICO use a combination of FDMA andTDMA. The available spectrum is dividedinto sub-bands and TDMA is used withineach sub-band. The capacity per satellitefor Iridium is approximately 1100simultaneous users, whereas each ICOsatellite is designed to support at least4500 telephone channels. Globalstar usesa combination of FDMA and CDMA(channelized CDMA). The availablespectrum is divided into 1.25 MHz sub-bands and multiple users simultaneouslyoccupy each sub-band via CDMA.

BANDWIDTH

There are numerous measures ofbandwidth and one must be careful todistinguish among them. The noisebandwidth is the bandwidth the noisepower would have if it were contained in arectangle whose height is the peak spectralpower density. The noise bandwidth B isthe bandwidth relating the thermal noisepower N to the system temperature T, suchthat N = k T B, where k is Boltzmann'sconstant. The occupied bandwidth is thebandwidth required for the signal to passthrough a band limited filter. In an FDMAsystem, it is the occupied bandwidth thatdetermines the system capacity. Theoccupied bandwidth is about 1.2 timesgreater than the noise bandwidth. Theextra margin is the value of the rolloff inthe pulse shaping, which is used tominimize intersymbol interference (ISI). This type of interference is caused whenthe tails of preceding and following pulsesoverlap the peak of the observed pulse. Nyquist showed that ISI could beeliminated if the pulses followed a sin x/xfunction. In practice, this is impossible toachieve and is approximated by raisedcosine pulse shaping. A third measure of bandwidth is thenull-to-null bandwidth. This bandwidth isthe width between the zeroes of the mainspectral lobe. Other measures of

bandwidth, such as the half-powerbandwidth, are also used.

FREQUENCY

The frequency is chosen on the basis ofmaximizing the performance of the systemand exploiting the portions of theelectromagnetic spectrum that areavailable. One important relation is thatthe gain of an antenna increases withincreasing frequency for a fixed antennasize. On the other hand, the antenna gainis determined by the area of coverage. Thus once the area of coverage isspecified, the gain is determined and thenfor a specified frequency the size of theantenna is determined. It can be shown that for fixed transmitantenna gain and fixed receive antennagain, the received carrier power ismaximum when the frequency is minimum. These conditions apply to mobiletelephony, since the satellite antenna gainis fixed by the terrestrial cell size and thehandset antenna gain is fixed by thecondition that the antenna must cover theentire sky. Thus L-band (1.6 GHz) is usedbecause it is the lowest practical frequencythat is available. Another factor is the availability ofspectrum. Initially, C-band (6/4 GHz) wasused exclusively for the fixed satelliteservice. Later, Ku-band (14/12 GHz) wasused, both because it was a frequencydomain that was available to expandcapacity and because the higher frequencypermits the use of smaller earth terminalantennas. However, more power isrequired to overcome the detrimentaleffects of rain. As the frequency increases the effectsof rain increase. Rain degrades a satellitecommunication link in two ways: byattenuating the signal over the signal pathand by increasing the system noisetemperature of the earth terminal. Attenuation is caused by scattering andabsorption of the electromagnetic waves. As the frequency increases, the wavelengthdecreases. To the extent that thewavelength is comparable to the size of atypical rain drop (about 1.5 mm), thesignal becomes more susceptible toscattering and absorption. The systemnoise temperature increases because the

antenna sees the warm rain at roomtemperature instead of the cold sky. At C-band (6 GHz) the wavelength is50 mm (5.0 cm) and the rain attenuationper kilometer of path is about 0.1 dB/kmfor a maximum rain rate of 22 mm/h,corresponding to an availability of 99.95percent in Washington, DC. At Ku-band(14 GHz), the wavelength is 21 mm (2.1cm) and the rain attenuation is 1 dB/kmunder the same conditions. New satellite systems for broadbandapplications are in various stages ofdevelopment. These new systems willextend the frequency domain into Ka-bandand V-band. Rain attenuation increasesdramatically at these frequencies. At Ka-band (30 GHz) the wavelength is 10 mmand the attenuation is 5 dB/km for 99.95%availability in Washington. At V-band (50GHz) the wavelength is only 6 mm and thecorresponding attenuation is 9 dB/km. Itwill thus not be possible to achieve thesame availability at Ka-band and at V-bandas we are accustomed to achieving at C-band or even Ku-band. Without mitigatingtechniques, such as spatial diversity andswitching to lower frequencies, theavailabilities will be in the neighborhoodof 98% for any reasonable rain attenuationallowance. Note that in addition toattenuating the signal, the rain alsoincreases the system noise temperature. This contribution to the total systemdegradation can be comparable inmagnitude to the attenuation itself.

MODULATION

A sinusoidal electromagnetic wave hasthree properties: amplitude, frequency,and phase. Any one of these parameterscan be modulated to convey information. The modulation may be either analog ordigital. In analog signals, the range ofvalues of a modulated parameter iscontinuous. In terrestrial radio systems,for example, AM and FM channelsrepresent amplitude and frequencymodulation, respectively. In digitalsignals, the modulated parameter takes ona finite number of discrete values torepresent digital symbols. The advantageof digital transmission is that signals canbe regenerated without any loss ordistortion to the baseband information.

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A fundamental parameter in digitalcommunication is the ratio of bit energy tonoise density Eb/N0. This parameterdepends on three characteristics: the biterror ratio (BER); the method ofmodulation; and the method of coding. By far the most common form ofmodulation in digital communication isM-ary phase shift keying (PSK). With thismethod, a digital symbol is represented byone of M phase states of a sinusoidalcarrier. For binary phase shift keying(BPSK), there are two phase states, 0° and180°, that represent a binary one or zero. With quaternary phase shift keying(QPSK), there are four phase statesrepresenting the symbols 11, 10, 01, and00. Each symbol contains two bits. AQPSK modulator may be regarded asequivalent to two BPSK modulators out ofphase by 90°. For M-ary PSK, the noise bandwidth isthe information bit rate divided by thenumber of bits per symbol. Thus foruncoded BPSK modulation, the noisebandwidth is equal to the information bitrate; for uncoded QPSK modulation thenoise bandwidth is one-half theinformation bit rate. The null-to-nullbandwidth is twice the noise bandwidth ineach case. QPSK is usually preferred over BPSKbecause for a given bit rate and BER itrequires the same power, yet requires onlyhalf the bandwidth. The saving inbandwidth using QPSK instead of BPSKwithout any greater power is the digitalcommunication equivalent of a "freelunch". The tradeoff is actually addedcomplexity in the modulator, but QPSKmodulators are commonplace and thedistinction between a QPSK chip and aBPSK chip is comparable to the distinctionbetween a Pentium computer chip and an80-286 computer chip: the Pentium chip ismuch more complex, yet it is ubiquitousand inexpensive. In some situations BPSK might bepreferred, such as when sufficientbandwidth is available and it desired tominimize the spectral power flux density tomeet a regulatory requirement. BPSK isalso used in CDMA systems, in which thebasic principle is maximizing thebandwidth.

Higher order PSK modulation schemesare also used, such as 8PSK. With 8PSKthe required bandwidth is only one thirdthe bandwidth of BPSK or two-thirds thebandwidth of QPSK. However, the phasestates are 45° closer than QPSK, whichmakes it more difficult for the receiver todistinguish them. Thus for a given BERthe required power is higher than that ofeither BPSK or QPSK. For example, at aBER of 10-8, 8PSK requires about 4 dBmore energy per bit. In M-ary PSK, symbols aredistinguished from one another by thecarrier phase, but the amplitude remainsthe same. It is possible to modulate boththe phase and the amplitude in order toincrease the number of bits per symbol andreduce the bandwidth even further. Forexample, in 16QAM there are twelvephases and four amplitudes. There arefour bits per symbol and the bandwidth isone-fourth the bandwidth of BPSK or one-half the bandwidth of QPSK. However,like 8PSK, this method requires morepower because it is more vulnerable totransmission impairments. For a BER of10-8 the required Eb/N0 is about 4 dB morethan QPSK. These higher order levels ofcarrier modulation are being developed inan effort to decrease the requiredbandwidth and thus increase the bandwidthefficiency of satellite communicationsystems. In offset QPSK (OQPSK) andminimum shift keying (MSK),discontinuous phase transitions areavoided to suppress out-of-bandinterference. These two methods have aconstant envelope and are attractive whenthe intermodulation effects of transpondernonlinearities are to be minimized. Another alternative is frequency shiftkeying (FSK). With this method ofmodulation the frequency of the carrierassumes one of a discrete number offrequencies during each bit period.

CODING

The amount of power, as represented byEb/N0, can be reduced through the use offorward error correction (FEC) coding. The reduction in the value of Eb/N0 iscalled the coding gain. The code rate is

the ratio of information bits to the numberof coded bits. Two types of codes are used: blockcodes and convolutional codes. In a blockcode a group of information bits areaccepted as a block to the encoder andparity bits are added to form a code word. Names associated with this type of codeinclude Hamming, Golay, BCH, and Reed-Solomon. In a convolutional code, bits areadded to a shift register continuously andaffect the formation of coded symbols overseveral bit periods. The number of bitperiods that a given bit occupies the shiftregister is called the constraint length. Theoptimum method of decoding employs theViterbi algorithm. It is now becoming common inadvanced communications systems to useconcatenated coding, involving both aninner convolutional code and an outerReed-Solomon block code. The Reed-Solomon code detects and corrects burstytype errors. Interleaving is sometimes alsoused to scramble the bits after coding andunscramble them before decoding so as tocause bursty errors that occur intransmission to be spread out in time andmake them appear to be random. However, interleaving introduces anincrease in the encoding delay. Coding reduces power at the expense ofincreased bandwidth. For example, a rate1/2 code doubles the required bandwidth. Thus the bandwidth of a rate 1/2 codedsignal using QPSK modulation is equal tothe bandwidth of an uncoded signal usingBPSK modulation. A rate 1/2 coded8PSK signal requires 2/3 the bandwidth ofuncoded BPSK or 2/3 the bandwidth ofrate 1/2 coded QPSK.

BIT RATE

The information bit rate Rb is determinedby the service or activity to be supportedby the communications link. The requiredcarrier to noise density ratio C/N0 is relatedto the energy per bit to noise density ratioEb/N0 through the fundamental relationC/N0 = Rb Eb/N0. Thus for a specified bitrate -- together with the specified BER,method of modulation, and method ofcoding -- the required C/N0 is determined. On the other hand, the available C/N0

provided on either the uplink or the

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downlink is determined by the transmitterequivalent isotropic radiated power(EIRP), the receiver figure of merit G/T,the free space loss, impairments due torain, any other losses, and various forms ofinterference. The transmitter EIRP andreceiver G/T must be designed to achievethe desired bit rate, or conversely, thegiven EIRP and G/T determine the bit ratethat the link can support. As an example, we return to theparadigm of telephony. For standard pulsecode modulation (PCM) to convert abaseband analog waveform to a digitalsignal, the analog signal must be sampledat the Nyquist rate, or twice the highestbaseband frequency, and each sample isencoded by n bits to represent one of 2n - 1levels. For a high quality voice channel,the highest baseband frequency is 4000Hz, and if each sample is encoded by 8 bitsto yield 255 levels, the required bit rate is2 × 4000 × 8 = 64,000 bps, or 64 kbps. This is the classic bit rate for a voicechannel. This recipe for PCM actually applies tothe analog-to-digital conversion of anywaveform without any knowledge of thenature of the signal. In the particular caseof human speech, however, it is possible todrastically reduce the required bit rate bymodelling speech patterns. In a vocoder(or voice coder), perceptually importantparameters describing the pitch, phoneticenvelope, and level of vowel sounds aretransmitted instead of the full digitalrepresentation of the analog waveform. Thus 4.8 kbps or even 2.4 kbps bit ratesare possible. Since bandwidth is at apremium, these are the rates that will usedin the satellite mobile telephony systems.

CONCLUSION

The design of a satellite communicationsystem involves a wide variety ofalternatives and tradeoffs. Often aparticular set of choices will reflect aparticular design philosophy or experiencein some other field of communication. Themobile telephony systems illustrate howdifferent designs can be adopted to achievesimilar objectives. For example, Iridium isa LEO satellite constellation with polarorbits providing global coverage using

FDMA/TDMA. Globalstar is also a LEOconstellation but uses inclined orbits forconcentration of coverage in mid-latitudesand employs CDMA technology. ICO isan FDMA/TDMA MEO constellation. Aces is a regional system using a singlegeostationary satellite. These various possibilities keep thesatellite engineer busy. The work,fortunately, is also highly interesting._______________

Dr. Robert A. Nelson, P.E. is president ofSatellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, MD. He isVia Satellite’s Technical Editor.

Satellite 2001 Daily

What Is theRadius of theGeostationaryOrbit?by Robert A. Nelson

Most communications satellites operatefrom the geostationary orbit, since fromthis orbit a satellite appears to hover overone point on the equator. An Earthstation antenna can therefore be pointedat a satellite in a fixed direction andtracking of the satellite across the sky isnot required. The basic question to bediscussed is, “What is the radius of thegeostationary orbit?” The geostationary orbit must satisfythree conditions: (1) the velocity must bein the direction and sense of the Earth’srotation; (2) the velocity must beconstant; and (3) the period of revolutionmust exactly match the period of rotationof the Earth in inertial space. The firstcondition implies that the orbit must be adirect orbit in the equatorial plane. Thesecond condition implies that the orbitmust be circular. To satisfy the thirdcondition, the radius of the orbit must bechosen to correspond to the requiredperiod given by Kepler’s third law.According to this law, the square of theorbital period is proportional to the cubeof the semimajor axis.1

The problem reduces to determiningthe value of the orbital period. However,it is not simply 24 hours, or one meansolar day. The mean solar day is equal tothe average time interval betweensuccessive transits of the Sun over agiven meridian and is influenced by boththe rotation of the Earth on its axis andthe motion of the Earth along its orbit.Instead, the appropriate period of thegeostationary orbit is the sidereal day,which is the period of rotation of theEarth with respect to the stars. Onesidereal day is equal to 23 h 56 m4.0905 s of mean solar time, or86 164.0905 mean solar seconds. Usingthis value in Kepler’s third law, wecompute the orbital radius as42 164.172 km.

Yet even this value for the orbitalperiod is not quite correct because theEarth’s axis precesses slowly, causing thebackground of stars to appear to rotatewith respect to the celestial referencesystem. The Earth’s axis is tilted by23.4° with respect to a line perpendicularto the orbital plane and executes a conicalmotion with a precessional period ofabout 26 000 years. Therefore, thesidereal day is less than the true period ofthe Earth’s rotation in inertial space by0.0084 seconds. On this account, theperiod of the geostationary orbit shouldbe 86 164.0989 mean solar seconds. Thecorresponding orbital radius is42 164.174 km. There is also a correction due to theunit of time itself. The mean solarsecond is defined as 1/86 400 of a meansolar day. However, in terms of thesecond of the International System ofUnits (SI), defined by the hyperfinetransition of the cesium atom, the presentlength of the mean solar day is about86 400.0025 seconds. The mean solar dayexceeds a day of exactly 86 400 secondsby about 2.5 milliseconds due to slowingof the Earth’s rotation caused by theMoon’s tidal forces on the shallow seas.This extra time accumulates to nearly onesecond in a year and is compensated bythe occasional insertion of a “leapsecond” into the atomic time scale ofCoordinated Universal Time (UTC).Adding this increment to the orbitalperiod, we obtain 86 164.1014 seconds.The corresponding orbital radius is42 164.175 km. The analysis so far has assumed thatthe Earth can be regarded as a perfectsphere. However, in reality the Earth’sshape is more nearly oblate. Theequatorial radius is 6378.137 km, while

the polar radius is 6356.752 km. Thegravitational perturbation due tooblateness causes the radius to beincreased by 0.522 km.2 The resultinggeostationary orbital radius is42 164.697 km. In practice, once the satellite isoperational in the geostationary orbit, it isaffected by a variety of perturbations thatmust be compensated by frequentstationkeeping maneuvers using thrustersonboard the spacecraft. Theseperturbations are caused by thegravitational attractions of the Sun andthe Moon, the slightly elliptical shape ofthe Earth’s equator, and solar radiationpressure. Because the orbit is constantlychanging, it is not meaningful to definethe orbit radius too precisely. Bycomparison, using recent data for 16Intelsat satellites, we obtain a semimajoraxis with a mean of 42 164.80 km and astandard deviation of 0.46 km. A perfectly geostationary orbit is amathematical idealization. Only thedistinction between the mean solar dayand the sidereal day needs to be takeninto account. Therefore, it is customary toquote a nominal orbital period of 86 164seconds and a radius of 42 164 km. Theheight above the equator is 35 786 kmand the orbital velocity is 3.075 km/s._________________________________1 Mathematically, Kepler’s third law maybe expressed as T 2 = (4 π 2 / GM) a 3,where T is the period, a is the semimajoraxis, and GM is the gravitational constantfor the Earth, whose value is 398 600.5km3 / s2. For a circular orbit, thesemimajor axis a is equal to the radius r.2 The correction is ∆r = ½ J2 ( RE / r )2 r,where r is the orbital radius, RE is theEarth’s radius, and J2 is the Earth’soblateness coefficient, 0.001 083.

Relationship between the sidereal day and the mean solar day.

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Via Satellite

Modulation, Power,and Bandwidth

Tradeoffs in CommunicationSystems Design

by Robert A. Nelson

Modulation is the process by whichinformation is conveyed by means of anelectromagnetic wave. The informationis impressed on a sinusoidal carrier waveby varying its amplitude, frequency, orphase. Methods of modulation may beeither analog or digital. The power and bandwidth necessaryfor the transmission of a signal with agiven level of quality depends on themethod of modulation. There is a classictradeoff between power and bandwidththat is fundamental to the efficient designof communication systems. This articlewill identify various methods of analogand digital modulation, describe theircharacteristics, and analyze theiradvantages and disadvantages. Thescope of the discussion will be restrictedto certain common types of modulationsystems.

TYPES OF MODULATION

The carrier wave can be represented bythe cosine function

s(t) = A(t) cos θ(t)

A sinusoidal carrier wave thus has twofundamental properties: amplitude A andangle θ. Either of these parameters canbe varied with time t to transmitinformation. Frequency and phasemodulation are special cases of anglemodulation. In analog modulation the amplitude,frequency, or phase can take on acontinuous range of values. Themodulated parameter must faithfullyfollow all of the inflections of the signalto be transmitted. Any variation in thisparameter due to propagation losses orinterference will result in a distortion ofthe received demodulated signal. The principal forms of analogmodulation are amplitude modulation

(AM) and frequency modulation (FM).These methods are familiar from theirapplication to terrestrial broadcast radioand television. In digital communication, themodulated parameter takes on only adiscrete set of values, each of whichrepresents a symbol. The symbolconsists of one or more bits, or binaryones and zeroes. Since the demodulatormust merely identify which amplitude,frequency, or phase state is most closelyrepresented in the received signal duringeach symbol period, the signal can beregenerated without any distortion. Errorcorrection coding is used to reduce bittransition errors caused by interference tomeet a specified performance objective. Two common forms of digitalmodulation used in satellitecommunication are phase shift keying(PSK), in which the carrier phase takeson one of a set of discrete values, andfrequency shift keying (FSK), in whichthe frequency may have one of two ormore discrete values.

FOURIER PRINCIPLE

A method of representing a time varyingfunction in terms of an infinitetrigonometric series was introduced bythe eighteenth century Frenchmathematician and physicist JeanBaptiste Fourier (1768 – 1830).According to the Fourier principle, anarbitrary periodic function defined over aspecified interval can be represented asthe sum of an infinite number of sine andcosine functions whose frequencies areintegral multiples of the repetition rate, orfundamental frequency, and whoseamplitudes depend on the given function.The frequencies above the fundamentalfrequency are called the harmonics. Thefrequency characteristics of a periodicfunction are determined by theamplitudes of the admixture ofharmonics. To a communicationsengineer, the Fourier principle provides amethod of understanding a complicatedsignal waveform in terms of theamplitudes of the individual harmonics. For example, the musical soundsproduced by a piano, trumpet, or clarinetall performing the tone of concert A(440 Hz) are distinguished by theharmonics that they produce. Thefundamental frequency is 440 Hz, but theinstruments sound different because theyeach produce a different set of harmonics.

For high fidelity reproduction of thesesounds, the range of frequencies shouldbe as high as possible. In the case of thehuman ear, the frequency range isapproximately between 50 Hz and 20,000Hz. If this range is truncated by thelimitations of the recording andreproduction equipment, then the originalsound will appear to be distorted and willbe easily detected as artificial. In a typical toll-quality telephonechannel, the bandwidth is about 4,000Hz. This bandwidth is considered to beadequate for the transmission of clearspeech. However, since all of thefrequencies above 4,000 Hz are filteredout, certain subtle distinctions betweensimilar sounds are lost. That is why, forexample, the sounds for m and n or for fand s are easily confused over thetelephone and we often find it necessaryto use phonetics when spelling out aname, even though they are easilydistinguished unconscientiously fromtheir higher harmonics when spoken inperson. A mathematical generalization of aFourier series is the Fourier transform.The Fourier transform permits theconversion of any continuous function inthe time domain to a correspondingfunction in the frequency domain andvice versa. However, the Fouriertransform and its inverse involve the useof complex variables. Thus to completelyrepresent the spectrum of atime-dependent function, it is necessaryto use the mathematical fiction of bothpositive and negative frequencies. Usingthe Fourier transform, one can analyzethe frequency spectral content of anytime-dependent signal. By a powerfulmathematical theorem known as theWiener-Khintchine Theorem, the powerspectral density of a given function oftime is the Fourier transform of itsautocorrelation function.

FREQUENCY REGIMES

There are three frequency regimes thatare involved in the transmission of asignal. These are the basebandfrequencies, the intermediate frequency(IF) band, and the radio frequency (RF)band. The baseband signals are the signalsthat carry the information, such as from atelephone, microphone, or video camera.The baseband is the range of frequenciesgenerated by the original source of

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information. For sound, these frequenciesare typically from 0 to a few kilohertz.For video, they may extend to a fewmegahertz. The intermediate frequencies are thefrequencies present in the signal that areproduced after modulation and filtering. The radio frequency band is the rangeof frequencies that are transmittedthrough space. The modulated signal isconverted from the intermediatefrequency regime to the radio frequencyregime by frequency translation. The RFfrequencies typically range from a fewhundred to a few thousand kilohertz forterrestrial broadcasting and from 1 to 30gigahertz for satellite communication.These satellite frequencies are in themicrowave region, corresponding towavelengths on the order of a fewcentimeters, and permit the use ofantennas with reasonably sized physicaldimensions.

AMPLITUDE MODULATION

With analog amplitude modulation (AM),the message signal m(t) is used to modifythe amplitude of the carrier wave. For100 percent modulation, the amplitudebecomes the time-dependent function

A(t) = A [ 1 + m(t) ]

The angle is given by θ = ωc t + φ. Thecarrier angular frequency ωc and phase φ(which can be taken to be zero) remainconstant. Thus the transmitted signalassumes the mathematical form

s(t) = A [ 1 + m(t) ] cos (ωc t)

= A cos (ωc t) + A m(t) cos (ωc t)

The carrier angular frequency ωc isrelated to the frequency fc by the relationωc = 2π fc , where ωc is expressed inradians per second and fc is expressed inhertz. Multiplication of the cosinefunction, which is generated in the localoscillator circuit of the modulator, by themessage signal produces a spectrum thatconsists of two sidebands in addition tothe frequency of the carrier. By the Fourier principle, the messagesignal can be analyzed in terms of itsindividual sinusoidal components. Thusif the local oscillator generates a carriercos(ωc t) at the intermediate frequency ωc

and it is modulated by one of thecomponents of the message signalrepresented by m(t) = cos(ωm t) atfrequency ωm , then by a trigonometric

identity the resulting waveform will be

cos(ωc t) cos(ω t) = ½ cos (ωc + ωm ) t

+ ½ cos (ωc – ωm ) t

The spectrum thus contains the twofrequencies ωc + ωm and ωc – ωm . Forexample, if the local oscillator generatedcosine function at 64 kHz is multipliedby the original baseband signalcomprising the set of the four frequencies1, 2, 3, and 4 kHz, then the resultingspectrum would comprise the frequencies65, 66, 67, and 68 kHz in the uppersideband and the frequencies 60, 61, 62,and 63 kHz in the lower sideband.Therefore, when the cosine function ismultiplied by the message signal, twothings happen: the frequencies aretranslated and the bandwidth is doubled. In the type of amplitude modulationknown as double sideband full carrier(DSB-FC) amplitude modulation, themodulated signal consists of the carrierwave with a time varying amplitude thatforms an envelope. The spectrum consistsof the carrier frequency, the uppersideband, and the lower sideband. Thesignal can be easily demodulated simplyby passing the modulated signal througha filter to remove the high frequencycomponents contributed by the carrier,leaving the low frequency components ofthe envelope representing the desiredsignal. The transmitted power consists of thecarrier power and the power in thesidebands. For 100 percent modulationby a sinusoidal message component, thepower in the two sidebands together isone-half the power in the carrier. That is,the total power is three times the powerin the sidebands. The sideband power isevenly divided between the twosidebands, giving them each one-fourththe carrier power. For example, fullmodulation of a 100 watt sinusoidalcarrier will add 50 watts to the sidebands,with 25 watts in each sideband, resultingin a total transmitted power of 150 watts. Since the carrier conveys noinformation while each sideband containsthe same information, this form ofmodulation is wasteful in both power andbandwidth. The advantage is that onlyenvelope detection is needed todemodulate the signal and the receivercan be built easily and inexpensively.The recovery circuit may be as simple asa diode followed by a low pass filter

consisting of a resistor and capacitor inparallel. In US commercial AM radio,the baseband is filtered to 5 kHz and thusthe bandwidth per channel is 10 kHz. TheAM band extends from 535 kHz to1705 kHz and the carriers are centered at540 kHz to 1700 kHz in 10 kHz steps. In double sideband supressed carrier(DSB-SC) amplitude modulation, bothsidebands are transmitted but the carrieris removed. The bandwidth is twice thebandwidth of the baseband signal. In single sideband (SSB) amplitudemodulation the signal is generated by abalanced modulator and filter and thetransmitted frequencies consist only of asingle sideband. The bandwidth istherefore the same as that of the basebandsignal. This method requires only onehalf the bandwidth as DSB-FC amplitudemodulation while transmitting only afraction of the power. Envelope detection is not possible ineither DSB-SC or SSB. Therefore, thereceiver must recover the frequency andphase of the transmitter and is morecomplex and costly. In DSB-SC a smallphase error causes a variation inamplitude, whereas in SSB it affects bothamplitude and phase. SSB is thus wellsuited for voice communication, since thehuman ear is relatively insensitive tophase distortion, but it is not well adaptedto other signals, such as video or digital.It is used in marine and citizens bandradio. Before they were replaced bydigital circuits, analog telephone channelswere combined by frequency divisionmultiplexing using SSB modulation.

FREQUENCY MODULATION

In analog frequency modulation (FM),the message signal is used to vary thefrequency of the carrier. The deviation ofthe instantaneous frequency is directlyproportional to the message signal. Theamplitude of the carrier remains constant.The range of values of the frequencyabout the carrier center frequency iscalled the peak deviation ∆ f . Theinstantaneous angular frequency is

ω(t) = dθ/dt = ωc + ∆ω m(t)

where ∆ω = 2π ∆f . For modulation by asinusoid at the single frequency fm , themessage signal is m(t) = cos (ωm t), whereωm = 2π fm . Then θ = ωc t + β sin ωm tand the signal has the mathematical form

s(t) = A cos (ωc t + β sin ωm t )

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where β = ∆f / fm . The parameter β,which is ratio of the peak deviation to thebaseband modulation frequency, is a keyproperty called the modulation index. This expression for s(t) can beexpanded into an infinite series ofdiscrete components involving the Besselfunction of integral orders, whichcharacteristically occur in mathematicalphysics when trigonometric functions oftrigonometric functions are involved.The resulting spectrum is a distribution of“spikes.” (The logo for Cisco Systems isbased on this pattern and is also intendedto resemble San Francisco’s Golden GateBridge.) The amplitudes are determinedonly by the modulation index andbecome more uniform as the modulationindex increases, e.g., for β > 10. Forexample, the telemetry, tracking, andcontrol (TT&C) subsystem of a satellitegenerally uses FM with high modulationindex to transmit three tones representinga binary one or zero and execute. In general, the FM spectrum is acomplex function of β consisting ofmultiple sidebands that occur at integralmultiples of the modulating frequency oneither side of the carrier rather than, as inAM, consisting of a single pair ofsideband frequencies. The spectrum canbe analyzed mathematically only in thesimplest cases since FM is inherentlynonlinear and superposition of individualsource signals is not applicable In principle, the required bandwidth isinfinite, but in practice it is givenapproximately by Carson’s rule,

B = 2 ( β + 1) fm = 2 (∆ f + fm )

where fm is the highest basebandfrequency. This well known empiricalestimate for determining the practicalbandwidth of FM was first suggested inan unpublished memorandum in 1939 byJohn Renshaw Carson, chief theoreticalmathematician at Bell Laboratories. Forexample, in US commercial FMmonaural radio, the highest basebandfrequency is 15 kHz and the peakdeviation is 75 kHz. Thus themodulation index β is 5 and the requiredbandwidth B is 180 kHz. Allowing for a10 kHz guardband on each side, thechannel bandwidth is 200 kHz. There are100 channels, each 200 kHz wide, in theFM band from 88 MHz to 108 MHz. Two characteristics of FM that arefamiliar to radio listeners are that thesignal quality is much better than AM

and that the signal drops out rapidlybeyond the nominal range of thetransmitter. The better performance is due to thefact that the signal to noise ratio at thedemodulator output is higher forwideband FM than for AM. It was EdwinHoward Armstrong who first recognizedthe noise-reducing potential of FM forradio broadcasting in the early 1930s. Ontheoretical grounds Carson had correctlyrejected narrowband FM as inferior toAM for the reduction of noise, since hewas principally interested in reducing thebandwidth of telephone circuits andhence increasing the system capacity. Onthe other hand, through experimentalmeasurements Armstrong found that bywidening the bandwidth the signal tonoise ratio could be increaseddramatically for radio. He designed anddemonstrated the first FM radio circuits. For a single-frequency sinusoidallymodulated signal, the FM output signal tonoise ratio at baseband Sb/Nb may beexpressed

Sb/Nb = 3 β2 (B / 2 fm ) (S/N)

= 3 β2 (β + 1) (S/N)

where S/N is the input signal to noiseratio in the RF channel. Thus afterdemodulation the output signal to noiseratio is greater than the input signal tonoise ratio by the factor 3 β2 (β + 1). Incontrast, when the same sideband poweris transmitted, the output signal to noiseratio is equal to the input signal to noiseratio for all types of amplitudemodulation. The FM noise density isN0 = N/B. For a double-sideband AMsystem with the same noise density, theinput noise power is N’ = 2 fm N0. If alsothe AM input signal power is S’ = S, then

Sb/Nb = 3 β2 S’/N’

Thus after demodulation the FM signal tonoise ratio is greater than thecorresponding AM signal to noise ratioby a factor of 3 β2. This factor is calledthe “FM improvement.” From the theoretical relation above, itis seen that as long as β > 0.6, FMdelivers better performance than AM forequal signal power and equal noise powerdensity. However, the FM bandwidth isexpanded to 2 (β + 1) times theinformation bandwidth fm , whereas theAM bandwidth is 2 fm . This is a classicexample of trading bandwidth for power.

For example, when β = 5 the FM outputsignal to noise ratio is 75 times that of anequivalent AM system (19 dB higher),but the bandwidth is 6 times larger.Therefore, the modulation index must besufficiently high that it provides thedesired FM improvement, but it is limitedby the need to preserve bandwidththrough Carson’s rule. In addition, below a certain thresholdinput signal to noise ratio that increasessomewhat with increasing β, thedemodulated signal to noise ratio falls offprecipitously. This property is why therange of an FM signal is limited. Theexistence of a threshold is characteristicof any system that reduces noise inexchange for extra bandwidth andbecomes pronounced when the reductionis large. For wideband FM the thresholdoccurs at roughly 10 dB. With analog frequency modulation theinstantaneous frequency varies directly asthe message signal and the phase variesas the integral of the message signal.Analog phase modulation is a closelyrelated form of angle modulation where itis the phase that varies directly as themessage signal and where the frequencyvaries directly as the derivative of themessage signal.

TELEVISION

In the United States, the broadcasttelevision standard is the NTSC (NationalTelevision System Committee) system.The video signal is modulated by a formof amplitude modulation called vestigialsideband (VSB) amplitude modulation, inwhich a portion of the lower sideband istransmitted with the upper sideband. VSBAM requires less bandwidth thanDSB-SC, overcomes the problem ofphase distortion present in SSB and thedifficulty of filtering the low frequencycontent, and permits simple envelopedetection. The highest luminancebaseband frequency is 4.2 MHz. Theupper sideband of the video signal has abandwidth of 4.2 MHz, while thevestigial lower sideband has a bandwidthof 1.25 MHz. The color signal istransmitted on a separate subcarrierinterlaced in the frequency domain withthe luminance signal. The audio signaluses frequency modulation, with ahighest baseband frequency of 10 kHzand a frequency deviation of 25 kHz.Thus the audio bandwidth is 70 kHz andis centered 4.5 MHz above the video

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carrier. The total bandwidth for both thevideo and audio signals is 6.0 MHz. For the transmission of a televisionsignal over a satellite, amplitudemodulation would be severely affected bylosses, various forms of interference, andnonlinearities in the transponder.Therefore, the video signal is frequencymodulated along with the audio signal.The peak frequency deviation of video onthe main carrier is 12 MHz and themodulation index is 2.86. By Carson’srule, the required bandwidth is 2 (12MHz + 4.2 MHz) = 32.4 MHz. Thus abandwidth of 36 MHz was originallychosen for a satellite transponder so thatit could safely accommodate one analogFM television channel. Since the FMtelevision channel occupies the entiretransponder bandwidth, the transpondercan be operated at full power without anyintermodulation interference caused bythe nonlinear transfer characteristic.

ANALOG TO DIGITALCONVERSION

In digital communication, information istransmitted in the form of a continuousstring of binary ones and zeroes. Thus itis necessary to convert the analogbaseband signal, such as a sound or videorecording, to a digital signal. Pulse code modulation (PCM) is aconventional technique that converts ananalog waveform into a sequence ofbinary numbers. The first step is toestablish a set of discrete times at whichthe input signal is sampled. According toa classic theorem of sampling theorystated by Harry Nyquist of BellLaboratories in 1933, the minimumsampling rate fs is twice the highestbaseband frequency fm , or fs = 2 fm . Thenext step is to represent each analogsample value by a binary number. Ifthere are n bits per sample, then there canbe 2n – 1 possible levels in each sample.The required bit rate is thereforeRb = n fs = 2 n fm . The original signalwaveform is recovered by using a lowpass filter. The restriction of each sampleto a discrete set of values results in asmall amount of quantization noise.This encoding/decoding technique isessentially independent of the nature ofthe analog signal. For example, in a conventionaltoll-quality telephone channel, thepractical band extends from about 200 Hz

to about 3400 Hz. Rounding up to 4,000Hz, the Nyquist sampling rate is thus8,000 samples per second. If 8 bits areallocated for each sample, resulting in255 possible levels per sample, therequired bit rate is 8 × 8,000 bits persecond, or 64 kbps, which is the basis ofthe standard bit rate for atelephone channel. In a digital compactdisc (CD) audio recording, the samplingrate is 44,100 samples per second toensure a perceived bandwidth of morethan 20 kHz. With 16 bits per sample foreach of two separate stereo channels, theaudio data rate is 1.411 Mbps. In terrestrial cell phone and satellitemobile telephony systems, the bit ratecan be as low as 2.4 kbps. Thissignificantly lower bit rate is madepossible because the voice coder(vocoder) is designed specifically forspeech. The vocoder uses a model of thehuman vocal tract and synthesizesspeech, much as a keyboard musicalsynthesizer can emulate the sounds ofvarious musical instruments. Only alimited set of perceptually importantparameters are transmitted, such as vowelsound, pitch, and level, resulting in fewerbits and smaller bandwidth. Althoughthe speech is intelligible, the quality isbelow telephone standards. Other formsof sound, such as music, cannot betransmitted. An NTSC digital television signalfollowing the ITU-R Rec. 601 standardhas 30 frames per second, 525 lines perframe, 858 samples for luminance and429 samples for each of two colordifferences per line (so-called 4:2:2component structure), and 8 bits persample. Theoretically, the required bitrate is 216 Mbps. In practice, there are480 active lines with 720 samples forluminance and 360 samples for each oftwo color differences per line, yielding166 Mbps. The luminance sampling ratesfor these two formats are 13.5 MHz and10.4 MHz, repectively, compared withthe Nyquist sampling rate of 8.4 MHz foranalog video. With compression the bitrate can be reduced to about 8 Mbps(MPEG-2 quality) or 1.5 Mbps (MPEG-1quality).

PULSE SHAPING

The baseband digital symbols must berepresented by a continuous string ofpulses of some appropriate form. For

example, a “1” may be represented by apositive rectangular pulse and a “0” maybe represented by a negative rectangularpulse. This type of pulse train is called“Non-Return to Zero” (NRZ) pulseshaping, because the pulse remains at aconstant amplitude over each full bitperiod. Numerous other pulse shapes arealso used, in which “notches” are addedto improve synchronization. However,since these pulses require greaterbandwidth, the NRZ signal format isgenerally preferred in satellitecommunication systems. Since the pulse train transmitsinformation, each successive pulse isindependent of those that came before it.Thus the probability of a given pulserepresenting a one or zero is random, andthe sequence of NRZ pulses is astochastic process. It can be shown thatthe autocorrelation function for this caseis a triangle function. Thus by theWiener-Khintchine Theorem, the powerspectral density (or power per unitbandwidth at frequency f ) is the Fouriertransform of the triangle function andhappens to be a function that has the formof (sin x/x)2 centered about 0, wherex = π f / Rb. In practice, the baseband pulse shapesare not nice, perfect rectangles with rightangle corners. To produce such pulses,the bandwidth would have to be infinite.Instead, because of the finite bandwidthof the filter, the pulses are actuallyrounded “blips.” The tails of these blipswill tend to overlap, causing aphenomenon known as intersymbolinterference (ISI). Nyquist showed that the pulse shapethat required the minimum bandwidthwithout intersymbol interference is onethat in the time domain has the form ofthe function sin (π Rb t)/ (π Rb t). For thisfunction, the tails of the preceding andfollowing pulses pass through zero at thepeak of the present pulse. In thefrequency domain, the Fourier transformlooks like a rectangular brick wall. Theminium required baseband bandwidth isone half the information bit rate, orb = Rb / 2. But it is impossible to realize thispulse shape in an actual filter. Instead aform of pulse shaping called “raisedcosine” filtering is used, characterized bya parameter called the rolloff ρ that isbetween 0 and 1. A typical value of ρ is0.2. For zero rolloff, the raised cosine

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pulse shape reduces to the ideal sin x/xpulse shape. The actual basebandbandwidth is thus b = k Rb / 2, wherek = 1 + ρ.

DIGITAL MODULATION

In digital communication, the carrier tonoise density ratio is given by the relation

C/N0 = Rb ( Eb / N0 )

where Rb is the information bit rate. Thequantity Eb / N0 is the ratio of the energyper information bit Eb and the total noisedensity N0 (noise power per unitbandwidth) and has fundamentalimportance. The value of Eb / N0 isdetermined by three design factors: thebit error rate, the method of modulation,and the method of forward errorcorrection coding. If the phase is the parameter that isvaried, the modulation is called phaseshift keying (PSK). Two common formsof digital modulation used for satellitecommunication are binary phase shiftkeying (BPSK) and quaternary phaseshift keying (QPSK). If the frequency isvaried instead of the phase, themodulation is called frequency shiftkeying (FSK). In BPSK modulation the carrier canhave one of two phase states, 0° and180°, which represent a binary one orzero. In a BPSK modulator, thebaseband pulse train simply multiplies acosine function generated by a localoscillator, usually at the intermediatefrequency of 70 MHz. Multiplication ofcos (ωc t) by a pulse of level + 1representing a binary 1 leaves the phaseof 0 unchanged. On the other hand,multiplication by a pulse of level – 1representing 0 yields – cos (ωc t) =cos (ωc t + π), which changes the phaseby 180°. Coherent detection is neededfor demodulation. In other words, thereceiving circuit must recover theabsolute phase of the transmitting circuit.This is usually done by either a Costasloop or a squaring loop. In QPSK modulation the carrier canassume one of four phase states,consisting of 0°, 90°, 180°, and 270°,which represent the symbols 00, 01, 11,and 10. A QPSK modulator is usuallythought of as two BPSK modulators thatare out of phase by 90°. As discussed for AM, forming aproduct with a cosine function results in a

spectrum containing sums anddifferences of the oscillator frequencyand each frequency in the basebandsignal. Thus with NRZ pulse shaping,the BPSK spectral density consists of two(sin x/x)2 functions, one centered at 70MHz and the other centered at – 70 MHzin the complex domain. The frequenciesare thus translated and the bandwidth isdoubled. In general, the required occupiedbandwidth for digital modulation,including forward error correctioncoding, is

B = k ( Rb / m )(1 / r )

where Rb is the bit rate, m is the numberof bits per symbol, r is the code rate, andk is the bandwidth expansion factor usedto minimize intersymbol interference.For example, if Rb = 64 kbps, m = 2 forQPSK modulation, r = 1/2, and k = 1.2,then B = 76.8 kHz. For a given bit error rate, the value ofEb / N0 required for transmission of bothBPSK and QPSK signals is the same andis less than that required for other formsof digital modulation, such as FSK.Hence for a given information bit rate Rb

the power is also the same. However,since each QPSK symbol consists of twobits while each BPSK symbol consists ofonly one bit, the bandwidth required forQPSK modulation is only half that forBPSK. This is the communicationsequivalent of a “free lunch.” (Actually,the tradeoff is in the increasedcomplexity of the QPSK modulator.)Therefore, until recently, QPSK has beenthe preferred form of digital modulationin satellite communications. The trend in power and bandwidthdoes not continue to higher order formsof PSK modulation. For example, in8-phase PSK (8PSK), there are three bitsper symbol, comprising the set 000, 001,011, 010, 110, 111, 101, and 100.Therefore, the bandwidth for 8PSK is onethird that of BPSK and 2/3 that of QPSK.However, since the phase states are closertogether and are harder to distinguish, thepower required for 8PSK is higher. The mapping sequences illustrated forQPSK and 8PSK are examples of Grayencoding, in which two symbolsrepresented by neighboring phases differby only one bit. This method is mostoften preferred because an error in thedemodulator will likely be caused by

choosing an adjacent phase state and thuswill result in at most one errored bit. It is possible to vary more than oneparameter. In quadrature amplitudemodulation (QAM), both the amplitudeand phase are modulated. In 16QAM, forexample, there are twelve possible phasestates and three possible amplitudes.There are four bits per symbol, e.g.,0000, 0001, 0011, etc., and the requiredbandwidth is one fourth that of BPSKand one-half that of QPSK. However,the required power is much higher. Thisform of modulation has been used forcomputer modems and wireless cabletelevision.

SUMMARY

Modulation may be described as theprocess by which information isimpressed on an electromagnetic carrierwave for transmission from one point toanother. This article has reviewedseveral forms of analog and digitalmodulation. In the design of acommunication system, the choice ofmodulation is of fundamental importanceand always involves a tradeoff betweenpower and bandwidth. In the past, frequency spectrum wasrelatively plentiful but the poweravailable on a satellite was limited. Asatellite typical of the 1980s had a powerof less than 1 kW for a payload of 24transponders. Today, the equation hasbeen reversed. Spectrum is now scarcebut a large spacecraft commonly provides10 to 15 kW for up to 100 transponders.In addition, faster computer processorsenable the use of more complex forwarderror correction coding techniques at highbit rates. Therefore, more spectrumefficient forms of digital modulation suchas 8PSK and 16QAM are becoming moreattractive, even though the powerrequirements are higher. Coupled withpowerful coding methods such asconcatenated Reed Solomon/Viterbicoding, these methods offer the prospectof enhanced spectral efficiency withvirtually error-free digital signaltransmission.__________________________

Dr. Robert A. Nelson, P.E. is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, Maryland.He is Via Satellite’s Technical Editor.

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Via Satellite, May 2000

RainHow It Affects theCommunications Link

by Robert A. Nelson

Rain affects the transmission of anelectromagnetic signal in threeways: (1) It attenuates the signal;(2) it increases the system noisetemperature; and (3) it changesthe polarization. All three of thesemechanisms cause a degradation inthe received signal quality andbecome increasingly significant asthe carrier frequency increases. At C-band the effects are minorand at Ku-band, while they arenoticable, can be accommodated.But at higher frequencies, such asKa-band or V-band, thedegradation can be so great that itsimply cannot be be compensatedat the level of availability usuallyexpected for lower frequencies.This article will explore thephysical mechanisms of raindegradation and will compare therelative effects in various frequencybands used for satellitecommunication.

ATTENUATION

The first, and most well known,effect of rain is that it attenuates thesignal. The attenuation is causedby the scattering and absorption ofelectromagnetic waves by drops ofliquid water. The scatteringdiffuses the signal, whileabsorption involves the resonanceof the waves with individualmolecules of water. Absorptionincreases the molecular energy,corresponding to a slight increasein temperature, and results in anequivalent loss of signal energy.Attenuation is neglible for snow orice crystals, in which the moleculesare tightly bound and do notinteract with the waves.

The attenuation increases as thewavelength approaches the size ofa typical raindrop, which is about1.5 millimeters. Wavelength andfrequency are related by theequation c = λ f, where λ is thewavelength, f is the frequency, andc is the speed of light(approximately 3 x 108 m/s). Forexample, at the C-band downlinkfrequency of 4 GHz, thewavelength is 75 millimeters. Thewavelength is thus 50 times largerthan a raindrop and the signalpasses through the rain withrelatively small attenuation. At theKu-band downlink frequency of12 GHz, the wavelength is 25millimeters. Again, the wavelengthis much greater than the size of araindrop, although not as much asat C-band. At Ka-band, with adownlink frequency of 20 GHz, thewavelength is 15 millimeters and atV-band, at a downlink frequency of40 GHz, it is only 7.5 millimeters.At these frequencies, thewavelength and raindrop size arecomparable and the attenuation isquite large. Considerable research has beencarried out to model rainattenuation mathematically and tocharacterize rainfall throughout theworld. For example, experimentalmeasurements and methods ofanalysis are discussed in the bookRadiowave Propagation in SatelliteCommunications by Louis J.Ippolito (Van Nostrand, 1986).The standard method ofrepresenting rain attenuation isthrough an equation of the form

Lr = α Rβ L = γ L

where Lr is the rain attenation indecibels (dB), R is the rain rate inmillimeters per hour, L is anequivalent path length (km), and αand β are empirical coefficientsthat depend on frequency and tosome extent on the polarization.The factor γ is called the specificrain attenuation, which is expressedin dB/km. The equivalent pathlength depends on the angle of

elevation to the satellite, the heightof the rain layer, and the latitude ofthe earth station. The rain rate enters into thisequation because it is a measure ofthe average size of the raindrops.When the rain rate increases, i.e. itrains harder, the rain drops arelarger and thus there is moreattenuation. Rain models differprincipally in the way the effectivepath length L is calculated. Twoauthoritative rain models that arewidely used are the Crane modeland the ITU-R (CCIR) model. The original Crane model is theglobal model. A revision of thismodel that accounts for both thedense center and fringe area of arain cell is the so-called twocomponent model. These modelsare discussed in detail in the bookElectromagnetic Wave PropagationThrough Rain by Robert K. Crane(Wiley, 1996), which isaccompanied by spreadsheet add-insoftware. In the design of any engineeringsystem, it is impossible toguarantee the perfomance underevery conceivable condition. Onesets reasonable limits based on theconditions that are expected tooccur at a given level ofprobability. For example, a bridgeis designed to withstand loads andstresses that are expected to occurin normal operation and towithstand the forces of wind andground movement that are mostlikely to be encountered. But eventhe best bridge design cannotcompensate for a tornado or anearthquake of unusual strength. Similarly, in the design of asatellite communications link oneincludes margin to compensate forthe effects of rain at a given levelof availability. The statisticalcharacterization of rain begins bydividing the world into rain climatezones. Within each zone, themaximum rain rate for a givenprobability is determined fromactual meteorological dataaccumulated over many years.

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Referring to a chart of rainclimate zones throught the UnitedStates, it might seem inconsistent atfirst glance that Seattle and SanFrancisco are in the same rainclimate region. Seattle is wellknown for its rainy climate,whereas San Francisco canjustifiably boast of fair weather.However, it is not the annualrainfall that matters, but rather theprobability of a given rain rate,since it is the rain rate thatdetermines the average size of araindrop. Thus in Seattle it rainsoften but it rarely rains hard. Theprobability of a cloudburst inSeattle is about the same as that inSan Francisco. It is more likely fora heavy rain shower to occur inWashington, DC. Washington, DC is in rainclimate ragion D2. With aprobability of 99.95 percent, themaximum rain rate is 22.3 mm/h.Thus if a total rain degradation forthis rain rate is compensated byadding sufficient margin to the linkbudget, there will be a 99.95percent probability that the signalcan be received with the specifiedsystem performance objective. Thatis, there is a probability of only0.05 percent that the anticipateddegradation will be exceeded. Thisprobability translates to a possibletotal unavailability of 4.38 hours inincrements distributed randomlyover the entire year. For a digital signal, the requiredsignal power is determined by thebit rate, the bit error rate, themethod of coding, and the methodof modulation. The performanceobjective is specified by the biterror rate. If the maximum allowedrain rate is exceeded, the bit errorrate would increase at the nominalbit rate, or else the bit rate wouldhave to decrease to maintain therequired bit error rate. At C-band, the rain attenuationfor an elevation angle of 40° and amaximum rain rate of 22.3 mm/h inWashington, DC is 0.1 dB. This ispractically a negligible effect. At

Ku-band, under the sameconditions, the attenuation is 4.5dB. This is a large but manageablecontribution to the link budget.However, at the Ka-band downlinkfrequency of 20 GHz, theattenuation is 12.2 dB. This wouldbe a significant effect, requiringover 16 times the power as in clearsky conditions. At the uplinkfrequency of 30 GHz, theattenuation would be 23.5 dB,requiring over 200 times the power.At the V-band downlink frequencyof 40 GHz, the attenuation wouldbe 34.6 dB and at the uplinkfrequency of 50 GHz theattenuation would be 43.7 GHz.These losses simply cannot beaccommodated and thus theavailability would be much less. In practice, these high rainattenuations are sometimes avoidedby using site diversity, in whichtwo widely separated earth stationsare used. The probability that bothearth stations are within the samearea of rain concentration is small.Alternatively, a portion of spectrumin a lower frequency band may beused where needed. For example, ahybrid Ka-band/Ku-band systemmight be designed in whichKa-band provides plentifulspectrum in regions of clearweather, but Ku-band is allocatedto regions in which the rain marginat Ka-band is exceeded.

SYSTEM TEMPERATURE

In addition to causing attenuation,rain increases the downlink systemnoise temperature. The figure ofmerit of the earth station receiveantenna is the ratio of the antennagain to the system temperature G/T.The effect of rain is to increase thesystem temperature and thus reducethe figure of merit. The clear sky systemtemperature is

T = Ta + Te

where Ta is the clear sky antennanoise temperature and Te is theequivalent temperature of the

receiver. The antenna temperatureis the integrated sky temperatureweighted by the antenna gain. At ahigh angle of elevation, the clearsky temperature is typically about25 K since the antenna looks atcold space. However, thetemperature of liquid water is about300 K. Thus the rain increases thesky temperature by an order ofmagnitude. Therefore, the noiseadmitted to the earth station receiveantenna increases and causesfurther signal degradation.However, rain does not affect thesystem noise temperature of thesatellite because its antenna looksat the warm earth. The rain layer acts very muchlike a lossy waveguide. Theequivalent temperature of the rainis

Tr = (Lr – 1) T0

where Lr is the rain loss and T0 isthe physical temperature of therain. The antenna noisetemperature in the presence of rainis given by

T’a = (Ta + Tr ) / Lr

where Ta is the clear sky antennanoise temperature. The systemtemperature in this case is thus

T’ = T’a + Te

where Te is the equivalenttemperature of the receiver, whichis the same as before. The increasein system temperature may thus beexpressed

∆T = T’ – T = (T0 – Ta) (Lr – 1)/Lr

The coefficient of the term on theright is about 275 K. The raincauses an increase in systemtemperature and produces adegradation effect that can becomparable to the attenuation itself.For large attenuation, the limitingratio of system temperatures is

T’ / T = (T0 + Te ) / (Ta + Te )

Thus the antenna temperatureapproaches the temperature of therain.

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DNPOLARIZATION

Rain also changes the polarizationof the signal somewhat. Due to theresistance of the air, a fallingraindrop assumes the shape of anoblate spheroid. Wind and otherdynamic forces cause the raindropto be rotated at a statisticaldistribution of angles.Consequently, the transmissionpath length through the raindrop isdifferent for different signalpolarizations and the polarizationof the received signal is altered. For a satellite communicationsystem with dual linearpolarizations, the change inpolarization has two effects. First,there is a loss in the signal strengthbecause of misalignment of theantenna relative to the clear skyorientation given by

L = 20 log(cos τ)

where τ is the tilt angle relative tothe polarization direction inducedby the rain. Second, there isadditional interference noise due tothe admission of a portion of thesignal in the opposite polarization.The average canting angle withrespect to the local horizon can betaken to be 25°. It is an interesting property ofearth-satellite geometry that alinearly polarized signal is notoriented with the local horizontaland vertical directions, even thougha horizontally polarized signal isparallel to the equatorial plane anda vertically polarized signal isperpendicular to the equatorialplane when transmitted from thesatellite. Thus the optics of theearth station antenna must becorrectly rotated in order to attainthe appropriate polarizationalignment with the satellite. Theearth station feed rotation angle θ isgiven by

tan θ = G sin ∆λ / tan φ

where φ is the latitude of the earthstation, ∆λ is the difference in

longitude, and G is a geometricalfactor that for a geostationarysatellite is nearly unity. Forexample, in Washington, DC, at alatitude of 39°, the antennapolarization must be rotated byabout 12° if the difference inlongitude between the earth stationand satellite is 10°. Thus theaverage effective rain canting anglerelative to the polarization directionis about 25° − 12° = 13°. Thecorresponding polarization loss is0.2 dB.

CONCLUSION

A variety of new satellite servicesare being developed in frequencyregimes higher than the usual C andKu bands due to the availability ofspectrum. These systems includethe broadband services planned forKa-band. Rain will have asignificant impact on theavailability. Mitigating techniquessuch as site diversity or theallocation of spectrum sparingly atlower frequencies where neededwill be necessary to ensureuninterrupted service.Alternatively, data rates andbandwidth capacity must beadjusted to maintain the specifedbit error rates. The mobile satellite service hasfailed to meet market expectationsprimarily because of theavailability of terrestrial servicesthat are cheaper, have greater signalstrength, and require simplerequipment to operate. Thisparadigm must be avoided ifbroadband satellite services are tosucceed. The competion with fiberand cable will be critically affectedby the level of access, the datarates, the complexity of the userequipment, and the availability.The effects of rain will have animportant influence on thesefactors.__________________________

Dr. Robert A. Nelson, P.E. ispresident of Satellite EngineeringResearch Corporation, a satellite

engineering consulting firm inBethesda, Maryland. He is ViaSatellite’s Technical Editor.

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Effects of Rain Degradation on the Satellite Communications Link

AssumptionsRain region D2Elevation angle 40°Earth station latitude 39°Earth station altitude 0 kmClear sky temperature 25 KReceiver equivalent temperature 120 KRain temperature 300 KPolarization vertical

Availability (percent) 99.99 99.95 99.90 99.50 99.00 98.00 97.00Unavailability (percent) 0.01 0.05 0.10 0.50 1.00 2.00 3.00Maximum rain rate (mm/h) 47.1 22.3 15.2 5.3 3.0 1.5 0.9

Attenuation (dB)C-band downlink 4 GHz 0.2 0.1 0.1 0.0 0.0 0.0 0.0C-band uplink 6 GHz 1.3 0.5 0.3 0.1 0.0 0.0 0.0Ku-band downlink 12 GHz 10.5 4.5 2.9 0.8 0.4 0.2 0.1Ku-band uplink 14 GHz 13.7 6.1 4.0 1.2 0.6 0.2 0.1Ka-band downlink 20 GHz 26.4 12.2 8.1 2.5 1.3 0.6 0.3Ka-band uplink 30 GHz 48.8 23.5 16.1 5.4 2.9 1.4 0.8V-band downlink 40 GHz 68.8 34.6 24.2 8.6 4.9 2.4 1.5V-band uplink 50 GHz 83.8 43.7 31.2 11.8 6.9 3.5 1.9

Decrease in G/T (dB)C-band downlink 4 GHz 0.4 0.2 0.1 0.0 0.0 0.0 0.0Ku-band downlink 12 GHz 4.4 3.5 2.8 1.2 0.7 0.3 0.2Ka-band downlink 20 GHz 4.6 4.4 4.2 2.6 1.8 0.9 0.6V-band downlink 40 GHz 4.6 4.6 4.6 4.2 3.6 2.6 1.9

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Via Satellite, September, 1999

AntennasThe Interface withSpace

by Robert A. Nelson

The antenna is the most visible part of thesatellite communication system. Theantenna transmits and receives themodulated carrier signal at the radiofrequency (RF) portion of theelectromagnetic spectrum. For satellitecommunication, the frequencies rangefrom about 0.3 GHz (VHF) to 30 GHz(Ka-band) and beyond. Thesefrequencies represent microwaves, withwavelengths on the order of one meterdown to below one centimeter. Highfrequencies, and the corresponding smallwavelengths, permit the use of antennashaving practical dimensions forcommercial use. This article summarizesthe basic properties of antennas used insatellite communication and derivesseveral fundamental relations used inantenna design and RF link analysis.

HISTORY OFELECTROMAGNETIC WAVES

The quantitative study of electricityand magnetism began with the scientificresearch of the French physicist CharlesAugustin Coulomb. In 1787 Coulombproposed a law of force for charges that,like Sir Isaac Newton’s law ofgravitation, varied inversely as the squareof the distance. Using a sensitive torsionbalance, he demonstrated its validityexperimentally for forces of bothrepulsion and attraction. Like the law ofgravitation, Coulomb’s law was based onthe notion of “action at a distance,”wherein bodies can interactinstantaneously and directly with oneanother without the intervention of anyintermediary. At the beginning of the nineteenthcentury, the electrochemical cell wasinvented by Alessandro Volta, professorof natural philosophy at the University ofPavia in Italy. The cell created an

electromotive force, which made theproduction of continuous currentspossible. Then in 1820 at the Universityof Copenhagen, Hans Christian Oerstedmade the momentous discovery that anelectric current in a wire could deflect amagnetic needle. News of this discoverywas communicated to the FrenchAcademy of Sciences two months later.The laws of force between currentbearing wires were at once investigatedby Andre-Marie Ampere and by Jean-Baptiste Biot and Felix Savart. Withinsix years the theory of steady currentswas complete. These laws were also“action at a distance” laws, that is,expressed directly in terms of thedistances between the current elements. Subsequently, in 1831, the Britishscientist Michael Faraday demonstratedthe reciprocal effect, in which a movingmagnet in the vicinity of a coil of wireproduced an electric current. Thisphenomenon, together with Oersted’sexperiment with the magnetic needle, ledFaraday to conceive the notion of amagnetic field. A field produced by acurrent in a wire interacted with amagnet. Also, according to his law ofinduction, a time varying magnetic fieldincident on a wire would induce avoltage, thereby creating a current.Electric forces could similarly beexpressed in terms of an electric fieldcreated by the presence of a charge. Faraday’s field concept implied thatcharges and currents interacted directlyand locally with the electromagneticfield, which although produced bycharges and currents, had an identity ofits own. This view was in contrast to theconcept of “action at a distance,” whichassumed bodies interacted directly withone another. Faraday, however, was aself-taught experimentalist and did notformulate his laws mathematically. It was left to the Scottish physicistJames Clerk Maxwell to establish themathematical theory of electromagnetismbased on the physical concepts ofFaraday. In a series of papers publishedbetween 1856 and 1865, Maxwellrestated the laws of Coulomb, Ampere,and Faraday in terms of Faraday’selectric and magnetic fields. Maxwellthus unified the theories of electricity andmagnetism, in the same sense that twohundred years earlier Newton had unifiedterrestrial and celestial mechanics

through his theory of universalgravitation. As is typical of abstract mathematicalreasoning, Maxwell saw in his equationsa certain symmetry that suggested theneed for an additional term, involving thetime rate of change of the electric field.With this generalization, Maxwell’sequations also became consistent with theprinciple of conservation of charge. Furthermore, Maxwell made theprofound observation that his set ofequations, thus modified, predicted theexistence of electromagnetic waves.Therefore, disturbances in theelectromagnetic field could propagatethrough space. Using the values ofknown experimental constants obtainedsolely from measurements of charges andcurrents, Maxwell deduced that the speedof propagation was equal to speed oflight. This quantity had been measuredastronomically by Olaf Romer in 1676from the eclipses of Jupiter’s satellitesand determined experimentally fromterrestrial measurements by H.L. Fizeauin 1849. He then asserted that light itselfwas an electromagnetic wave, therebyunifying optics with electromagnetism aswell. Maxwell was aided by his superiorknowledge of dimensional analysis andunits of measure. He was a member ofthe British Association committee formedin 1861 that eventually established thecentimeter-gram-second (CGS) system ofabsolute electrical units. Maxwell’s theory was not accepted byscientists immediately, in part because ithad been derived from a bewilderingcollection of mechanical analogies anddifficult mathematical concepts. Theform of Maxwell’s equations as they areknown today is due to the Germanphysicist Heinrich Hertz. Hertzsimplified them and eliminatedunnecessary assumptions. Hertz’s interest in Maxwell’s theorywas occasioned by a prize offered by theBerlin Academy of Sciences in 1879 forresearch on the relation betweenpolarization in insulators andelectromagnetic induction. By means ofhis experiments, Hertz discovered how togenerate high frequency electricaloscillations. He was surprised to findthat these oscillations could be detectedat large distances from the apparatus. Upto that time, it had been generally

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assumed that electrical forces decreasedrapidly with distance according to theNewtonian law. He therefore sought totest Maxwell’s prediction of the existenceof electromagnetic waves. In 1888, Hertz set up standingelectromagnetic waves using an oscillatorand spark detector of his own design andmade independent measurements of theirwavelength and frequency. He found thattheir product was indeed the speed oflight. He also verified that these wavesbehaved according to all the laws ofreflection, refraction, and polarizationthat applied to visible light, thusdemonstrating that they differed fromlight only in wavelength and frequency.“Certainly it is a fascinating idea,” Hertzwrote, “that the processes in air that wehave been investigating represent to us ona million-fold larger scale the sameprocesses which go on in theneighborhood of a Fresnel mirror orbetween the glass plates used inexhibiting Newton’s rings.” It was not long until the discovery ofelectromagnetic waves was transformedfrom pure physics to engineering. Afterlearning of Hertz’s experiments through amagazine article, the young Italianengineer Guglielmo Marconi constructedthe first transmitter for wirelesstelegraphy in 1895. Within two years heused this new invention to communicatewith ships at sea. Marconi’s transmissionsystem was improved by Karl F. Braun,who increased the power, and hence therange, by coupling the transmitter to theantenna through a transformer instead ofhaving the antenna in the power circuitdirectly. Transmission over longdistances was made possible by thereflection of radio waves by theionosphere. For their contributions towireless telegraphy, Marconi and Braunwere awarded the Nobel Prize in physicsin 1909. Marconi created the AmericanMarconi Wireless Telegraphy Companyin 1899, which competed directly withthe transatlantic undersea cable operators.On the early morning of April 15, 1912, a21-year old Marconi telegrapher in NewYork City by the name of David Sarnoffreceived a wireless message from theMarconi station in Newfoundland, whichhad picked up faint SOS distress signalsfrom the steamship Titanic. Sarnoffrelayed the report of the ship’s sinking to

the world. This singular eventdramatized the importance of the newmeans of communication. Initially, wireless communication wassynonymous with telegraphy. Forcommunication over long distances thewavelengths were greater than 200meters. The antennas were typicallydipoles formed by long wires cut to asubmultiple of the wavelength. Commercial radio emerged during the1920s and 1930s. The AmericanMarconi Company evolved into theRadio Corporation of America (RCA)with David Sarnoff as its director.Technical developments included theinvention of the triode for amplificationby Lee de Forest and the perfection ofAM and FM receivers through the workof Edwin Howard Armstrong and others.In his book Empire of the Air: The MenWho Made Radio, Tom Lewis creditsde Forest, Armstrong, and Sarnoff as thethree visionary pioneers most responsiblefor the birth of the moderncommunications age. Stimulated by the invention of radarduring World War II, considerableresearch and development in radiocommunication at microwave frequenciesand centimeter wavelengths wasconducted in the decade of the 1940s.The MIT Radiation Laboratory was aleading center for research on microwaveantenna theory and design. The basicformulation of the radio transmissionformula was developed by Harald T. Friisat the Bell Telephone Laboratories andpublished in 1946. This equationexpressed the radiation from an antennain terms of the power flow per unit area,instead of giving the field strength involts per meter, and is the foundation ofthe RF link equation used by satellitecommunication engineers today.

TYPES OF ANTENNAS

A variety of antenna types are used insatellite communications. The mostwidely used narrow beam antennas arereflector antennas. The shape isgenerally a paraboloid of revolution. Forfull earth coverage from a geostationarysatellite, a horn antenna is used. Hornsare also used as feeds for reflectorantennas. In a direct feed reflector, such as on asatellite or a small earth terminal, the

feed horn is located at the focus or maybe offset to one side of the focus. Largeearth station antennas have a subreflectorat the focus. In the Cassegrain design,the subreflector is convex with anhyperboloidal surface, while in theGregorian design it is concave with anellipsoidal surface. The subreflector permits the antennaoptics to be located near the base of theantenna. This configuration reduceslosses because the length of thewaveguide between the transmitter orreceiver and the antenna feed is reduced.The system noise temperature is alsoreduced because the receiver looks at thecold sky instead of the warm earth. Inaddition, the mechanical stability isimproved, resulting in higher pointingaccuracy. Phased array antennas may be used toproduce multiple beams or for electronicsteering. Phased arrays are found onmany nongeostationary satellites, such asthe Iridium, Globalstar, and ICOsatellites for mobile telephony.

GAIN AND HALF POWERBEAMWIDTH

The fundamental characteristics of anantenna are its gain and half powerbeamwidth. According to the reciprocitytheorem, the transmitting and receivingpatterns of an antenna are identical at agiven wavelength The gain is a measure of how much ofthe input power is concentrated in aparticular direction. It is expressed withrespect to a hypothetical isotropicantenna, which radiates equally in alldirections. Thus in the direction (θ, φ),the gain is

G(θ, φ) = (dP/dΩ)/(Pin /4π)

where Pin is the total input power and dPis the increment of radiated output powerin solid angle dΩ. The gain is maximumalong the boresight direction. The input power is Pin = Ea

2 A / η Z0

where Ea is the average electric field overthe area A of the aperture, Z0 is theimpedance of free space, and η is the netantenna efficiency. The output powerover solid angle dΩ is dP = E2 r2 dΩ / Z0,where E is the electric field at distance r.But by the Fraunhofer theory ofdiffraction, E = Ea A / r λ along theboresight direction, where λ is the

3

wavelength. Thus the boresight gain isgiven in terms of the size of the antennaby the important relation

G = η (4 π / λ2) A

This equation determines the requiredantenna area for the specified gain at agiven wavelength. The net efficiency η is the product ofthe aperture taper efficiency ηa , whichdepends on the electric field distributionover the antenna aperture (it is the squareof the average divided by the average ofthe square), and the total radiationefficiency η* = P/Pin associated withvarious losses. These losses includespillover, ohmic heating, phasenonuniformity, blockage, surfaceroughness, and cross polarization. Thus η= ηa η*. For a typical antenna, η = 0.55. For a reflector antenna, the area issimply the projected area. Thus for acircular reflector of diameter D, the areais A = π D2/4 and the gain is

G = η (π D / λ)2

which can also be written

G = η (π D f / c)2

since c = λ f, where c is the speed of light(3 × 108 m/s), λ is the wavelength, and fis the frequency. Consequently, the gainincreases as the wavelength decreases orthe frequency increases. For example, an antenna with adiameter of 2 m and an efficiency of 0.55would have a gain of 8685 at the C-banduplink frequency of 6 GHz andwavelength of 0.050 m. The gainexpressed in decibels (dB) is10 log(8685) = 39.4 dB. Thus the powerradiated by the antenna is 8685 timesmore concentrated along the boresightdirection than for an isotropic antenna,which by definition has a gain of 1 (0dB). At Ku-band, with an uplinkfrequency of 14 GHz and wavelength0.021 m, the gain is 49,236 or 46.9 dB.Thus at the higher frequency, the gain ishigher for the same size antenna. The boresight gain G can be expressedin terms of the antenna beam solid angleΩA that contains the total radiated poweras

G = η* (4π / ΩA )

which takes into account the antennalosses through the radiation efficiencyη*. The antenna beam solid angle is the

solid angle through which all the powerwould be concentrated if the gain wereconstant and equal to its maximum value.The directivity does not include radiationlosses and is equal to G / η*. The half power beamwidth is theangular separation between the halfpower points on the antenna radiationpattern, where the gain is one half themaximum value. For a reflector antennait may be expressed

HPBW = α = k λ / D

where k is a factor that depends on theshape of the reflector and the method ofillumination. For a typical antenna, k =70° (1.22 if α is in radians). Thus thehalf power beamwidth decreases withdecreasing wavelength and increasingdiameter. For example, in the case of the 2meter antenna, the half power beamwidthat 6 GHz is approximately 1.75°. At 14GHz, the half power beamwidth isapproximately 0.75°. As an extremeexample, the half power beamwidth ofthe Deep Space Network 64 meterantenna in Goldstone, California is only0.04 ° at X-band (8.4 GHz). The gain may be expressed directly interms of the half power beamwidth byeliminating the factor D/λ. Thus,

G = η (π k / α)2

Inserting the typical values η = 0.55 andk = 70°, one obtains

G = 27,000/ (α°)2

where α° is expressed in degrees. This isa well known engineering approximationfor the gain (expressed as a numeric). Itshows directly how the size of the beamautomatically determines the gain.Although this relation was derivedspecifically for a reflector antenna with acircular beam, similar relations can beobtained for other antenna types andbeam shapes. The value of the numeratorwill be somewhat different in each case. For example, for a satellite antennawith a circular spot beam of diameter 1°,the gain is 27,000 or 44.3 dB. For a Ku-band downlink at 12 GHz, the requiredantenna diameter determined from eitherthe gain or the half power beamwidth is1.75 m. A horn antenna would be used toprovide full earth coverage fromgeostationary orbit, where the angular

diameter of the earth is 17.4°. Thus, therequired gain is 89.2 or 19.5 dB.Assuming an efficiency of 0.70, the horndiameter for a C-band downlinkfrequency of 4 GHz would be 27 cm.

EIRP AND G/T

For the RF link budget, the tworequired antenna properties are theequivalent isotropic radiated power(EIRP) and the “figure of merit” G/T.These quantities are the properties of thetransmit antenna and receive antenna thatappear in the RF link equation and arecalculated at the transmit and receivefrequencies, respectively. The equivalent isotropic radiatedpower (EIRP) is the power radiatedequally in all directions that wouldproduce a power flux density equivalentto the power flux density of the actualantenna. The power flux density Φ isdefined as the radiated power P per unitarea S, or Φ = P/S. But P = η* Pin ,where Pin is the input power and η* is theradiation efficiency, andS = d2 ΩA ,where d is the slant range tothe center of coverage and ΩA is the solidangle containing the total power. Thuswith some algebraic manipulation,

Φ = η* (4π / ΩA )( Pin / 4π d2) = G Pin /4π d2

Since the surface area of a sphere ofradius d is 4π d2, the flux density in termsof the EIRP is

Φ = EIRP / 4π d2

Equating these two expressions, oneobtains

EIRP = G Pin

Therefore, the equivalent isotropicradiated power is the product of theantenna gain of the transmitter and thepower applied to the input terminals ofthe antenna. The antenna efficiency isabsorbed in the definition of gain. The “figure of merit” is the ratio of theantenna gain of the receiver G and thesystem temperature T. The systemtemperature is a measure of the totalnoise power and includes contributionsfrom the antenna and the receiver. Boththe gain and the system temperature mustbe referenced to the same point in thechain of components in the receiversystem. The ratio G/T is important

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because it is an invariant that isindependent of the reference point whereit is calculated, even though the gain andthe system temperature individually aredifferent at different points.

ANTENNA PATTERN

Since electromagnetic energypropagates in the form of waves, itspreads out through space due to thephenomenon of diffraction. Individualwaves combine both constructively anddestructively to form a diffraction patternthat manifests itself in the main lobe andside lobes of the antenna. The antenna pattern is analogous tothe “Airy rings” produced by visible lightwhen passing through a circular aperture.These diffraction patterns were studiedby Sir George Biddell Airy, AstronomerRoyal of England during the nineteenthcentury, to investigate the resolvingpower of a telescope. The diffractionpattern consists of a central bright spotsurrounded by concentric bright ringswith decreasing intensity. The central spot is produced by wavesthat combine constructively and isanalogous to the main lobe of theantenna. The spot is bordered by a darkring, where waves combine destructively,that is analogous to the first null. Thesurrounding bright rings are analogous tothe side lobes of the antenna pattern. Asnoted by Hertz, the only difference in thisbehavior is the size of the pattern and thedifference in wavelength. Within the main lobe of anaxisymmetric antenna, the gain G(θ) in adirection θ with respect to the boresightdirection may be approximated by theexpression

G(θ) = G − 12 (θ / α)2

where G is the boresight gain. Here thegains are expressed in dB. Thus at thehalf power points to either side of theboresight direction, where θ = α/2, thegain is reduced by a factor of 2, or 3 dB.The details of the antenna, including itsshape and illumination, are contained inthe value of the half power beamwidth α.This equation would typically be used toestimate the antenna loss due to a smallpointing error. The gain of the side lobes can beapproximated by an envelope. For newearth station antennas withD/λ > 100, the side lobes must fall within

the envelope 29 − 25 log θ byinternational regulation. This envelope isdetermined by the requirement ofminimizing interference betweenneighboring satellites in the geostationaryarc with a nominal 2° spacing.

TAPER

The gain pattern of a reflector antennadepends on how the antenna isilluminated by the feed. The variation inelectric field across the antenna diameteris called the antenna taper. The total antenna solid anglecontaining all of the radiated power,including side lobes, is

ΩA = η* (4π / G) = (1/ηa) (λ2 / A)

where ηa is the aperture taper efficiencyand η* is the radiation efficiencyassociated with losses. The beamefficiency is defined as

ε = ΩM / ΩA

where ΩM is the solid angle for the mainlobe. The values of ηa and are εcalculated from the electric fielddistribution in the aperture plane and theantenna radiation pattern, respectively. For a theoretically uniformillumination, the electric field is constantand the aperture taper efficiency is 1. Ifthe feed is designed to cause the electricfield to decrease with distance from thecenter, then the aperture taper efficiencydecreases but the proportion of power inthe main lobe increases. In general,maximum aperture taper efficiencyoccurs for a uniform distribution, butmaximum beam efficiency occurs for ahighly tapered distribution. For uniform illumination, the halfpower beamwidth is 58.4° λ/D and thefirst side lobe is 17.6 dB below the peakintensity in the boresight direction. Inthis case, the main lobe contains about 84percent of the total radiated power andthe first side lobe contains about 7percent. If the electric field amplitude has asimple parabolic distribution, falling tozero at the reflector edge, then theaperture taper efficiency becomes 0.75but the fraction of power in the main lobeincreases to 98 percent. The half powerbeamwidth is now 72.8° λ/D and the firstside lobe is 24.6 dB below peak intensity.Thus, although the aperture taper

efficiency is less, more power iscontained in the main lobe, as indicatedby the larger half power beamwidth andlower side lobe intensity. If the electric field decreases to afraction C of its maximum value, calledthe edge taper, the reflector will notintercept all the radiation from the feed.There will be energy spillover with acorresponding efficiency ofapproximately 1 − C2. However, as thespillover efficiency decreases, theaperture taper efficiency increases. Thetaper is chosen to maximize theillumination efficiency, defined as theproduct of aperture taper efficiency andspillover efficiency. The illumination efficiency reaches amaximum value for an optimumcombination of taper and spillover. For atypical antenna, the optimum edge taperC is about 0.316, or −10 dB (20 log C).With this edge taper and a parabolicillumination, the aperture taper efficiencyis 0.92, the spillover efficiency is 0.90,the half power beamwidth is 65.3° λ/D,and the first side lobe is 22.3 dB belowpeak. Thus the overall illuminationefficiency is 0.83 instead of 0.75. Thebeam efficiency is about 95 percent.

COVERAGE AREA

The gain of a satellite antenna isdesigned to provide a specified area ofcoverage on the earth. The area ofcoverage within the half powerbeamwidth is

S = d2 Ω

where d is the slant range to the center ofthe footprint and Ω is the solid angle of acone that intercepts the half power points,which may be expressed in terms of theangular dimensions of the antenna beam.Thus

Ω = K α β

where α and β are the principal plane halfpower beamwidths in radians and K is afactor that depends on the shape of thecoverage area. For a square orrectangular area of coverage, K = 1,while for a circular or elliptical area ofcoverage, K = π /4. The boresight gain may beapproximated in terms of this solid angleby the relation

G = η′ (4π / Ω) = (η′ / K)(41,253 / α°β°)

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where α° and β° are in degrees and η′ isan efficiency factor that depends on thethe half power beamwidth. Although η′is conceptually distinct from the netefficiency η, in practice these twoefficiencies are roughly equal for atypical antenna taper. In particular, for acircular beam this equation is equivalentto the earlier expression in terms of α ifη′ = (π k / 4)2 η. If the area of the footprint S isspecified, then the size of a satelliteantenna increases in proportion to thealtitude. For example, the altitude ofLow Earth Orbit is about 1000 km andthe altitude of Medium Earth Orbit isabout 10,000 km. Thus to cover the samearea on the earth, the antenna diameter ofa MEO satellite must be about 10 timesthat of a LEO satellite and the gain mustbe 100 times, or 20 dB, as great. On the Iridium satellite there are threemain mission L-band phased arrayantennas. Each antenna has 106elements, distributed into 8 rows withelement separations of 11.5 cm and rowseparations of 9.4 cm over an antennaarea of 188 cm × 86 cm. The patternproduced by each antenna is divided into16 cells by a two-dimensional Butlermatrix power divider, resulting in a totalof 48 cells over the satellite coveragearea. The maximum gain for a cell at theperimeter of the coverage area is 24.3 dB. From geostationary orbit the antennasize for a small spot beam can beconsiderable. For example, thespacecraft for the Asia Cellular SatelliteSystem (ACeS), being built by LockheedMartin for mobile telephony in SoutheastAsia, has two unfurlable mesh antennareflectors at L-band that are 12 metersacross and have an offset feed. Havingdifferent transmit and receive antennasminimizes passive intermodulation (PIM)interference that in the past has been aserious problem for high power L-bandsatellites using a single reflector. Theantenna separation attenuates the PIMproducts by from 50 to 70 dB.

SHAPED BEAMS

Often the area of coverage has anirregular shape, such as one defined by acountry or continent. Until recently, theusual practice has been to create thedesired coverage pattern by means of abeam forming network. Each beam has

its own feed and illuminates the fullreflector area. The superposition of allthe individual circular beams producesthe specified shaped beam. For example, the C-band transmithemi/zone antenna on the Intelsat 6satellite is 3.2 meters in diameter. This isthe largest diameter solid circularaperture that fits within an Ariane 4launch vehicle fairing envelope. Theantenna is illuminated by an array of 146Potter horns. The beam diameter α foreach feed is 1.6° at 3.7 GHz. Byappropriately exciting the beam formingnetwork, the specified areas of coverageare illuminated. For 27 dB spatialisolation between zones reusing the samespectrum, the minimum spacing σ isgiven by the rule of thumb σ ≥ 1.4 α, sothat σ ≥ 2.2°. This meets thespecification of σ = 2.5° for Intelsat 6. Another example is provided by theHS-376dual-spin stabilized Galaxy 5 satellite,operated by PanAmSat. The reflectordiameter is 1.80 m. There are two linearpolarizations, horizontal and vertical. Ina given polarization, the contiguousUnited States (CONUS) might becovered by four beams, each with a halfpower beamwidth of 3° at the C-banddownlink frequency of 4 GHz. Fromgeostationary orbit, the angulardimensions of CONUS are approximately6° × 3°. For this rectangular beampattern, the maximum gain is about 31dB. At edge of coverage, the gain is 3 dBless. With a TWTA ouput power of 16W (12 dBW), a waveguide loss of 1.5dB, and an assumed beam-formingnetwork loss of 1 dB, the maximum EIRPis 40.5 dBW. The shaped reflector represents a newtechnology. Instead of illuminating aconventional parabolic reflector withmultiple feeds in a beam-formingnetwork, there is a single feed thatilluminates a reflector with an undulatingshape that provides the required region ofcoverage. The advantages are lowerspillover loss, a significant reduction inmass, lower signal losses, and lower cost.By using large antenna diameters, therolloff along the perimeter of thecoverage area can be made sharp. Thepractical application of shaped reflectortechnology has been made possible bythe development of composite materials

with extremely low coefficients ofthermal distortion and by the availabilityof sophisticated computer softwareprograms necessary to analyze theantenna. One widely used antennasoftware package is called GRASP,produced by TICRA of Copenhagen,Denmark. This program calculates thegain from first principles using the theoryof physical optics.

SUMMARY

The gain of an antenna is determinedby the intended area of coverage. Thegain at a given wavelength is achieved byappropriately choosing the size of theantenna. The gain may also beexpressed in terms of the half powerbeamwidth. Reflector antennas are generally usedto produce narrow beams forgeostationary satellites and earth stations.The efficiency of the antenna isoptimized by the method of illuminationand choice of edge taper. Phased arrayantennas are used on many LEO andMEO satellites. New technologiesinclude large, unfurlable antennas forproducing small spot beams fromgeostationary orbit and shaped reflectorsfor creating a shaped beam with only asingle feed.

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Dr. Robert A. Nelson, P.E. is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, Maryland.Dr. Nelson is instructor for the courseSatellite Communication SystemsEngineering: LEO, MEO, GEO offeredby Applied Technology Institute. He is aLecturer in the Department of AerospaceEngineering at the University ofMaryland and is Technical Editor of ViaSatellite magazine.

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Via Satellite May, 1998

Earth StationTechnology

The Smarts Behind the Dish

by Robert A. Nelson

The earth station is the link between theterrestrial data sources and the remotesatellite resource. Its most familiarcomponent is the earth station antenna,which can be tens of meters in diameter ora small portable dish. In addition, thereare numerous, less obvious devices in thechain of devices that transmit or receivethe signal. This article will brieflysummarize some of the most importantaspects of earth station operation.

TRANSMITTER CHAIN

Information to be transmitted is deliveredto the earth station via coaxial cable, fiber,terrestrial microwave, or satellite. Thedevices in the transmitter chain typicallyconsist of the multiplexer, the modulator,the upconvertor, a high power amplifier,and the antenna. The multiplexercombines the individual channels onto asingle data stream. The information canbe encrypted and encoded with a forwarderror correction code. The modulatormodulates the baseband signal containingthe desired information onto anintermediate frequency (IF) carrier,usually at 70 MHz. The upconverterchanges the carrier to the radio frequency(RF) signals used to transmit the signal,such as C-band (6 GHz) or Ku-band(14 GHz). The high power amplifier(HPA) amplifies the modulated RF signalsfrom the output of the upconvertors to therequired power at the input terminals ofthe antenna. Finally, the antenna transmitsthe amplified RF signal to the satellite. A common form of modulation used indigital satellite communication is M-aryphase shift keying. In this technique, thecarrier can assume one of M phase states,each of which represents a symbol. Inbinary phase shift keying (BPSK), thereare two phase states, 0° and 180°,representing a binary one or zero. Inquaternary phase shift keying (QPSK),

there are four phase states that representthe four symbols 11, 01, 00, and 10. AQPSK modulator is equivalent to twoBPSK modulators out of phase by 90°. Itcan be shown that both BPSK and QPSKmodulation require the same power per bitfor the same bit error rate (BER), butQPSK modulation requires only half thebandwidth. Moreover, all other forms ofdigital modulation require more power.Thus QPSK is by far the most prevalentform of modulation used in satellitecommunication and is the industrystandard. Analog frequency modulation (FM) isstill commonly used for the transmissionof television signals. This has been aconvenient mode due to the widespreaduse of standard equipment. However,there is a slow but deliberate transition todigital technology for television. The HPA can be either a klystron, atraveling wave tube (TWT), or a solidstate power amplifier (SSPA). Thebandwidth of a klystron is fairly narrowand is the same as the bandwidth of atransponder, or about 40 MHz at 6 GHzand 80 MHz at 14 GHz. A C-bandklystron can have a typical power of 3.3kW. Although it has a narrow bandwidth,a klystron has relatively high efficiency(about 40 percent) and is generallyeconomical to operate. A TWT is a broadband device with abandwidth of about 500 MHz, or about thefull bandwidth of a 24 transponder satellitecomprising 12 transponders at eachpolarization. The TWT is more flexible,since it can put the same carrier into all 12transponders. However, since it is anonlinear device, it must be backed off tooperate in the linear region when multiplecarriers are present. A 350 watt Ku-bandTWT with 6 dB of backoff has an outputpower of about 90 watts. The loss can bepartially reduced using equalizing devicescalled linearizers. Helix TWTAs areavailable at Ku-band with a power of 700W and at C-band with a power of about 3kW. Still higher power, at around 10 kW,can be attained with coupled-cavityTWTs. An SSPA is very efficient and thusdoes not produce much heat. A typicalSSPA power is 2 or 3 watts, but can be ashigh as 80 or 100 watts. At Ku-band the HPA must be locatednear the antenna to minimize losses, but atC-band it can be farther away, such as inthe control building, since the loss per unit

length of the waveguide diminishes withfrequency. For a typical ellipticalwaveguide, the loss per 30 meters (100feet) is about 5 dB at Ku-band, comparedto about 1 dB at C-band.

RECEIVER CHAIN

The devices in the receiver chain reversethis process. The antenna receives themodulated RF signals from the satellite.The power level at the output terminals ofthe antenna is about a picowatt. Thisextremely low power level is comparableto the sound level from a barely audiblemosquito. A low noise amplifier (LNA)amplifies the received RF signals. Thedownconverter changes the received RFsignals to IF signals for the demodulators.The information is extracted from thereceived IF signal by the demodulator andis decoded and decrypted. Thedemultiplex equipment then distributes thebaseband information to the customersthrough the router and switch after a checkof key parameters and rebalancing. Datarates are usually in some standard format,such as a 1.544 Mbps T1 channel or a 45Mbps DS3 channel, consisting of 28 T1's. The LNA is mounted on the antennaitself to minimize waveguide loss. This isthe first active component and itsperformance is the primary factor indetermining the capability of the receiver.The LNA must have a high gain butcontribute very little noise. During the1980s it was difficult to produce aKu-band LNA with a noise temperature of160 K. Today, using field effecttransistors, it is possible to reduce thisvalue to around 75 K. Because of themanner in which the noise temperaturescombine in a series of devices to producethe overall system temperature, it isessential to place the LNA, with a highgain and low noise temperature, at thehead of the receiver chain. Instead of an LNA, a low noise blockdownconverter (LNB) may be used. AnLNA only amplifies the signal, while anLNB both amplifies the signal anddownconverts the frequency to L-band,again to minimize losses. Systems atC-band use both LNA and LNB designs,but Ku-band systems employ LNBsalmost exclusively.

ANTENNA

Since electromagnetic energy propagatesin the form of waves, the spreading of theenergy as it leaves the antenna is described

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by the theory of diffraction. The larger theantenna reflector is in comparison with thewavelength, the less spreading there is.The physics of radio waves is identical tothe physics of visible light and thus thespreading of radio frequency waves froman antenna reflector is analogous to thetransmission of light through an aperture.In fact, a reflector antenna is often referredto as an aperture antenna. Monochromatic light, such as from alaser, will produce a series of concentricAiry rings when passed through a smallcircular hole and projected on a screen.The central bright spot is like the mainlobe of an antenna pattern. Thesurrounding dark and bright rings areanalogous to the nulls and side lobes of theantenna pattern. The antenna reflector is usually aparaboloid of revolution. Theconfiguration of the antenna is called adirect feed if the feed horn or low noiseamplifier (LNA) is located at the primefocus. Large antennas usually have asubreflector, of either the convexhyperbolic Cassegrain type or the concaveellipsoidal Gregorian type. Thesubreflector permits the LNA to look intocold space and away from the warmground, so as to significantly reduce theantenna noise temperture. In an offsetantenna, the feed is located to one side.The advantage of the offset design is thatit eliminates blockage effects fromsubreflectors. Many antennas have tracking capabilitythat permit them to follow a satellite in ageosynchronous, but inclined, orbit.Inclined orbit operation is now a commonpart of the business plan of satelliteoperators to extend the useful life of asatellite. The tracking mechanism may beprogrammed with an ephemeris thatdetermines the look angle as a function oftime of day, or it may have an automaticservo loop with a memory that maximizesthe received power. The gain of the antenna is the measureof its ability to concentrate the radiofrequency electromagnetic energy in aspecified direction, in comparison to ahypothetical isotropic antenna that radiatesits energy equally in all directions. It isdetermined by the size of the physicalaperture, the frequency of the radiation,and the efficiency. The gain is proportional to the squareof the antenna diameter and to the squareof the frequency. For example, an

Andrew 4.6 meter earth station antennawith a Gregorian feed when operated at C-band has a transmit gain of 48.2 dB at6.175 GHz and a receive gain of 44.4 dBat 4.0 GHz. The same antenna can beused at Ku-band with a transmit gain of55.1 dB at 14.25 GHz and a receive gainof 53.8 dB at 11.95 GHz. Factors that affect the efficiencyinclude the geometrical shape of theaperture, the method of illumination (so-called taper), the amount of spillover ofenergy past the edge of the antenna,surface roughness, blockage, and phasecoherence. Another fundamental parameter is thehalf power beamwidth. This is the anglebetween the half power points of the mainlobe of the antenna pattern. The halfpower beamwidth varies in inverseproportion to the frequency and theantenna diameter. For example, theAndrew 4.6 meter antenna at C-band has atransmit half power beamwidth of 0.63°and a receive half power beamwidth of0.92°, while at Ku-band these values are0.28° and 0.34°, respectively. On theother hand, a huge 64 m deep spacetracking antenna at X-band (8.4 GHz) mayhave a half power beamwidth of only0.04°. Two key parameters are the equivalentisotropic radiated power (EIRP) and theantenna figure of merit. The EIRP isassociated with a transmit antenna and isthe product of the power P to the inputterminals of the antenna and the antennatransmit gain Gt. The figure of merit isassociated with a receive antenna. It is theratio of the antenna receive gain Gr andthe system temperature T, which is ameasure of the noise power accepted bythe antenna and must be as low aspossible.

EARTH STATION STANDARDS

Earth stations are characterized by theantenna size, the type of service, thefrequency band, the EIRP, and the G/T. Transmit antennas must conform tointernational and domestic regulations.The sidelobes must fall within a specifiedenvelope in order to mitigate interferencewith neighboring satellites and terrestrialsystems. The standard internationalspecification for the sidelobe gain of newantennas with diameter to wavelengthratio greater than 100 and operating with ageostationary satellite is given by

G = 29 - 25 log θ dB, where θ is theoff-axis angle. The earth station antennaside lobe pattern is the primarycharacteristic that determines theminimum spacing between satellites alongthe geostationary arc. In addition, the EIRP in a givenbandwidth must be within specified valuesat various bands and the antenna mustmeet certain radiation hazard constraints.The document governing satellitecommunications in the United States isPart 25 of the Rules of the FederalCommunications Commission (FCC). Satellite operators also establishstandards for their individual systems. Forexample, INTELSAT has establishedtechnical parameters that must be met foracceptance within a particular application.

EARTH STATION FACILITIES

A good example of a commercial earthstation facility is the WashingtonInternational Teleport, located inAlexandria, Virginia just inside theWashington Capital Beltway. This facilityis a hub for voice, data, video, internet,and other services to customers rangingfrom major television broadcasters totelemedicine and distance learningproviders. Another example is the Hughes SpringCreek earth station, located in southeastBrooklyn, which is the primary TT&Cfacility for the Hughes C-band and dualpayload Galaxy satellites. It also providesbackup for the Hughes Ku-bandspacecraft. Spring Creek provides uplinkaccess for C-band customers in the NewYork City area. One of the antennas isused by Hughes Network Systems for ashared VSAT (very small apertureterminal) hub, which supports customerswho operate private data networks.

INDUSTRY TRENDS

The legacy of analog video is bigtransmitters using big antennas. Thecurrent trend is to shift the burden ofclosing the satellite link from the earthstation to the satellite, thereby permittingsmaller and smaller earth station antennas.Whereas satellites launched during the1980s were simple repeater ``bent pipe''satellites, with a typical primary power of1 to 2 kW, today's generation satelliteshave extensive onboard processing and atotal power of 10 to 15 kW or more.

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In addition, there is an emphasis onbroadband applications at highfrequencies, including Ka-band(30/20 GHz) and the new V-band (50/40GHz). As noted by Teledesic presidentRussell Daggatt at the Satellite 98Conference, the paradigm for broadbandapplications used to be video on demand.Today it is internet access via satellite. There is also changing emphasis ontypes of services. In the past, satelliteshave almost entirely provided voice,video, and data connectivity forinternational and domestic commoncarriers and operators of television anddata networks. Now there is an emphasison consumer services to meet a globaldemand for information and aconvergence of telephone, data, and videoapplications.

CONCLUSION

The technology of earth stations has beenreviewed and a few illustrative systemshave been described. In coming years thenumber of large earth station facilities thatwe are accustomed to seeing will continueto grow. However, in addition, there willbe an exponential growth of small earthterminals for consumer services. Like aweb, the major nodes will be filled in by adense network of smaller nodes of variestypes and sizes.

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Dr. Robert A. Nelson, P.E., is presidentof Satellite Enginering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, MD.

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Via Satellite, October, 1998

Earth Station HighPower Amplifiers

KPA, TWTA, or SSPA?

by Robert A. Nelson

The high power amplifier (HPA) in anearth station facility provides the RFcarrier power to the input terminals of theantenna that, when combined with theantenna gain, yields the equivalentisotropic radiated power (EIRP) requiredfor the uplink to the satellite. Thewaveguide loss between the HPA and theantenna must be accounted for in thecalculation of the EIRP.

The output power typically may be afew watts for a single data channel, arounda hundred watts or less for a low capacitysystem, or several kilowatts for highcapacity traffic.

The choice of amplifier is highlydependent on its application, the cost ofinstallation and long term operation, andmany other factors. This article willsummarize the technologies, describe theirimportant characteristics, and identifysome issues important to understandingtheir differences and relative merits.

TYPES OF AMPLIFIERS

Earth station terminals for satellitecommunication use high power amplifiersdesigned primarily for operation in theFixed Satellite Service (FSS) at C-band(6 GHz), military and scientificcommunications at X-band (8 GHz), fixedand mobile services at Ku-band (14 GHz),the Direct Broadcast Service (DBS) in theDBS portion of Ku-band (18 GHz), andmilitary applications in the EHF/Q-band(45 GHz). Other frequency bands includethose allocated for the emergingbroadband satellite services in Ka-band(30 GHz) and V-band (50 GHz). Generally, the frequency used for theearth-to-space uplink is higher than thefrequency for the space-to-earth downlink

within a given band.An earth station HPA can be one of

three types: a klystron power amplifier(KPA), a traveling wave tube amplifier(TWTA), or a solid state power amplifier(SSPA). The KPA and TWTA achieveamplification by modulating the flow ofelectrons through a vacuum tube. Solidstate power amplifiers use gallium arsenide(GaAs) field effect transistors (FETs) thatare configured using power combiningtechniques. The klystron is a narrowband,high power device, while TWTAs andSSPAs have wide bandwidths and operateover a range of low, medium, and highpowers.

The principal technical parameterscharacterizing an amplifier are itsfrequency, bandwidth, output power, gain,linearity, efficiency, and reliability. Size,weight, cabinet design, ease ofmaintenance, and safety are additionalconsiderations. Cost factors include thecost of installation and the long term costof ownership.

KPAs are normally used for high powernarrowband transmission to specificsatellite transponders, typically fortelevision program transmission anddistribution. TWTAs and SSPAs are usedfor wideband applications or wherefrequency agility is required.

Originally, TWTAs provided highpower but with poor efficiency andreliability. Compared to a KPA, thesedisadvantages were regarded as necessarypenalties for wide bandwidth. SSPAs firstbecame available about 20 years ago. They were restricted to low power systemsrequiring only a few watts, such as smallearth stations transmitting a few telephonechannels.

Within the past decade, however,TWTA and SSPA technologies have bothadvanced considerably. Today there isvigorous competition between these twotechnologies for wideband systems.

KPA

The klystron power amplifier (KPA) is anarrowband device capable of providinghigh power and high gain with relativelyhigh efficiency and stability. Thebandwidth is about 45 MHz at C-band andabout 80 MHz at Ku-band. Thus a

separate KPA is usually required for eachsatellite transponder.

In a klystron tube an electron beam isformed by accelerating electrons emittedfrom a heated cathode through a positivepotential difference. The electrons enter aseries of cavities, typically five in number,which are tuned around the operatingfrequency and are connected by cylindrical"drift tubes".

In the input cavity the electrons arevelocity-modulated by a time-varyingelectromagnetic field produced by theinput radio frequency (RF) signal. Thedistribution in velocities results in a densitymodulation further down the tube as theelectrons are bunched into clusters whenhigher velocity electrons catch up withslower electrons in the drift tubes.

Optimum bunching of electrons occursin the output cavity. Large RF currents aregenerated in the cavity wall by the density-modulated beam, thereby generating anamplified RF output signal. The energy ofthe spent electron beam is dissipated asheat in the collector.

The intermediate cavities are used tooptimize the saturated power, gain, andbandwidth characteristics. Additionalbunching of electrons is provided, yieldinghigher gain.

The gain is typically 15 dB per cavity,so that a five-cavity klystron can provide atotal gain of about 75 dB if synchronouslytuned. However, by "stagger tuning" theindividual cavities to slightly differentfrequencies, the bandwidth can beincreased with a reduction in gain. Atypical gain is on the order of 45 dB.

For a cavity device like a klystron, thebandwidth is a fixed percentage of thefrequency of operation. The bandwidth isproportional to the frequency and inverselyproportional to the Q (quality) factor,which is defined as 2π times the ratio ofthe energy stored and the average energylost in one cycle. Thus at C-band (6 GHz),a typical bandwidth is 45 MHz. But at Ku-band (14 GHz) the bandwidth is about 80MHz. These bandwidths are well suitedfor C-band and Ku-band satellitetransponders. By adding a sixth, filtercavity the KPA bandwidth can be doubled. Thus 80 MHz KPAs are also available atC-band.

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Klystrons can be made with "extendedinteraction" circuits in one or more cavitiesthat increase the bandwidth substantially. This technology can provide a bandwidthof 400 MHz at 30 GHz. Output powers upto 1 kW can also be achieved at differentbandwidths.

Although the bandwidth is relativelysmall, a conventional klystron can bemechanically tuned over a wide frequencyrange. A klystron can be capacitively orinductively tuned. All satcom klystronsare inductively tuned because of betterefficiency and repeatability. Theinductance is varied by moving a wall inthe cavity (sliding short).

The output power of a KPA is about3 kW at C-band and 2 kW at Ku-band. The lowest power KPA offered forcommercial satellite communications isaround 1 kW, although for certainapplications powers under 1 kW areavailable.

TWTA

The traveling wave tube amplifier(TWTA) consists of the traveling wavetube (TWT) itself and the power supply. The TWT can have either a helix orcoupled-cavity design.

The TWT is a broadband device with abandwidth capability of about an octave,which easily covers the 500 MHzbandwidth typical of satellites in the FSS.It also covers the typical 800 MHz DBSbandwidth requirement, as well as evenbroader bandwidths in Ka-band and higherbands.

The TWT, like the klystron, is anexample of a device based on modulatingthe flow of electrons in a linear beam, butdiffers from the klystron by the continuousinteraction of the electrons with the RFfield over the full length of the tube insteadof within the gaps of a few resonantcavities.

The TWT has a heritage of over half acentury. The original concept wasproposed in 1944 by Rudolf Kompfner,who investigated experimental laboratorymicrowave tubes while working for theBritish Admiralty during World War II.

The first practical TWT was developedat the Bell Telephone Laboratories in 1945by John Pierce and L.M. Field. Bell Labs

was interested in the technology for itspossible application to communication. By the early 1960s, the TWT was adaptedfor use in satellite power amplifiers in theTelstar program.

In a TWT, amplification is attained bycausing a high density electron beam tointeract with an electromagnetic wave thattravels along a "slow-wave structure",which usually takes the form of a helicalcoil. A helix is the widest bandwidthstructure available. The electrons areemitted from a heated cathode and areaccelerated by a positive voltage applied toan aperture that forms the anode. Theelectrons are absorbed in a collector at theend of the tube.

The RF signal is applied to the helix. Although the signal travels at nearly thespeed of light, its phase velocity along theaxis of the tube is much slower because ofthe longer path in the helix, as determinedby the pitch and diameter of the coil, and isnearly equal to the velocity of theelectrons. For example, if the electrons areaccelerated by a 3,000 volt potentialdifference on the anode, the speed of theelectrons is about one tenth the speed oflight. Thus the length of the helix wireshould be about ten times the axial lengthof the tube to bring about synchronismbetween the RF traveling wave and theelectron beam.

The electrons interact with the travelingwave and form clusters that replicate theRF waveform. Midway down the tube, anattenuator, called a "sever", absorbs the RFsignal and prevents feedback, which wouldresult in self-oscillation. On the other sideof the attenuator, the electromagnetic fieldof the electron clusters induces a waveformin the helix having the same time-dependence as the original signal but withmuch higher energy, resulting inamplification. The gain is typically on theorder of 40 to 60 dB.

The beam-forming optics are criticalparts of the tube. To minimize heatdissipation caused by electrons striking thehelix, the beam must be highly focused andthe transmission from one end of the tubeto the other must be close to 100 percent. When the electrons reach the end of thetube, they impact with the walls of thecollector, where most of the heat is

generated.The efficiency of the tube can be

improved by applying a negative potentialto the collector, which retards the electronbeam as the electrons enter it. A collectordesigned to operate in this way is called a"depressed collector". Less energy isconverted to heat as the electron beamimpinges on the collector, andconsequently less energy is lost as thermalwaste.

However, the distribution of electronenergies is not uniform. In a multi-stagedepressed collector, high energy electronsare directed to stages with high retardingfields and low energy electrons aredirected to stages with low retarding fields. This configuration improves the efficiencyfurther, but with greater complexity.

Another means of achieving greaterefficiency is through improving beamsynchronization. As the electrons travelalong the tube and interact with the RFsignal, they give up energy and losevelocity. Thus with an ordinary helix, theytend to fall behind the signal. Thisproblem can be mitigated by brute force byincreasing the accelerating potential but atthe expense of degrading the TWTlinearity.

A more elegant method is through theuse of a tapered helix, in which the pitch ofthe helix decreases along the tube. Thesignal velocity is thus retarded tocompensate for beam slowing. Theselection of optimum helix configurationshas been made possible through advancedcomputer modeling techniques.

Another type of TWT is a coupled-cavity device, used for high powerapplications. In this case a series of cavitysections are connected to form the slow-wave structure and is similar to theklystron in this respect. However, in theklystron the cavities are independent, whilein the TWT the cavities are coupled by aslot in the wall of each cavity.

The output power of a helix TWTA atC-band ranges from a few watts to about3 kW, while power levels of 10 kW can beattained with coupled-cavity TWTAs. Helix TWTAs at Ku-band have lesspower, with a maximum power of around700 W.

Higher frequency TWTAs are also

3

available, including those at Ka-band(20 - 30 GHz) and V-band (40 - 50 GHz)where new broadband satellite services areunder development. However, because themarket is not well established, there arefewer manufacturers of tubes at thesefrequencies.

The dimensions of the slow-wavestructure -- whether a helix, a coupledcavity, or any other type -- are determinedby the frequency of operation. Theproduct of wavelength and frequency isequal to the speed of light, so that as thefrequency increases the wavelengthdecreases. The dimensions areproportional to the wavelength. Thus thestructure dimensions are approximatelyinversely proportional to frequency. It ismuch more difficult to satisfy the criteriafor operation at high frequencies such asKa-band or V-band than at C-band or Ku-band.

The gain of a TWTA can be from45 dB to 75 dB, depending on the numberof active wavelengths in the helix circuit.

SSPA

A solid state power amplifier (SSPA) usesa gallium arsenide (GaAs) metallicsemiconductor field effect transistor (FET)as the amplifier gain element. The fieldeffect transistor is a voltage-controlled,unipolar device that conducts onlymajority carriers and has good thermalstability. In contrast, an ordinary junctiontransistor is a current-controlled bipolardevice, in which both minority andmajority carriers participate in conductingan electrical current, and can be thermallyunstable. Gallium arsenide FETs canoperate at higher frequencies than silicondevices, but the power output is limited bythe poor thermal conductivity and lowerbreakdown voltage.

The maximum continuous output powerof a single microwave FET can be from afew watts to several tens of watts. Thelimiting factor is the generation of heat. Atthe thermal limit the maximum power istheoretically inversely proportional to thesquare of the frequency. Thus in thepresent state of the art, a typical GaAs FETat C-band might have a maximum outputpower of between 30 W and 45 W, whileat Ku-band it is 15 W.

Transistors are combined to formmodules. For example, a C-band modulecontaining twelve FETs might beconfigured with four FETs in parallel in apower-combining output stage, precededby an intermediate stage with two FETs inparallel and six driver stages in series withone FET per stage. Each FET has a gainof about 8 dB, so that in this case there areeight stages of amplification with a totalgain, including losses, of about 60 dB or afactor of 1,000,000. If each of the fourFETs in the final stage had an outputpower of 30 W, the total output powerwould be 120 W. With a gain of 60 dB,the input power to the first stage would be0.12 mW.

Higher powers are obtained byassembling modules using standard powercombining techniques. The modules areconnected in parallel by waveguideelements, such as hybrids or magic tees, toobtain the required total output power. However, the number of parallel modulesis limited by combination losses.

SSPAs are readily available with ratedpowers up to about 500 W at C-band or100 W at Ku-band.

A new solid state technology is themicrowave monolithic integrated circuit(MMIC). This device combines activeFETs with passive circuit elements that aredeposited on a chip in a single process. The maximum power of a single MMIC isabout 20 W at C-band and about 5 W atKu-band. The total power can beincreased by the combination of severalMMICs in a series-parallel assembly, butis limited by combination losses whichincrease as the frequency increases.

Low power MMICs are sometimes usedas gain stages to drive high power devices. MMICs can provide higher gain with lessspace and complexity than discrete lowpower FETs.

LINEARITY

An important characteristic of any HPA isits linearity. This property is a measure ofhow well the transfer characteristic ofoutput power vs. input power follows astraight line.

In practice, HPAs are inherentlynonlinear devices. Nonlinearity means thatthe output power is not simply proportional

to the input power. Instead, as shown inthe figure, the graph representing theoutput power as a function of input poweris more nearly represented by a third orderpolynomial than by a straight line. Thusthere is a region of approximate linearitybeyond which the graph curves downwardand reaches a plateau. The output power at this plateau is calledthe "saturated power" (PS). The saturatedpower is the maximum power that can begenerated. The point of inflection on thecurve that is 1 dB below the linearextrapolation is called the "1 dBcompression point" (P1).

The transfer characteristic for an SSPAapproaches saturation within about 1 dB ofthe 1 dB compression point, whereas for aTWTA or KPA it bends more gradually,reaching saturation about 3 dB above thispoint. Therefore, an SSPA has superiorlinearity to that of a TWTA or KPA overthe full range of operation to saturation. However, below the 1 dB compressionpoint, the linearities are similar.

The physical effect of nonlinearity is thegeneration of harmonics of thefundamental carrier frequency. Highfrequency harmonics can be eliminated byfiltering. For example, at C-band thesecond harmonic is at 12 GHz and thethird harmonic is at 18 GHz, which arewell out of band.

For single channel per carrier (SCPC)frequency division multiple access(FDMA) systems, nonlinearity causesintermodulation interference amongneighboring channels. The principalsource of interference is the third orderintermodulation (IM3) product, whichcomes from the cubic term in thepolynomial representation of the transfercharacterstic. This contribution to thenonlinearity generates frequencies formedby mixing the second harmonic of onecarrier with the fundamental of another. Thus given two carriers with frequencies f1and f2, the intermodulation products willhave frequencies 2 f2 - f1 and 2 f1 - f2,which are the same as the frequencies ofadjacent channels if they are equallyspaced, and cause unacceptable levels ofinterference. The figure of merit is theso-called two-tone "third order interceptpoint" (IP3), where the graph of the

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intermodulation power intercepts the graphof linear gain. In this case, the HPA must have a "backoff" (BO) to operate at a power (P) in aregion that is sufficiently linear where theintermodulation products are withinacceptable limits as specified by themaximum carrier to interference powerratio (D3). This ratio may be estimatedfrom the third order intercept and thesingle carrier ouput power by the relationD3 = 2 (IP3 - P).

Intermodulation interference does notexist if only one carrier occupies the entirebandwidth of the HPA, such as a single 36MHz analog FM video channel in a KPAor multiple wideband digital time divisionmultiple access (TDMA) channels in aTWTA or SSPA. At any given instant thecarrier occupies the full bandwidth of theHPA and there are no neighboringchannels with which to interfere. In thiscase, an HPA can be run at full saturatedpower.

RATED POWER

The comparison between TWTA andSSPA output power ratings has beenobscured by differences in traditionalmeasures of output power. For a TWTA,the rated power is the saturated power,because TWTAs operate at this power forsingle carrier applications. On the otherhand, for an SSPA the rated power is the 1dB compression point. The "advertised"power of an SSPA is sometimes thesaturated power, which is about 1 dBhigher. No standards for equal comparisonexist in the industry.

Another issue is the distinction betweenthe output power of the TWT and thepower at the TWTA output flange, whichis about 0.5 to 0.7 dB lower. Allowancemust also be made for tube aging. Thepower delivered to the output flange mustbe used in system planning. For example,a TWTA with a rated power of 400 W atsaturation would actually deliver about350 W to the antenna waveguide.

For multiple carrier operation, backoffis always referenced with respect to therated power. A typical output backoff fora TWTA would be about 6 or 7 dB (withrespect to saturation). Since every 3 dBcorresponds to a factor of 2, a 6 dB

backoff would deliver only one-fourth ofthe rated power. At the sameintermodulation specification, an SSPAwould require about 2 or 3 dB of backoff(with respect to 1 dB compression),delivering about half the rated power. Thus, as noted by TWTA industryrepresentative Stephan Van Fleteren inSatellite Online Magazine, 6 dB of backoffin a TWTA would be roughly equivalentto 3 dB of backoff in an SSPA for thesame 1 dB compression point.

For example, in SCPC FDMAapplications a C-band TWTA rated at 400W at saturation would have a practicaloutput power of less than 100 W. On theother hand, an SSPA rated at 175 W at 1dB compression (or 200 W at saturation)would have a similar practical outputpower. Therefore, in this situation, anSSPA rated at 175 W would beoperationally equivalent to a TWTA ratedat 400 W. They would each provide about- 25 dBc separation for two-tone, thirdorder intermodulation performance, whichis a standard figure of merit for earthstation operation (where dBc refers to thelevel in decibels of the spuriousintermodulation product relative to thecarrier).

The same TWTA would have twice theuseful power if combined with a linearizer. A linearizer is a network of solid statecomponents that increases gain and phaselead as the input power increases, thuscompensating for the gain reduction andphase lag as the TWT approachessaturation. The linearizer reduces theintermodulation level. The output backoffcan be reduced by about 3 dB, therebydoubling the output power. Therefore,with a linearizer the traffic capacity couldbe doubled; alternatively, for a givencapacity the required TWTA saturatedpower could be halved.

If only a single carrier is present, suchas in digital TDMA systems, then nobackoff is required at all. In this case, the400 W TWTA without a linearizer wouldhave four times the useful power comparedto multicarrier FDMA operation.

In the presence of rain fade, the KPAand TWTA have about 3 dB more marginthan an SSPA for extra power whennominally operating in the linear region.

There is a tradeoff between increasedintermodulation interference and rainattenuation and noise that can be exploitedwith automatic power control.

EFFICIENCY

The efficiency may be defined as the ratioof the useful output power and the requiredprime power consumption. Values maydiffer with different definitions of outputpower. It is thus best to completely specifythe conditions under which the efficiencyis calculated. The efficiency depends onthe output power and the frequency ofoperation. A few examples may beillustrative.

In single carrier operation, a typical C-band TWTA rated at 75 W at saturationdelivers 70 W to the output flange and hasa required prime power consumption ofabout 350 W. The efficiency is thus70/350 = 20 percent. A C-band TWTArated at 400 W delivers 350 W to theflange and requires about 1300 W for anefficiency of 27 percent, and a Ku-band500 W TWTA delivers 450 W andrequires 1900 W for an efficiency of24 percent. TWTA efficiency has steadilyincreased, in part due to the developmentof depressed collector technology andimprovements in beam focusing andsynchronization.

A representative C-band 100 W SSPAat saturation requires a power of 700 Wwith an efficiency of about 14 percent. AtKu-band, a typical 100 W SSPA has apower requirement of 1000 W for anefficiency of about 10 percent.

At Ka-band current off-the-shelf TWTAperformance is 125 W with a typicalefficiency of 20 percent. Current SSPAperformance is less than 2 W at about 2percent efficiency.

As another example, in multiple carrieroperation a Ku-band TWTA rated at 125W at saturation would deliver about 100 Wat the output flange. With 6 dB of backoff,the useful power would be 25 W. Themaximum prime power consumptionwould be about 650 W, but in this modethe input power would be about 500 W. The efficiency is thus 5 percent.

This unit would be operationallyequivalent to an SSPA rated at 50 W at 1dB compression, yielding 25 W of useful

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power with 3 dB of backoff. The primepower consumption would beapproximately 550 W, so the efficiency isabout 5 percent.

For the SSPA the power consumptionstays the same, regardless of backoff andresulting output power. Until about 10years ago, this was also true for TWTAs. With multistage depressed collectortechnology, however, the required inputpower drops monotonically with outputpower, albeit not proportionately. Thus inthis example, the efficiency of the TWTAis comparable to that of the SSPA. The efficiency of a KPA is about 40percent, which is relatively high comparedto TWTAs and SSPAs.

RELIABILITY

Reliability is an important consideration inthe design of a satellite communicationsystem.

The overall reliability of a TWTA isaffected by the failure rates of both theTWT and the power supply. Thelife-limiting factor of a TWT is cathodedepletion. When SSPAs were introduced20 years ago, TWTs used "B" typecathodes with a relatively short design lifeof less than 25,000 hours. These aredispenser cathodes made from poroustungsten and filled with metalliccompounds of barium, calcium, andaluminum. The operating temperature isabout 1000 °C.

Today TWTs employ "M" typecathodes with a design life of over 100,000hours. These cathodes have a surface layerof osmium, which due to the lower workfunction enhances electron emission andallows a lower temperature to extend life. The TWT mean time before failure(MTBF) has also improved significantly,from approximately 8,000 hours toapproximately 40,000 hours.

The overall TWTA reliability mustinclude the MTBF of the high voltagepower supply. The power supplies aresusceptible to arcing if they becomecontaminated. Advances in power supplyreliability have in part been the result of alarge market for high voltage power supplycircuit components with attendant highproduction and improved quality control. Components used in TWTAs are also used

extensively in the consumer productindustries to manufacture power suppliesfor microwave ovens, copiers, andelectronic equipment.

SSPAs are not subject to any known lifelimiting factors. They do not degrade withtime, they use low voltage power suppliesthat are reliable and safe to operate, andthey are not affected by vibration. However, SSPAs are sensitive to voltagespikes and fluctuations in temperature.

In redudant 1:1 configurations, thestandby SSPA can be inhibited to savepower with no penalty in switchover timeif the primary SSPA fails. On the otherhand, TWTAs have a long warmup time,which requires that the spare be kept in aready-to-transmit state, consuming fullpower.

SSPA manufacturers state that SSPAshave a MTBF ten times better than aTWTA's. Additionally, high power SSPAswith multiple FETs in the output stage willcontinue to operate in the event of a FETfailure, although at reduced power.

So far, no authoritative study has beenperformed on the failure histories of earthstation high power amplifiers. Theprincipal data come from studiesperformed on space-borne satellite poweramplifiers. A study of 2400 amplifiersonboard over 70 commercial satellites wasreported by R. Strauss in the InternationalJournal of Satellite Communications in1993. Surprisingly, it was concluded thatC-band TWTAs had about 33 percentbetter reliability than C-band SSPAs, whilethe reliability of Ku-band TWTAs wasabout the same as that of C-band SSPAs.

The KPA is the most reliable amplifierof all. It has a proven field MTBF ofapproximately 100,000 hours, or eightyears average life.

SUMMARY

There is increasing competition betweenTWTA and SSPA technologies in C-bandand Ku-band. SSPAs compete effectivelywith TWTAs in efficiency and cost forrated powers up to around 250 W inC-band and 50 W in Ku-band. In thesebands TWTAs have several competitiveadvantages over solid state at higher powerlevels.

The performance of SSPAs is optimized

at lower power levels, where theircharacteristics include better linearity,lower cost of ownership, and improvedsafety because of lower voltages. Ease ofmaintenance is also a consideration, butreplacement of the RF module cannot bedone easily in the field. As the power increases, the size andweight of the equipment must increasebecause of the need for heat sinks. Cooling is accomplished by eitherconduction or forced air systems. At high frequencies, TWTAs dominatefor high power wideband applications,especially in Ku-band and beyond. At Ka-band and V-band their advantages maybecome overwhelming. Present widebandamplifiers at Ka-band are all TWTAs. Atthis time SSPAs are not economicallyfeasible in the DBS band or in Ka-band.

It is often stated that a lower powerSSPA can replace a higher power TWTAin multiple carrier FDMA operation due toits superior linearity. However, thecomparison may be misleading because ofdifferences in definitions of rated power. In addition, if a linearizer is added, aTWTA will approach the performance ofsolid state but at higher cost.

When comparing backoffs, poweroutputs, and efficiencies, the differentmeasures of rated power and any losses inthe HPA must be taken into account. Theissue of backoff becomes moot for singlecarrier operation, such as digital TDMAsystems, where backoff is not required andthe maximum saturated power can be fullyutilized.

KPAs have high efficiency and aregenerally economical to operate. Traditionally, the klystron power amplifierhas been a workhorse in the satellitecommunication industry. For narrowbandsystems with fixed frequency assignments,especially for television broadcasting, theyremain an attractive alternative. Thedemand continues to grow andcontemplated advances in design willfurther strengthen their role.________________________________Dr. Robert A. Nelson, P.E., is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, MD, and isTechnical Editor of Via Satellite.

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Satellite 2000 Daily

Advances inSpacecraftTechnology

by Robert A. Nelson

Several technical advances over the pastdecade have resulted in dramaticallyenhanced spacecraft for the twenty-firstcentury. As a result, power has increasedto around 15 kW, the beginning of lifemass is in excess of 3000 kg, andpayloads have become more complex.These developments have been madepossible by improvements in electricpower subsystems, propulsion, antennas,on-board processing, and launch vehicles. Electric power is provided by the solararray during daylight and by batteriesduring eclipse. The standard solar cellused since the inception of the satelliteage has been the silicon cell. This cellhas an efficiency of about 15 percent.However, the newest generation satellitesuse a cell made from gallium arsenide.The efficiency of this cell is 18 percent,but with a dual junction configuration,the efficiency can be increased to 25percent. Still higher efficiencies areforeseen with triple junction cells. Inaddition, many spacecraft useconcentrators on the solar wings tointensify the incident sunlight. The samepower must be provided by the batteryduring an eclipse. Today, the nickel-hydrogen cell is the chemistry of choice,with a specific energy of30 W h/kg. However, the lithium ioncell, having an energy density of 110 Wh/kg, offers the promise of reducing thebattery mass to approximately one-fourthof what is now required for a givenpower. At this time, the cycle life limitsits use for space applications. There have been severalbreakthroughs in propulsion. One hasbeen the arcjet technology used in theLockheed Martin A2100 and Intelsat 8spacecraft. The specific impulse is 500seconds, compared to 300 seconds froman integrated propulsion bipropellantsystem or 220 seconds for the simple

catalytic hydrazine thrusters used in thepast. However, the most dramaticimprovement is in the field of electric ionpropulsion. The thrusters have a specificimpulse of between 2000 and 4000seconds and expel ions of xenon. Theyhave a thrust on the order ofmicronewtons and are operated forperiods of about an hour. The xenon ionpropulsion system (XIPS) on the HS-702satellite consumes some 4.5 kW of powerfrom the 15 kW solar array, but requiresonly 5 kg of xenon per year, and permitsa reduction of propellant mass by up to90 percent for a 12 to 15 year mission lifecompared to chemical propulsion. A significant advance in the design ofantennas has been the ability to makeshaped reflectors. A shaped reflector is alightweight structure that resembles anoversized “potato chip.” It uses a singlefeed instead of multiple beams to providethe specified earth coverage. Thus themass of the antenna subsystem is reducedand the power loss due to the beamforming network is eliminated. Thisdevelopment has been made possible bythe fabrication of epoxy graphitematerials with extremely low coefficientsof thermal expansion that minimize shapedistortion and by the creation ofsophisticated computer softwareprograms that can analyze the requiredantenna shape. Another technicaladvance has been the ability to producelarge unfurlable antennas to producesmall spot beams, such as those used bythe Lockheed Martin Aces satellite formobile telephony in the Pacific Rim. As satellites have become larger, theyhave also become smarter. With on-board computers, the satellites have alarge degree of autonomy. Thus insteadof stationkeeping and attitude controlmaneuvers being performed manually,modern spacecraft are capable ofmaintaining their orbital position andorientation with a minimum amount ofintervention from the ground. It would not be possible to build suchlarge satellites without the ability to putthem in space. The Ariane V has ageostationary transfer orbit capability of5900 kg and is expected to eventuallyreach 11 000 kg. The Atlas IIIB can puta 4500 kg payload into GTO, while aZenit Sea Launch rocket has a payloadcapability of 5000 kg. In the engineering design ofcommunications satellites, there has been

a classic tradeoff between bandwidth andpower. In the past, bandwidth wasavailable but the limitations of satellitesand launch vehicles constrained theavailable power. Now the equation hasbeen reversed. There is a tremendousdemand for bandwidth, but power is nolonger a major problem. As a result, theadvances we shall see over the nextdecade will be in the exploitation of newfrequency regimes, such as Ka-band (20to 30 GHz), Q-band (30 to 40 GHz), andV-band (40 to 50 GHz). The effects ofrain at these frequencies will be achallenging obstacle, however. Inaddition, we can expect to see advancesin more spectrum efficient methods ofmodulation. In the past QPSK has beenthe industry standard, but other forms ofmodulation such as 8-PSK and 16-QAMwill begin to be used more often.Although these methods require morepower, they reduce the bandwidth byfactors of 2/3 and 1/2 , respectively,compared to QPSK, thereby requiringless spectrum or permitting higher datarates

Via Satellite, February, 1999

Spacecraft BatteryTechnology

by Robert A. Nelson

The electrical power subsystem of aspacecraft consists of three basiccomponents: the solar array, the battery,and the power control electronics. Thesolar array converts light energy from thesun into electrical energy and is theprimary source of power. The solar arraymust also recharge the battery in sunlight. The battery provides electrical powerduring periods when the sun is eclipsed bythe earth and is the secondary source ofpower. The power control electronicsmaintain the bus voltage at the desiredlevel.

This article will review the present stateof battery technology. The types ofbatteries available, their physicalcharacteristics, and their advantages anddisadvantages will be discussed. Inparticular, reasons for the trend to usenickel-hydrogen batteries in high power,long lifetime satellite missions will beexplained.

ELECTRICAL POWERSUBSYSTEM

In the mid-1980s a typical spacecraft ingeostationary orbit had a power of about1 kW, such as the Hughes HS-376 spin-stabilized spacecraft or the RCA/GE Series3000 three-axis stabilized spacecraft. By1990, a power of several kilowatts wascommon. Beyond 1 kW, three-axisconfigurations are preferable because theyare more mass efficient than spinners.

Today, a typical high performancethree-axis stabilized spacecraft has a powerbetween 10 and 15 kW and a nominallifetime of 15 to 17 years. The SpaceSystems/Loral Tempo direct broadcastsatellite was the first commercialspacecraft in orbit to offer more than 10kW of power. The Lockheed MartinA2100 Astrolink spacecraft will have 13kW for broadband services. TheAerospatiale Spacebus 4000 and the

Hughes 702 spacecraft will provide 15kW. Industry analysts predict a powerlevel of 20 kW in the near future. Within adecade, 30 kW satellites may becomeoperational.

The battery must provide this powerduring each eclipse over the entire satellitelifetime. The battery mass --indeed theentire spacecraft mass -- scales with thetotal power. Thus the battery must havehigh reliability with maximum possibleenergy density.

In geostationary orbit, it has been thepractice to design the spacecraft electricalpower subsystem as two half-systems, eachusing one wing of the solar array and onebattery. Recently, however, electricaldesigns using only one battery have beenused, due to the proven reliability ofnickel-hydrogen batteries and the masssavings that can be realized. For smallLow Earth Orbit satellites, a single batteryis also advantageous.

The selection of bus voltage is oftenbased on the desire to use provenequipment that has flown on previoussatellite programs. In the 1960s, busvoltages of 20 to 30 V were common. Bythe 1970s and early 1980s, bus voltageshad reached 40 to 50 V.

Higher voltages are desirable in order toreduce the required current for a givenpower, and thus reduce resistive losses andthe mass of electric power distributioncomponents. The upper limit of the busvoltage is determined by the power-switching semiconductors. Largespacecraft now in production, such as theHughes 702 spacecraft, use a bus voltageof around 100 V to handle the increasedpower.

Achieving high power is not the majorproblem. Rather, it is managing the heatthat is produced as waste. This problem isaddressed by designing more efficientcomponents and heat dissipation systems.

ECLIPSES

In geostationary orbit, at an altitude of35,786 km, the angular radius of the earthis 8.7°. Therefore, the sun is eclipsed bythe earth during a portion of the orbitwhenever the sun is within 8.7° of theequatorial plane.

There are two eclipse seasons centeredabout the equinoxes (March 21 and

September 21). Each eclipse season lasts45 days, which is the time the sun takes tomove from 8.7° below the equatorial planeto 8.7° above the equatorial plane relativeto the earth. Thus in geostationary orbit,there are 90 eclipses per year, requiring 90charge/discharge cycles of the battery.

The maximum length of an eclipse is 72minutes (1.2 hours), which occurs at theequinoxes when the sun crosses theequator. The battery must provide powerduring this time. There are nearly 23 hoursavailable in each revolution to recharge thebattery, and typically the battery isrecharged in about half that time. Betweeneclipse seasons, the battery is trickle-charged.

In Low Earth Orbit, at a typical altitudeof 1000 km, the orbital period isapproximately 100 minutes. Themaximum eclipse duration isapproximately 35 minutes, which is aboutone-third of the orbital period, and occurswhen the orbital plane is parallel to theearth-sun direction. Only 65 minutes areavailable to recharge the battery before thenext eclipse occurs. For this orbit, thereare as many as 14 eclipses per day. Depending on the orbital altitude andinclination, there can be 5000 or moreeclipses per year.

BATTERY CHARACTERISTICS

Batteries are either of the primary orsecondary type and are classifiedaccording to their electrochemistry.

A primary battery is designed for use inlieu of a photovoltaic system. It isdischarged to completion and cannot berecharged. It is used for short life missionsor for applications that require very littlepower. A secondary battery isrechargeable and provides power duringeclipse periods when the primary source ofpower, the solar array, is unavailable.

The leading primary battery forspacecraft is the silver-zinc battery. Thereare also a variety of lithium-based primarybatteries, including lithium sulphurdioxide, lithium carbon monofluride, andlithium thionyl chloride. Although lithiumhas a higher energy density, silver zinc iseasier to handle and can be discharged at amuch higher rate.

The principal types of secondary(rechargeable) batteries that are designed

for spacecraft use include the nickel-cadmium (NiCd) battery, the nickel-hydrogen (NiH2) battery, and the super(advanced) nickel-cadmium battery. Silver-zinc (AgZn), lithium ion (Li), andnickel-metal-hydride (NMH) batteries areused for limited applications. The sodium-sulphur (NaS) battery is a technology stillin the process of development. Each typeof battery has certain applicationsdepending on its performance parameters,such as its energy density, cycle life, andreliability.

The fundamental electrochemical unit isthe voltaic cell. A battery consists ofseveral cells connected in series. The busdischarge voltage is equal to the cellvoltage multiplied by the number of cells,diminished by the losses.

In each cell, the negative electrode isthe source of electrons to the externalcircuit (oxidation) and thus represents theanode. The positive electrode accepts theelectrons from the external circuit(reduction) and thus represents thecathode. The electrolyte is a conductingmedium that transfers ions produced at theanode and cathode inside the cell. Theseparator is a porous material that holdsthe electrolyte in place and isolates theanode and cathode materials so thatelectron transfer must occur through theexternal circuit.

A battery is rated in terms of itscapacity. The capacity is the total storedcharge. Since charge is the product of theelectric current and the time, capacity ismeasured in ampere hours. The totalbattery energy, measured in watt hours, isthe product of the capacity and the busvoltage. The energy density (specificenergy), in watt hours per kilogram, is animportant figure of merit for spacecraftapplications.

The index of utilization of the battery isthe depth of discharge (DoD), defined asthe amount of charge drained from thebattery expressed as a percentage of itsrated capacity.

The charging current, or C-rate, isexpressed in the form C/h, where h is thetime in hours to completely charge thebattery from its ground state.

The life-limiting property of aspacecraft battery is the number ofcharge/discharge cycles at a given depth ofdischarge. The cycle life increases as the

depth of discharge decreases. Consequently, a nickel-hydrogen batteryrated for 12 years in GEO with 1080cycles at a depth of discharge of 80 percentmight have a life of only 5 years in LEOwith 25,000 cycles at a 50 percent DoD.

For example, an INTELSAT VIIsatellite, built by Space Systems/Loral, hastwo nickel-hydrogen batteries, consistingof 27 cells each. The cells are grouped intwo 15 cell modules and two 12 cellmodules. The total power requirementduring eclipse is approximately 3,100 W atan average discharge voltage of 33.3 V. Each battery has a capacity of 85.5 A h,which provides a total energy of 2847 W h. At 70 percent DoD, the available energyper battery is 1993 W h.

During sunlight operation, the availablepower from the two solar array wings is3927 W at autumnal equinox, end of life,and the bus voltage is regulated at 42.0 V. The battery high charge rate is C/13(6.7 A), and the time to recharge bothbatteries is about 14 hours.

The total spacecraft dry mass is 1450kg. The mass budget includes 125 kg forthe solar array, 187 kg for the electricalpower subsystem, and 62 kg for electricalintegration. The batteries alone contributeabout 10 percent to the overall spacecraftmass.

NICKEL-CADMIUM

The conventional nickel-cadmium batterywas widely used during the first 30 years inthe aerospace industry. It consists of fourprincipal components: the nickel positiveelectrode, the cadmium negative electrode,the aqueous 35 percent potassiumhydroxide (KOH) electrolyte, and a nyloncloth separator. Capacities are available inthe range of 10 to 40 A h. Nickel-cadmium batteries have high cyclelife but have a low energy density ofapproximately 25 W h/kg.

The cell voltage is approximatelyconstant until it is nearly fully discharged. The temperature is a critical parameter thataffects the battery life and must bemaintained within a narrow range. Inpractice, a radiator is used to keep thebattery temperature below 24°C, whileheaters are used to keep the temperatureabove 4°C.

Repeated cycling to a deep depth ofdischarge will cause cracking in the cell

plate structures. Over a lifetime of 10years in geostationary orbit, there will be900 charge/discharge cycles. Therefore,the depth of discharge is limited tobetween 50 and 60 percent.

The primary modes of degradation arecadmium migration, hydrolysis andoxidation of the nylon separator material,and electrolyte redistribution. The firsttwo modes are time and temperaturedependent, while the third mode isprimarily DoD dependent.

In the past, the nylon separator hasoccasionally posed some difficulties forquality control. In the late 1960scontamination of the Pellon 2505ml nylonmaterial was a problem. A secondproblem developed in the late 1970s whenenvironmental pollution restrictions causedPellon to stop producing its 2505ml nyloncloth separator material. Thus substitutematerials, such as Pellon 2536, were usedthat had different physical properties andessentially the nickel-cadmium battery cellhad to be redesigned. Stricterenvironmental laws also increased the costof working with cadmium, a toxic material,for the negative plate.

NICKEL-HYDROGEN

The nickel-hydrogen battery is now theindustry standard. Nickel plates form thepositive electrode. Since hydrogen is agas, the negative electrode contains aplatinum catalyst. An aqueous KOHsolution is used as the electrolyte. Originally, the separator material was anonwoven mat of asbestos fibers. Zircar(zirconium oxide) is now commonly usedas a separator instead of asbestos.

The nickel-hydrogen battery combinesthe most stable electrodes of the nickel-cadmium and the oxygen-hydrogen cells. Nickel-hydrogen batteries have fewerinherent failure mechanisms than nickel-cadmium when operated at the same depthof discharge, resulting in higher reliabilityand longer lifetime in orbit.

The key improvement was the removalof cadmium as the negative electrode. This improvement eliminates cadmiummigration as one of the two life-limitingdegradation modes within the cell and alsocircumvents the environmental problemsassociated with the use of cadmium. Theother life-limiting factor, the separator, hasalso been improved by its replacement first

by asbestos and later by Zircar. Also, thestability of the electrode and the separatorstrongly reduces electrolyte redistribution. Thus the nickel-hydrogen battery has aconsiderably longer lifetime than that ofnickel-cadmium.

The optimum temperature range formaximum nickel-hydrogen batterycapacity is between 10°C and 15°C. Oneither side of the optimum temperaturerange, the capacity decreases at the rate of1 A h per °C of variation.

Three alternative configurations arefound in combining cells to form anickel-hydrogen spacecraft battery: theIndividual Pressure Vessel (IPV), whichcontains one cell per vessel; the CommonPressure Vessel (CPV), which containstwo cells per vessel; and the SinglePressure Vessel (SPV), which containstwenty-two cells per vessel.

The Individual Pressure Vessel (IPV) isa widely-used configuration in which eachelementary cell is packaged in its ownpressure vessel. Each cell generates 1.25volts. The cells are connected in series toprovide the required bus discharge voltage. The mechanical structure required by thehigh pressure design contributes about 40percent of the total battery mass.

Nickel-hydrogen cells are manufacturedin a wide variety of sizes and capacities. Representative capacities are 5 to 30 A hfor a 64 mm cell, 30 to 100 A h for a 90mm cell, and 100 to 250 A h for a 114 mmcell. The specific energy is approximately30 W h/kg at 80 percent DoD includingpackaging.

The Dependent Pressure Vessel (DPV)is a modular IPV type design. The DPVdiffers from the IPV cell primarily ingeometry. The DPV cells are designed tobe sandwiched between two endplates.

To reduce mass inefficiency, theCommon Pressure Vessel (CPV) designuses two cells in a container. Two cells areconnected in series internally within thecontainer and each CPV cell delivers 2.5volts.

The IPV and CPV cells are typicallypackaged into multiple cell batteries toprovide 28 to 32 V for the spacecraft bus. One additional cell is usually included inan IPV design to allow for a cell failure. The cells are vertically mounted on alightweight honeycomb baseplate, whichprovides mechanical structure and a

thermal path to remove heat to the radiator.In the Single Pressure Vessel (SPV)

design, all of the cells are packaged in asingle container. This design offers theadvantages of reductions in mass, volume,and cost. However, the reliability is lessbecause a failure of one cell will result inthe failure of the entire battery. Bypasscircuits that are generally used in the IPVdesign cannot be used in this case. Thesystem is designed to operate at internalhydrogen pressures up to 1000 psia.

The trend in communications satelliteshas been to use nickel-hydrogen in place ofnickel-cadmium batteries. There are nowwell over 5000 nickel-hydrogen cells inover 200 batteries in orbit. This trend inGEO has carried over to LEO. With fewexceptions, nearly all GEO and LEOspacecraft are now using or will be usingnickel-hydrogen batteries. There is noother chemistry presently available with itsunique combination of advantages ofenergy density, cycle life, and reliability.

SUPER NICKEL-CADMIUM

The super (advanced) nickel-cadmium(S-nickel-cadmium) battery is a proprietaryHughes replacement technology that isnow used for some small spacecraft. Itconsists of nickel plates, cadmium plates, aZircar separator, and potassium hydroxideelectrolyte. The battery is available incapacities ranging from 5 to 50 A h. Thespecific energy is 31 W h/kg.

The super nickel-cadmium technologyhas been developed by Hughes as acompromise between the conventionalnickel-cadmium and the nickel-hydrogencells. The goal was to produce a cell withmany of the advantages of the nickel-hydrogen cell to prolong lifetime, butretain the packaging advantages offered bythe prismatic shape of the conventionalnickel-cadmium. They use the same Zircarseparator as nickel-hydrogen and haveother improvements that are proprietary toHughes. The few that have been producedand flown are expected to have longer lifethan the conventional nickel-cadmiumbatteries. Super nickel-cadmiumcells are low pressure, prismatic cellswhich package as easily as theconventional nickel-cadmium cells. Theiruse has been mainly on small, LEOmissions where they are perceived to havea packaging advantage over nickel-

hydrogen. Their disadvantages are thatthey are both heavier and more expensivethan either the conventional nickel-cadmium or the nickel-hydrogen cells.

SILVER-ZINC

The silver-zinc battery is attractive becauseof its high energy density, which is roughly110 to 130 W h/kg. Overcharge must becontrolled because oxygen that is evolveddoes not recombine easily. The majordisadvantage is low cycle life. It thus haslimited application as a secondary battery,but as noted above, it is used widely as aprimary battery.

LITHIUM ION

Lithium ion is another high energy densitytechnology. The interest in lithium ion isdue to its high specific energy of 85 to130 W h/kg on a cell basis. It has higherenergy density than the nickel-cadmium ornickel-hydrogen technology with fewerhazardous concerns than many otherlithium technologies, such as lithium-thyenol-chloride. It can also accept deepdischarges, which means more of theavailable energy can be used.

This technology provides hope that itmay eventually be developed to accept alarge number of cycles. For these reasons,rechargeable lithium ion development isbeing watched by all of the primespacecraft manufacturers for its possibleuse on selected missions.

Lithium ion does not yet have acompetitive cycle life. Typical 20 A hcells have exhibited a 20 percent loss incapacity after less than 200 cycles. At thisstage of development, the technology canonly be considered for those missions thatrequire very few cycles, such as in sunsynchronous orbits or on deep spacescientific missions. They are not yet usefulfor either LEO or GEO orbits.

NICKEL-METAL-HYDRIDE

Nickel-metal-hydride electrochemistry wasdeveloped to replace the nickel-cadmiumcell with a technology that did not have theproblems caused by the cadmium plate. Itis seldom used, since its cycle life neverapproached that of the nickel-cadmium. After significant development by severalcompanies, it was determined that NMHwould not have the mass, size, and cyclelife that was initially expected.

SODIUM-SULPHUR

The sodium-sulphur battery is still adevelopment technology. It promises tohave potentially 50 percent better specificenergy than nickel-hydrogen, but is notexpected to have as much promise aslithium ion.

Sodium sulphur is a unique technologythat must operate at 350°C. Some of theheat required for this high temperature isgenerated by the battery. But the batterypresents a significant impact on thespacecraft thermal design. To minimizethis impact, it must be thermally connectedto the rest of the spacecraft through a veryhigh, well controlled, thermal resistance.

PROJECTION

There is an enormous market for nickel-hydrogen batteries. These batteries havebeen demonstrated to be more reliable andmass efficient, with longer cycle life, thantheir chief competitor, nickel-cadmium. State of the art technologies includelithium ion and sodium sulphur, but thesebatteries do not have the required cycle lifeand are difficult to operate.

Spacecraft are being designed with everhigher power and longer lifetimes. Spacecraft powers are now typicallyaround 10 kW and will soon reach 15 to 20kW. Power levels at 30 kW are foreseenwithin the next decade.

As these powers increase, so do thesatellite lifetimes in orbit. In the 1980s aten year life was typical. Today, satellitesare designed for 15 or more years ingeostationary orbit. This lifetime can beextended for another two or three yearsusing inclined orbit techniques, which isbecoming standard practice for satellitesnearing end of life.

These trends will dictate the use ofhighly reliable battery technologies,permitting high bus voltages and long life. Nickel-hydrogen will be the likelytechnology of choice to meet these criteria.________________________________

Dr. Robert A. Nelson, P.E., is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, MD, and isTechnical Editor of Via Satellite.

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Via Satellite, June, 1999

Rocket ScienceTechnology Trends inPropulsion

by Robert A. Nelson

A satellite is launched into space on arocket, and once there it is inserted intothe operational orbit and is maintained inthat orbit by means of thrusters onboardthe satellite itself. This article willsummarize the fundamental principles ofrocket propulsion and describe the mainfeatures of the propulsion systems usedon both launch vehicles and satellites.

The law of physics on which rocketpropulsion is based is called the principleof momentum. According to thisprinciple, the time rate of change of thetotal momentum of a system of particlesis equal to the net external force. Themomentum is defined as the product ofmass and velocity. If the net externalforce is zero, then the principle ofmomentum becomes the principle ofconservation of momentum and the totalmomentum of the system is constant. Tobalance the momentum conveyed by theexhaust, the rocket must generate amomentum of equal magnitude but in theopposite direction and thus it acceleratesforward. The system of particles may bedefined as the sum of all the particlesinitially within the rocket at a particularinstant. As propellant is consumed, theexhaust products are expelled at a highvelocity. The center of mass of the totalsystem, subsequently consisting of theparticles remaining in the rocket and theparticles in the exhaust, follows atrajectory determined by the externalforces, such as gravity, that is the same asif the original particles remained togetheras a single entity. In deep space, wheregravity may be neglected, the center ofmass remains at rest.

ROCKET THRUST

The configuration of a chemicalrocket engine consists of the combustion

chamber, where the chemical reactiontakes place, and the nozzle, where thegases expand to create the exhaust. Animportant characteristic of the rocketnozzle is the existence of a throat. Thevelocity of the gases at the throat is equalto the local velocity of sound and beyondthe throat the gas velocity is supersonic.Thus the combustion of the gases withinthe rocket is independent of thesurrounding environment and a change inexternal atmospheric pressure cannotpropagate upstream. The thrust of the rocket is given by thetheoreticalequation

F = λ m! ve + ( pe - pa ) Ae

This equation consists of two terms. Thefirst term, called the momentum thrust,is equal to the product of the propellantmass flow rate m! and the exhaustvelocity ve with a correction factor λ fornonaxial flow due to nozzle divergenceangle. The second term is called thepressure thrust. It is equal to thedifference in pressures pe and pa of theexhaust velocity and the ambientatmosphere, respectively, acting over thearea Ae of the exit plane of the rocketnozzle. The combined effect of bothterms is incorporated into the effectiveexhaust velocity c. Thus the thrust is alsowritten

F = m! c

where an average value of c is used, sinceit is not strictly constant. The exhaust exit pressure isdetermined by the expansion ratio givenby

ε = Ae / At

which is the ratio of the area of the nozzleexit plane Ae and the area of the throat At

. As the expansion ratio ε increases, theexhaust exit pressure pe decreases. The thrust is maximum when the exitpressure of the exhaust is equal to theambient pressure of the surroundingenvironment, that is, when pe = pa. Thiscondition is known as optimumexpansion and is achieved by properselection of the expansion ratio.Although optimum expansion makes thecontribution of the pressure thrust zero, itresults in a higher value of exhaustvelocity ve such that the increase inmomentum thrust exceeds the reductionin pressure thrust.

A conical nozzle is easy tomanufacture and simple to analyze. Ifthe apex angle is 2α, the correction factorfor nonaxial flow is

λ = ½ (1 + cos α)

The apex angle must be small to keep theloss within acceptable limits. A typicaldesign would be α = 15°, for which λ =0.9830. This represents a loss of 1.7percent. However, conical nozzles areexcessively long for large expansionratios and suffer additional losses causedby flow separation. A bell-shaped nozzleis therefore superior because it promotesexpansion while reducing length.

ROCKET PROPULSIONPARAMETERS

The specific impulse Isp of a rocket isthe parameter that determines the overalleffectiveness of the rocket nozzle andpropellant. It is defined as the ratio of thethrust and the propellant weight flowrate, or

Isp = F / m! g = c / g

where g is a conventional value for theacceleration ofgravity (9.80665 m/s2 exactly). Specificimpulse is expressed in seconds. Although gravity has nothingwhatever to do with the rocket propulsionchemistry, it has entered into thedefinition of specific impulse because inpast engineering practice mass wasexpressed in terms of the correspondingweight on the surface of the earth. Byinspection of the equation, it can be seenthat the specific impulse Isp is physicallyequivalent to the effective exhaustvelocity c, but is rescaled numericallyand has a different unit because ofdivision by g. Some manufacturers nowexpress specific impulse in newtonseconds per kilogram, which is the sameas effective exhaust velocity in metersper second. Two other important parameters arethe thrust coefficient CF and thecharacteristic exhaust velocity c*. Thethrust coefficient is defined as

CF = F / At pc = m! c / At pc

where F is the thrust, At is the throatarea, and pc is the chamber pressure.This parameter is the figure of merit ofthe nozzle design. The characteristic

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exhaust velocity is defined as

c* = At pc / m! = c / CF

This parameter is the figure of merit ofthe propellant. Thus the specific impulsemay be written

Isp = CF c* / g

which shows that the specific impulse isthe figure of merit of the nozzle designand propellant as a whole, since itdepends on both CF and c*. However, inpractice the specific impulse is usuallyregarded as a measure of the efficiency ofthe propellant alone.

LAUNCH VEHICLE PROPULSIONSYSTEMS

In the first stage of a launch vehicle,the exit pressure of the exhaust is equal tothe sea level atmospheric pressure101.325 kPa (14.7 psia) for optimumexpansion. As the altitude of the rocketincreases along its trajectory, thesurrounding atmospheric pressuredecreases and the thrust increasesbecause of the increase in pressure thrust.However, at the higher altitude the thrustis less than it would be for optimumexpansion at that altitude. The exhaustpressure is then greater than the externalpressure and the nozzle is said to beunderexpanded. The gas expansioncontinues downstream and manifestsitself by creating diamond-shaped shockwaves that can often be observed in theexhaust plume. The second stage of the launch vehicleis designed for optimum expansion at thealtitude where it becomes operational.Because the atmospheric pressure is lessthan at sea level, the exit pressure of theexhaust must be less and thus theexpansion ratio must be greater.Consequently, the second stage nozzleexit diameter is larger than the first stagenozzle exit diameter. For example, the first stage of a DeltaII 7925 launch vehicle has an expansionratio of 12. The propellant is liquidoxygen and RP-1 (a kerosene-likehydrocarbon) in a mixture ratio (O/F) of2.25 at a chamber pressure of 4800 kPa(700 psia) with a sea level specificimpulse of 255 seconds. The secondstage has a nozzle expansion ratio of 65and burns nitrogen tetroxide andAerozene 50 (a mixture of hydrazine and

unsymmetrical dimethyl hydrazine) in amixture ratio of 1.90 at a chamberpressure of 5700 kPa (830 psia), whichyields a vacuum specific impulse of 320seconds. In space, the surrounding atmosphericpressure is zero. In principle, theexpansion ratio would have to be infiniteto reduce the exit pressure to zero. Thusoptimum expansion is impossible, but itcan be approximated by a very largenozzle diameter, such as can be seen onthe main engines of the space shuttle withε = 77.5. There is ultimately a tradeoffbetween increasing the size of the nozzleexit for improved performance andreducing the mass of the rocket engine. In a chemical rocket, the exhaustvelocity, and hence the specific impulse,increases as the combustion temperatureincreases and the molar mass of theexhaust products decreases. Thus liquidoxygen and liquid hydrogen are nearlyideal chemical rocket propellants becausethey burn energetically at hightemperature (about 3200 K) and producenontoxic exhaust products consisting ofgaseous hydrogen and water vapor with asmall effective molar mass (about 11kg/kmol). The vacuum specific impulseis about 450 seconds. These propellantsare used on the space shuttle, the AtlasCentaur upper stage, the Ariane-4 thirdstage, the Ariane-5 core stage, the H-2first and second stages, and the LongMarch CZ-3 third stage.

SPACECRAFT PROPULSIONSYSTEMS

The spacecraft has its own propulsionsystem that is used for orbit insertion,stationkeeping, momentum wheeldesaturation, and attitude control. Thepropellant required to perform amaneuver with a specified velocityincrement ∆v is given by the “rocketequation”

∆m = m0 [ 1 − exp(− ∆v / Isp g) ]

where m0 is the initial spacecraft mass.This equation implies that a reduction invelocity increment or an increase inspecific impulse translates into areduction in propellant. In the case of a geostationary satellite,the spacecraft must perform a criticalmaneuver at the apogee of the transferorbit at the synchronous altitude of

35,786 km to simultaneously remove theinclination and circularize the orbit. Thetransfer orbit has a perigee altitude ofabout 200 km and an inclination roughlyequal to the latitude of the launch site.To minimize the required velocityincrement, it is thus advantageous to havethe launch site as close to the equator aspossible. For example, in a Delta or Atlaslaunch from Cape Canaveral the transferorbit is inclined at 28.5° and the velocityincrement at apogee is 1831 m/s; for anAriane launch from Kourou theinclination is 7° and the velocityincrement is 1502 m/s; while for a Zenitflight from the Sea Launch platform onthe equator the velocity increment is1478 m/s. By the rocket equation,assuming a specific impulse of 300seconds, the fraction of the separatedmass consumed by the propellant for theapogee maneuver is 46 percent fromCape Canaveral, 40 percent from Kourou,and 39 percent from the equator. As arule of thumb, the mass of ageostationary satellite at beginning of lifeis on the order of one half its mass whenseparated from the launch vehicle. Before performing the apogeemaneuver, the spacecraft must bereoriented in the transfer orbit to face inthe proper direction for the thrust. Thistask is sometimes performed by thelaunch vehicle at spacecraft separation orelse must be carried out in a separatemaneuver by the spacecraft itself. In alaunch from Cape Canaveral, the anglethrough which the satellite must bereoriented is about 132°. Once on station, the spacecraft mustfrequently perform a variety ofstationkeeping maneuvers over itsmission life to compensate for orbitalperturbations. The principal perturbationis the combined gravitational attractionsof the sun and moon, which causes theorbital inclination to increase by nearlyone degree per year. This perturbation iscompensated by a north-southstationkeeping maneuver approximatelyonce every two weeks so as to keep thesatellite within 0.05° of the equatorialplane. The average annual velocityincrement is about 50 m/s, whichrepresents 95 percent of the totalstationkeeping fuel budget. Also, theslightly elliptical shape of the earth'sequator causes a longitudinal drift, which

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is compensated by east-weststationkeeping maneuvers about once aweek, with an annual velocity incrementof less than 2 m/s, to keep the satellitewithin 0.05° of its assigned longitude. In addition, solar radiation pressurecaused by the transfer of momentumcarried by light and infrared radiationfrom the sun in the form ofelectromagnetic waves both flattens theorbit and disturbs the orientation of thesatellite. The orbit is compensated by aneccentricity control maneuver that cansometimes be combined with east-weststationkeeping. The orientation of thesatellite is maintained by momentumwheels supplemented by magnetictorquers and thrusters. However, thewheels must occasionally be restored totheir nominal rates of rotation by meansof a momentum wheel desaturationmaneuver in which a thruster is fired tooffset the change in angular momentum. Geostationary spacecraft typical ofthose built during the 1980s have solidpropellant rocket motors for the apogeemaneuver and liquid hydrazine thrustersfor stationkeeping and attitude control.The apogee kick motor uses a mixture ofHTPB fuel and ammonium perchlorateoxidizer with a specific impulse of about285 seconds. The hydrazinestationkeeping thrusters operate bycatalytic decomposition and have aninitial specific impulse of about 220seconds. They are fed by the pressure ofan inert gas, such as helium, in thepropellant tanks. As propellant isconsumed, the gas expands and thepressure decreases, causing the flow rateand the specific impulse to decrease overthe mission life. The performance of thehydrazine is enhanced in anelectrothermal hydrazine thruster (EHT),which produces a hot gas mixture atabout 1000 °C with a lower molar massand higher enthalpy and results in ahigher specific impulse of between 290and 300 seconds. For example, the Ford Aerospace(now Space Systems/Loral)INTELSAT V satellite has a ThiokolAKM that produces an average thrust of56 kN (12,500 lbf) and burns to depletionin approximately 45 seconds. On-orbitoperations are carried out by an array offour 0.44 N (0.1 lbf) thrusters for rollcontrol, ten 2.0 N (0.45 lbf) thrusters forpitch and yaw control and E/W

stationkeeping, and two 22.2 N (5.0 lbf)thrusters for repositioning andreorientation. Four 0.3 N (0.07 lbf)EHTs are used for N/S stationkeeping.The nominal mass of the spacecraft atbeginning of life (BOL) is 1005 kg andthe dry mass at end of life (EOL) is 830kg. The difference of 175 kg representsthe mass of the propellant for a designlife of 7 years. Satellites launched in the late 1980sand 1990s typically have an integratedpropulsion system that use a bipropellantcombination of monomethyl hydrazine asfuel and nitrogen tetroxide as oxidizer.The specific impulse is about 300seconds and fuel margin not used for theapogee maneuver can be applied tostationkeeping. Also, since the apogeeengine is restartable, it can be used forperigee velocity augmentation andsupersynchronous transfer orbit scenariosthat optimize the combined propulsioncapabilities of the launch vehicle and thespacecraft. For example, the INTELSAT VIIsatellite, built by Space Systems/Loral,has a Marquardt 490 N apogee thrusterand an array of twelve 22 Nstationkeeping thrusters manufactured byAtlantic Research Corporation with a150:1 columbium nozzle expansion ratioand a specific impulse of 235 seconds.For an Ariane launch the separated massin GTO is 3610 kg, the mass at BOL is2100 kg, and the mass at EOL is 1450 kg.The mission life is approximately 17years. The Hughes HS-601 satellite has asimilar thruster configuration. The massis approximately 2970 kg at launch, 1680kg at BOL, and 1300 kg for a nominal 14year mission. An interesting problem is theestimation of fuel remaining on thespacecraft at any given time during themission life. This information is used topredict the satellite end of life. There areno “fuel gauges” so the fuel mass must bedetermined indirectly. There are threeprincipal methods. The first is called the“gas law” method, which is based on theequation of state of an ideal gas. Thepressure and temperature of the inert gasin the propellant tanks is measured bytransducers and the volume of the gas iscomputed knowing precisely the pressureand temperature at launch. The volumeof the remaining propellant can thus be

deduced and the mass determined fromthe known density as a function oftemperature. Corrections must be appliedfor the expansion of the tanks and thepropellant vapor pressure. The secondmethod is called the “bookkeeping”method. In this method the thruster timefor each maneuver is carefully measuredand recorded. The propellant consumedis then calculated from mass flow rateexpressed in terms of the pressure usingan empirical model. The third method ismuch more sophisticated and is based onthe measured dynamics of the spacecraftafter a stationkeeping maneuver todetermine its total mass. In general,these three independent methods provideredundant information that can be appliedto check one another.

NEW TECHNOLOGIES

Several innovative technologies havesubstantially improved the fuel efficiencyof satellite stationkeeping thrusters. Thesavings in fuel can be used to increase theavailable payload mass, prolong themission life, or reduce the mass of thespacecraft. The first of these developments is theelectric rocket arcjet technology. Thearcjet system uses an electric arc tosuperheat hydrazine fuel, which nearlydoubles its efficiency. An arcjet thrusterhas a specific impulse of over 500seconds. Typical thrust levels are from0.20 to 0.25 N. The arcjet concept wasdeveloped by the NASA Lewis ResearchCenter in Cleveland and thrusters havebeen manufactured commercially byPrimex Technologies, a subsidiary of theOlin Corporation. AT&T’s Telstar 401 satellite,launched in December 1993 (andsubsequently lost in 1997 due to anelectrical failure generally attributed to asolar flare) was the first satellite to usearcjets. The stationkeeping propellantrequirement was reduced by about 40percent, which was critical to theselection of the Atlas IIAS launchvehicle. Similar arcjet systems are usedon INTELSAT VIII and the LockheedMartin A2100 series of satellites.INTELSAT VIII, for example, has a dualmode propulsion system incorporating abipropellant liquid apogee engine thatburns hydrazine and oxidizer for orbitinsertion and four arcjets that use

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monopropellant hydrazine in the reactioncontrol subsystem for stationkeeping. Electrothermal hydrazine thrusterscontinue to have applications on variousgeostationary satellites and on somesmall spacecraft where maneuvering timeis critical. For example, EHTs are usedon the IRIDIUM satellites built byLockheed Martin. The most exciting development hasbeen in the field of ion propulsion. Thepropellant is xenon gas. Although thethrust is small and on the order of a fewmillinewtons, the specific impulse isfrom 2000 to 4000 seconds, which isabout ten to twenty times the efficiencyof conventional bipropellantstationkeeping thrusters. Also, the lowerthrust levels have the virtue ofminimizing attitude disturbances duringstationkeeping maneuvers. The xenon ion propulsion system, orXIPS (pronounced “zips”), is a griddedion thruster developed by Hughes. Thissystem is available on the HS-601 HP(high power) and HS-702 satellite modelsand allows for a reduction in propellantmass of up to 90 percent for a 12 to 15year mission life. A typical satellite hasfour XIPS thrusters, including twoprimary thrusters and two redundantthrusters. Xenon atoms, an inert monatomic gaswith the highest molar mass (131kg/kmol), are introduced into a thrusterchamber ringed by magnets. Electronsemitted by a cathode knock off electronsfrom the xenon atoms and form positivexenon ions. The ions are accelerated by apair of gridded electrodes, one with ahigh positive voltage and one with anegative voltage, at the far end of thethrust chamber and create more than3000 tiny beams. The beams areneutralized by a flux of electrons emittedby a device called the neutralizer toprevent the ions from being electricallyattracted back to the thruster and toprevent a space charge from building uparound the satellite. The increase in kinetic energy of theions is equal to the work done by theelectric field, so that

½ m v2 = q V

where q, m, and v are the charge, mass,and velocity of the ions and V is theaccelerating voltage, equal to thealgebraic difference between the positive

voltage on the positive grid and thenegative voltage on the neutralizer. Thecharge to mass ratio of xenon ions is 7.35× 105 C/kg. The HS-601 HP satellite uses 13-centimeter diameter XIPS engines toperform north-south stationkeeping andto assist the spacecraft’s gimballedmomentum wheel for roll and yawcontrol. The accelerating voltage is about750 volts and the ions have a velocity of33,600 m/s. The specific impulse is 3400seconds with a mass flow rate of 0.6 mg/sand18 mN of thrust. Each ion thrusteroperates for approximately 5 hours perday and uses 500 W from the available 8kW total spacecraft power. The HS-702 spacecraft has higherpower25-centimeter thrusters to perform allstationkeeping maneuvers and tocomplement the four momentum wheelsarranged in a tetrahedron configurationfor attitude control. The acceleratingvoltage is 1200 volts, which produces anion beam with a velocity of42,500 m/s. The specific impulse is 4300seconds, the mass flow rate is 4 mg/s, andthe thrust is 165 mN. Each HS-702 ionthruster operates for approximately 30minutes per day and requires 4.5 kWfrom the 10 to 15 kW solar array. Thestationkeeping strategy maintains atolerance of ± 0.005° that allows for thecollocation of several satellites at a singleorbital slot. The HS-702 satellite has a launchmass of up to 5200 kg and an availablepayload mass of up to1200 kg. The spacecraft can carry up to118 transponders, comprising 94 activeamplifiers and 24 spares. A bipropellantpropulsion system is used for orbitacquisition, with a fuel capacity of 1750kg. The XIPS thrusters need only 5 kg ofxenon propellant per year, a fraction ofthe requirement for conventionalbipropellant or arcjet systems. The HS-702 also has the option of using XIPSthrusters for orbit raising in transfer orbitto further reduce the required propellantmass budget. The first commercial satellite to useion propulsion was PAS-5, which wasdelivered to the PanAmSat Corporationin August 1997. PAS-5 was the firstHS-601 HP model, whose xenon ionpropulsion system, together with gallium

arsenside solar cells and advanced batteryperformance, permitted the satellite toaccommodate a payload twice aspowerful as earlier HS-601 models whilemaintaining a 15 year orbital life. Fourmore Hughes satellites with XIPStechnology were in orbit by the end of1998. In addition, Hughes also produceda 30-centimeter xenon ion engine forNASA’s Deep Space 1 spacecraft,launched in October 1998. Another type of ion thruster is the Halleffect ion thruster. The ions areaccelerated along the axis of the thrusterby crossed electric and magnetic fields.A plasma of electrons in the thrustchamber produces the electric field. Aset of coils creates the magnetic field,whose magnitude is the most difficultaspect of the system to adjust. The ionsattain a speed of between 15,000 and20,000 m/s and the specific impulse isabout 1800 seconds. This type of thrusterhas been flown on several Russianspacecraft.

SUMMARY

The demand for ever increasingsatellite payloads has motivated thedevelopment of propulsion systems withgreater efficiency. Typical satellites offifteen to twenty years ago had solidapogee motors and simplemonopropellant hydrazine stationkeepingthrusters. Electrically heated thrusterswere designed to increase the hydrazineperformance and the principle was furtheradvanced by the innovation of the arcjetthruster. Bipropellant systems are nowcommonly used for increasedperformance and versatility. The future will see a steady transitionto ion propulsion. The improvements infuel efficiency permit the savings in massto be used for increasing the revenue-generating payloads (with attendantincrease in solar arrays, batteries, andthermal control systems to power them),extending the lifetimes in orbit, orreducing the spacecraft mass to permit amore economical launch vehicle._________________________________

Dr. Robert A. Nelson, P.E. is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, Maryland.Dr. Nelson is Via Satellite’s TechnicalEditor.

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Via Satellite March, 1995

SatelliteConstellationGeometry

by Robert A. Nelson

Satellite constellation geometry has beenstudied as a theoretical problem since theearly 1960s. The analysis originally hadlimited application to photographicreconnaissance and Earth resourcemissions. However, at present it hasachieved particular relevance for thenumerous satellite systems underdevelopment that offer a variety of newservices, including mobile telephony,message and data transfer, and positiondetermination. The problem combinesthe physics of orbits with optimization ofthe orbit geometry so as to provide therequired Earth coverage whileminimizing the number of satellites. Notable contributions to the theory ofconstellation geometry have been madeby Walker, Draim, Ballard, and Adamsand Rider. Walker made an extensivestudy and found that at least fivesatellites are required for continuousglobal coverage from circular orbits at acommon altitude and inclination. Hismethod of classifying constellation typeswith the notation T/P/F is frequentlyused, where T is the total number ofsatellites, P is the number of evenlyspaced orbital planes and F determinesthe phase spacing between adjacentplanes. Draim found that continuouscoverage could be attained by only foursatellites in elliptical orbits. Ballard alsostudied the optimization of satellites ininclined circular orbits, which he called“rosette constellations,” using a satellitetriad approach. This method minimizesthe largest distance between theobservation point and any subsatellitepoint. Adams and Rider deduced theoptimum configurations for polar orbitconstellations for single or multiplesatellite levels of coverage over the entireEarth or above a specified latitude, usinga street-of-coverage approach. Thismethod considers a ground swath that iscontinuously covered.

ALTITUDE

The altitude of the satellite orbit is theprimary characteristic of the satelliteconstellation. It is chosen on the basis ofboth physical and geometricconsiderations, including signalpropagation delay, signal power,avoidance of the Van Allen radiationbelts, time of satellite visibility andcoverage area. The altitude regimes have beendivided by convention into Low EarthOrbit (LEO), Medium Earth Orbit (MEO)and Geostationary Orbit (GEO). Thealtitude of LEO is roughly between 500krn and 1,500 km. The lower bound ischosen to avoid excessive stationkeepingdue to residual atmospheric drag. Theupper bound is chosen so as to lie belowthe first Van Allen radiation belt. Thealtitude of MEO can be taken to beapproximately within the range 5,000 krnto 15,000 krn so as to be within the firstand second Van Allen belts. The limitsare ten times those of LEO. The altitudeof GEO is uniquely 35,786 km in theequatorial plane. At this altitude theperiod of revolution is exactly equal tothe period of rotation of the Earth(23.934 h), so that a satellite appears toremain over a fixed point on the equator.A fourth orbit category is the highlyelliptical orbit (HEO), in which theapogee may be beyond the geostationaryorbit. The two principal factors that havecreated interest in LEO and MEO forsatellite communications are the lowsignal propagation delay and thelimitations on gain and power of theEarth terminal. The round trip signaldelay for a two-way conversation viasatellite at an altitude of 10,000 km is130 ms, and for a satellite at an altitudeof 1,000 km it is only 13 ms. In contrast,the propagation delay from GEO for atwo-way conversation is over half asecond, which is distracting at best andcan be intolerable for digital datatransmission using error correctingprotocols that require retransmission ofblocks with detected errors. Handheld telephones by their naturemust have low gain (on the order of1 dB) because they must be omni-directional and have fixed power limits(on the order of 350 mW) to safeguardhuman health. The Earth terminal gainand power determine the required size of

the satellite antenna, which must be largeenough to provide sufficient link margin.Also, the bandwidth available is limited,so the total coverage area is usuallydivided into a cellular pattern of spotbeams to permit frequency reuse. The cellsize is determined by the size of theantenna and the orbit altitude. As theorbit gets higher, it is necessary to use alarger antenna on the spacecraft toachieve a given spot size on the Earth.For example, at L-band (1615 MHz), a17 meter spacecraft antenna in GEOwould be required for the same cell sizeas a 0.5 meter antenna in LEO. Thus,LEO and MEO are preferable to GEO formobile hand-held telephony. Other considerations that affect thechoice of altitude are satellite visibilityand eclipse time. At Low Earth Orbit theperiod of revolution is approximately 100minutes. For a typical pass, the satellite isvisible for only about ten minutes. Thus,frequent handover is required for mobiletelephony. In addition, during times ofthe year when the orbital plane is parallelto the direction to the Sun, the satellite iseclipsed for about 30 minutes, or aboutone third of the orbital period.Consequently, there is a significantdemand on battery power, with up to5,000 charge/discharge cycles per year inLow Earth Orbit. With present nickel-hydrogen battery technology, a batteryrated for 10 to 15 years in GEO wouldhave a life of about 5 years in LEO. Onthe other hand, in Medium Earth Orbitthe orbital period is six to eight hours andthe time of visibility of a single satelliteis over an hour. There are fewer eclipsecycles and battery lifetime is typicallyseven years.

INCLINATION

The second fundamental parameter of asatellite constellation is its orbitalinclination. The choice is governed bythe global coverage requirement, thelevel of coverage, and the minimumangle of elevation. Inclinations of directcircular orbits are generally around 50°.This inclination permits coverage oftemperate zones and populated regions ofthe Earth, while allowing more than onesatellite to be visible from a given pointfor reasonable constellation sizes. Polarconstellations have inclinations near 90°,which permits global coverage with thefewest satellites. Retrograde orbits (such

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as Sun-synchronous orbits) have inclin-ations greater than 90°. A great advantage of inclined or polarLEO and MEO constellations is that theyafford high angles of elevation. Elevationangles of from 20° to 40° may berequired to avoid blockage from tallbuildings in urban areas. These anglesare not possible from GEO, even atmoderate latitudes of 45°. Many of thecapitals of Europe, including Paris,London, Berlin, Warsaw and Moscow,are north of this latitude. Furthermore, ageostationary satellite is below thehorizon if the latitude is greater than 81°.

ECCENTRICITY

The third important orbital parameter isthe eccentricity, which determines theorbit’s shape. For circular orbits, theeccentricity is zero and the satellitemoves at uniform speed. For ellipticalorbits, however, the eccentricity isbetween 0 and 1. The satellite movesfastest at perigee, or the point closest tothe Earth, and slowest at apogee, or thepoint farthest from the Earth. Byadjusting the position of the apogee, thedwell time of the satellite can bemaximized over the region of interest. Earth oblateness perturbations restrictthe inclination of elliptical orbits to 63.4°or 116.6° for satellite communications.These are the only two inclinations atwhich the major axis remains fixed, sothat the apogee remains over thespecified latitude. At all otherinclinations the gravitational harmonicsof the Earth due to its oblate shape causethe major axis to rotate. For example, theRussian 12 hour Molniya orbit is a highlyelliptical orbit inclined at 63.4°. Theperigee altitude is 1,006 km and theapogee altitude is 39,362 km with apogeeover the northern hemisphere. A Molniyasatellite spends nearly 11 hours over thenorthern hemisphere and only 1 hourover the southern hemisphere perrevolution.

CONSTELLATIONCONFIGURATION

The configuration of the constellation isdefined by the number of orbital planes pand the number of satellites per plane s.The values of p and s should be chosenso as to minimize the total number ofsatellites N that are required to provide

the specified level of coverage, whereN = p s. For a given minimum angle ofelevation θ, the angle γ with respect tothe Earth's center between thesubsate1lite point and edge of coverage isgiven by

θθγ −

+

=ERh /1

cosarccos

where h is the satellite altitude and RE isthe radius of the Earth (6,378 km). Thetotal coverage area may be estimatedfrom the formula

)cos1(2 2 γπ −= ERS

Ideally, S should be as large as possible,but it is usually subdivided into an arrayof cells to permit frequency reuse. It maybe limited by the required satelliteantenna gain, which is approximatelygiven by G = 4 π h2 (n / S), where n is thenumber of cells. The diameter D of theantenna is then given by G = η (π D /λ )2,where λ is the wavelength and η is theefficiency. These relations imply that theantenna diameter is proportional to thealtitude for a given cell size. The coverage geometry problem issimplest for polar constellations. Forglobal coverage with optimum phasing,the point of intersection of overlappingcircles of coverage in one plane coincideswith the boundary of a circle of coveragein a neighboring plane. Satellites inadjacent planes revolve in the samedirection. However, there is a “seam” inthe constellation pattern between the firstand last planes, where the satellitesrevolve in opposite directions. For agiven number of planes p and number ofsatellites per plane s, the Earth centralangle γ and ground swath half-width Γare determined by the equations

)/cos(

coscos

sπγ=Γ

and( p – 1) α + β = π

where α = Γ + γ is the spacing betweenco-rotating planes and β = 2 Γ is thespacing between counter-rotating planes. For example, the original Iridiumconstellation, based on a paper by Adamsand Rider, consisted of 77 satellitesdistributed into seven planes with 11satellites per plane. (The constellation

was named after the element iridium,whose atomic structure consists of 77electrons orbiting the nucleus.)Therefore, the Earth central angle γ was18.5° and the ground swath half-width Γwas 8.6°. Also, α was 27.1° and β was17.2°. For a minimum elevation of 10° atedge of coverage, the correspondingaltitude was 765 km. This altitudesatisfied the constraints that it wassufficiently high that atmospheric dragwas negligible, it was sufficiently lowthat it avoided the Van Allen radiationenvironment, and the cost of satellitedeployment was moderate. The Iridiurn constellation has beenrevised by the elimination of one plane toreduce the number of satellites. It nowconsists of 66 satellites distributed intosix planes with 11 satellites per plane atan altitude of 780 km. The planeseparation is 31.6° and the orbitalinclination has been changed to 86° as aprecaution against collisions at the poles.The angle of elevation at edge ofcoverage on the equator is 8.2°. The geometric problem for inclinedconstellations is somewhat morecomplicated. Walker, Ballard and Riderhave examined this problem using avariety of assumptions and techniques.For example, the Globalstar constellationconsists of 48 satellites, with 6 satellitesin each of 8 orbital planes, at an altitudeof 1406 km and inclined at 52°. Thisconstellation was based on the Walker48/8/1 “delta” pattern and was refined bycomputer modeling. A basic requirementof this system is that two satellites mustbe visible from any point. Thecommunications link uses code divisionmultiple access (CDMA) with pathdiversity. Each mobile telephone receivesa signal from each of two satellites at halfpower to minimize blockage andmultipath effects.

EARTH OBLATENESS

Earth oblatness has two important effectson a orbit. First, as mentioned previously,it causes the major axis to rotate. The rateof change of the perigee angle is

)1cos5()1(

982.4 2

5.3

22−

−= i

a

R

edt

d Eω

expressed in degrees per day, where a isthe semimajor axis, e is the eccentricityand i is the inclination. This equation

3

implies that the major axis is stable onlyfor inclinations of 63.4° and 116.6°,which are the only angles that make theright hand side of the equation equal tozero. Oblateness also causes the ascendingnode of the orbit to drift. The rate of driftis given by the formula

ia

R

edt

d E cos)1(

964.95.3

22

−−=Ω

expressed in degrees per day. Forinclinations less than 90° the ascendingnode drifts westward, while forinclinations greater than 90° theascending node drifts eastward. Theascending node does not drift for polarconstellations, for which the inclination is90°. For example, for the Globalstarconstellation, the ascending node driftswestward at the rate of 3° per day. The operational impact of ascendingnode drift on LEO constellations withintermediate inclinations is the penalty onstationkeeping fuel. In principle, if allthe satellites had identical circular orbitaltitudes and inclinations, the orbit planeswould drift in unison and the relativegeometry would remain constant.However, in practice, there are inevitableorbit insertion errors during deployment.In the preceding example, the differencein ascending nodes would accumulate to0.5° in one year for each kilometer oferror in altitude and would accumulate to2.5° in one year for each 0.1° of error ininclination, compared to the nominalorbit.

SUN-SYNCHRONOUS ORBITS

The drift in ascending node has oneimportant practical application. If thealtitude, inclination and eccentricity arechosen so that the ascending node driftseastward at the same rate as the Earthrevolves around the Sun (0.9856° perday), then the Earth−Sun line wouldmaintain a constant orientation withrespect to the orbital plane. This type oforbit was first used by the Landsatsatellites for Earth photography missions.Landsat-1 was launched in July 1972 intoa 910 km altitude orbit inclined at 99°. If the orbital plane is initially orientedperpendicular to the direction of the Sun,the satellite will always remainilluminated. The solar array would not

require a tracking mechanism andbatteries would be needed only forcontingencies. Another advantage ofSun-synchronous orbits is that the orbitalperiod can be synchronous with the meansolar day instead of the sidereal day overa given point on Earth, so that thesatellite maintains the same time-of-dayschedule. The E-Sat satellite system provides anexample based on these considerations.This system will provide data messagingand data retrieval services for publicutilities and petroleum companies, direct-to-home television broadcast services andthe financial services industry. Thesatellite orbit, is a Sun-synchronouscircular orbit with a period of revolutionthat is a submultiple of a mean solar day.It has thus been given the name of“doubly-synchronous orbit.” Since theorbit is Sun-synchronous, the satellitemaintains the same time-of-day schedule.The orbital plane is to be orientedperpendicular to the Earth-Sun line andthe satellite solar array will be constantlyilluminated. The ground trace will repeatitself every day. It was also required thatthe altitude must be within the range1,000 km < h < 1,500 km so that theatmospheric drag would be negligibleand would not impinge on the first VanAllen radiation belt. Therefore, a circularorbit with an altitude of 1,262 km and aninclination of 100.7° was chosen. For a minimum elevation angle of 20°,the Earth central angle γ is 18.3°. Thecorresponding coverage area is 13 millionsquare kilometers, or roughly the size ofCONUS. This coverage area implies thatthe maximum satellite gain must be1.9 dB at 149.5 MHz. Therefore, for thegiven Earth terminal power and gain,method of modulation and coding, andvarious losses, the maximum data ratethat can be supported by thecommunications link is determined.Three satellites will be deployed into oneplane to meet the required capacity of theanticipated market. An additional threesatellites may be added at a later time. Ifthe latter satellites are deployed into adifferent orbit plane, they will have therequired modifications to the electricalpower subsystem to permit solar trackingand accommodate eclipse periods. A satellite orbit based on similarconsiderations was proposed in a 1984NASA-Lewis study for the Voice ofAmerica as one of several concepts for a

direct broadcast satellite system. In thiscase, elliptical Sun-synchronous orbitswith an integral number of revolutionsper mean solar day were investigated. Ane1liptical orbit was considered because itwould provide a long dwell time over theregion to be covered with properpositioning of the apogee. Since themajor axis could not rotate and since theinclination of a Sun-synchronous orbitmust be greater than 90°, the inclinationof 116.6° was required. With thisadditional level of synchronism, the orbitwas given the name “triply-synchronousorbit.” The only orbit with an integralnumber of revolutions per day that doesnot intersect the Earth is the three hourorbit, with a perigee altitude of 521 kmand an apogee altitude of 7,843 km. Anidentical orbit concept has been adoptedby Mobile Communications Holdings,Inc. (MCHI) for thc “Borealis orbit” ofits proposed Ellipsat constellation.

NAVIGATION SATELLITES

The Global Positioning System (GPS) isa fully operational satellite system forhigh precision position determinationdeveloped by the U.S. Department ofDefense. The GPS constellation consistsof 21 operational satellites and threein-orbit spares in circular orbits at analtitude of 20,182 km. The orbital periodis one-half a sidereal day, or 11.967hours. The ground track repeats itselfevery two revolutions, with the result thata given satellite appears over the samepoint 4.1 minutes earlier than theprevious day. Four satellites are deployedinto each of six orbital planes inclined at55°. At least four satellites are visible atall times from any point on Earth. Each satellite carries two cesium andtwo rubidium atomic clocks that maintaina highly stable time and frequencyreference. The satellite orbit and clockinformation is transmitted on each of twoL-band carriers (1575.42 MHz and1227.60 MHz). Two frequencies are usedto measure and compensate for the effectof ionosphere and troposphere delay. Thebaseband signal is modulated by twospread-spectrum pseudorandom noisecodes: a precision (P) code at 10.23 Mbpsfor military use that repeats every 38weeks and a clear access (C/A) code at1.023 Mbps for satellite acquisition andcivilian use that repeats every 1 ms.Different satellites use different portions

4

of the same P code. The user's receivergenerates an identical code and measuresthe distance to the satellite by means ofan autocorrelation circuit that determinesthe phase difference needed to align thetwo codes. The simultaneousmeasurement of PRN signals from foursatellites permits a three-dimensionaldetermination of position with aresolution of better than 10 meters usingthe P code or between 100 meters and300 meters with the C/A code. GPSsatellites are also used for timecomparison between standardslaboratories by common viewmeasurements with a precision of a fewnanoseconds. The Russian Global OrbitalNavigation Satellite System (GLONASS)is a similar system under development,consisting of 24 satellites at an altitude of19,132 km evenly distributed into threeorbital planes inclined at 64.8°. Theorbital period is 11.263 hours, so theground track repeats itself every eightdays. In contrast to GPS, which uses onlytwo frequencies for the entire system,each GLONASS satellite is assigned itsown two frequencies within the bands1240 - 1260 MHz and 1597 -1617 MHz.Satellites are distinguished by radio-frequency channel instead of bypseudorandom noise code. A single codeis used, repeating every 1 ms.

CONCLUSION

The basic principles of satelliteconstellation design have been reviewedand several actual examples have beendescribed. These examples illustrate howvarious design considerations lead to thechoice of orbit, which then drives thechoice of link parameters to meet thesystem requirements.

1

Via Satellite, September 1998

Iridium:From Conceptto Realityby Robert A. Nelson

On the 23rd day of this month, arevolutionary communication system willbegin service to the public. Iridium will bethe first mobile telephony system to offervoice and data services to and fromhandheld telephones anywhere in theworld. Industry analysts have eagerlyawaited this event, as they have debatedthe nature of the market, the economics,and the technical design.

As with any complex engineeringsystem, credit must be shared among manypeople. However, the three keyindividuals who are recognized as havingconceived and designed the system areBary Bertiger,Dr. Raymond Leopold, and KennethPeterson of Motorola, creators of theIridium system.

The inspiration was an occasion that hasentered into the folklore of Motorola. (Thestory, as recounted here, was the subject ofa Wall Street Journal profile on Monday,December 16, 1996.) On a vacation to theBahamas in 1985, Bertiger's wife, Karen,wanted to place a cellular telephone callback to her home near the Motorolafacility in Chandler, AZ to close a real-estate transaction. After attempting tomake the connection without success, sheasked Bertiger why it wouldn't be possibleto create a telephone system that wouldwork anywhere, even in the remoteCaribbean outback.

Bertiger took the problem back tocolleagues Leopold and Peterson atMotorola. Numerous alternative terrestrialdesigns were discussed and abandoned.

In 1987 research began on aconstellation of low earth orbiting satellitesthat could communicate directly withtelephones on the ground and with oneanother -- a kind of inverted cellulartelephone system.

But as they left work one day in 1988,Leopold proposed a crucial element of thedesign. The satellites would becoordinated by a network of "gateway"earth stations connecting the satellitesystem to existing telephone systems. They quickly agreed that this was thesought-after solution and immediatelywrote down an outline using the nearestavailable medium -- a whiteboard in asecurity guard's office.

Originally, the constellation was to haveconsisted of 77 satellites. Theconstellation was based on a study byWilliam S. Adams and Leonard Rider ofthe Aerospace Corporation, who publisheda paper in The Journal of the AstronauticalSciences in 1987 on the configurations ofcircular, polar satellite constellations atvarious altitudes providing continuous,full-earth coverage with a minimumnumber of satellites. However, by 1992several modifications had been made to thesystem, including a reduction in thenumber of satellites from 77 to 66 by theelimination of one orbital plane.

The name Iridium was suggested by aMotorola cellular telephone systemengineer, Jim Williams, from the Motorolafacility near Chicago. The 77-satelliteconstellation reminded him of the electronsthat encircle the nucleus in the classicalBohr model of the atom. When heconsulted the periodic table of the elementsto discover which atom had 77 electrons,he found Iridium -- a creative name thathas a nice ring. Fortunately, the systemhad not yet been scaled back to 66satellites, or else he might have suggestedthe name Dysprosium.

The project was not adopted by seniormanagement immediately. On a visit tothe Chandler facility, however, Motorolachairman Robert Galvin learned of the ideaand was briefed by Bertiger. Galvin atonce endorsed the plan and at a subsequentmeeting persuaded Motorola's presidentJohn Mitchell. Ten years have elapsedfrom this go-ahead decision, and thirteenyears since Bertiger's wife posed thequestion.

In December 1997 the first Iridium testcall was delivered by orbiting satellites. Shortly after completion of theconstellation in May 1998, ademonstration was conducted for franchise

owners and guests. The new system wasready for operation, and Iridium is now onthe threshold of beginning service.

REGULATORY HURDLES

In June, 1990 Motorola announced thedevelopment of its Iridium satellite systemat simultaneous press conferences inBeijing, London, Melbourne, and NewYork. The Iridium system was describedin an application to the FederalCommunications Commission (FCC) filedin December of that year, in a supplementof February 1991, and an amendment inAugust 1992.

At the time, an internationally allocatedspectrum for this service bynongeostationary satellites did not evenexist. Thus Motorola proposed to offerRadio Determination Satellite Service(RDSS) in addition to mobile digital voiceand data communication so that it mightqualify for use of available spectrum in theRDSSL-band from 1610 to 1626.5 MHz. Awaiver was requested to provide both two-way digital voice and data services on aco-primary basis with RDSS.

Following the submission of Motorola'sIridium proposal, the FCC invitedapplications from other companies forsystems to share this band for the newMobile Satellite Service (MSS). Anadditional four proposals fornongeostationary mobile telephonysystems were submitted to meet the June 3,1991 deadline, includingLoral/Qualcomm's Globalstar, TRW'sOdyssey, MCHI's Ellipsat, andConstellation Communications' Aries.Collectively, these nongeostationarysatellite systems became known as the"Big LEOs". The American MobileSatellite Corporation (AMSC) also soughtto expand existing spectrum for itsgeostationary satellite into the RDSS band.

At the 1992 World AdministrativeRadio Conference (WARC-92) inTorremolinos, Spain, L-band spectrumfrom 1610 to 1626.5 MHz wasinternationally allocated for MSS for earth-to-space (uplink) on a primary basis in allthree ITU regions. WARC-92 alsoallocated to MSS the band 1613.8 to1626.5 MHz on a secondary basis and

2

spectrum in S-band from 2483.5 to 2500MHz on a primary basis for space-to-earth(downlink).

In early 1993 the FCC adopted aconforming domestic spectrum allocationand convened a Negotiated Rulemakingproceeding. This series of meetings wasattended in Washington, DC byrepresentatives of the six applicants andCelsat, which had expressed an intention tofile an application for a geostationarysatellite but did not meet the deadline.

The purpose of the proceeding was toprovide the companies with theopportunity to devise a frequency- sharingplan and make recommendations. Thesedeliberations were lively, and at timescontentious, as Motorola defended itsFDMA/TDMA multiple access designagainst the CDMA technologies of theother participants.

With frequency division multiple access(FDMA), the available spectrum issubdivided into smaller bands allocated toindividual users. Iridium extends thismultiple access scheme further by usingtime division multiple access (TDMA)within each FDMA sub-band. Each user isassigned two time slots -- one for sendingand one for receiving -- within a repetitivetime frame. During each time slot, thedigital data are burst between the mobilehandset and the satellite.

With code division multiple access(CDMA), the signal from each user ismodulated by a pseudorandom noise(PRN) code. All users share the samespectrum. At the receiver, the desiredsignal is extracted from the entirepopulation of signals by multiplying by areplica code and performing anautocorrelation process. The key to thesuccess of this method is the existence ofsufficient PRN codes that appear to bemathematically orthogonal to one another. Major advantages cited by CDMAproponents are inherently greater capacityand higher spectral efficiency. Frequencyreuse clusters can be smaller becauseinterference is reduced betweenneighboring cells.

In April, 1993 a majority report ofWorking Group 1 of the NegotiatedRulemaking Committee recommended fullband sharing across the entire MSS bandby all systems including Iridium.

Coordination would be based on anequitable allocation of interference noiseproduced by each system. TheFDMA/TDMA system would be assignedone circular polarization and the CDMAsystems would be assigned the oppositepolarization. This approach required thateach system would be designed withsufficient margin to tolerate the level ofinterference received from other licensedsystems.

Motorola issued a minority report whichstated that the Iridium system must have itsown spectrum allocation. It proposedpartitioning of the MSS L-band spectruminto two equal 8.25 MHz segments for theFDMA/TDMA and CDMA accesstechnologies, with the upper portion beingused by the FDMA/TDMA system whereit would be sufficiently isolated fromneighboring frequencies used by radioastronomy, GPS, and Glonass.

Faced with this impasse, the FCC inJanuary 1994 adopted rulemakingproposals which allocated the upper 5.15MHz of the MSS L-band spectrum to thesole FDMA/TDMA applicant, Iridium,and assigned the remaining 11.35 MHz tobe shared by multiple CDMA systems. However, if only one CDMA system wereimplemented, the 11.35 MHz allotmentwould be reduced to 8.25 MHz, leaving3.10 MHz available for additionalspectrum to Iridium or a new applicant.

The response to the Commission'sproposals from the Big LEO applicantswas generally favorable. Without thiscompromise, the alternative would havebeen to hold a lottery or auction to allocatethe spectrum. The Iridium system wasdesigned to operate with the full spectrumallocation. However, with 5.15 MHz, thesystem is a viable business proposition. The additional 3.10 MHz, should itbecome available, further adds to thesystem's attractiveness.

The FCC also proposed that the MSSspectrum could be used only by Low EarthOrbit (LEO) and Medium Earth Orbit(MEO) satellite systems. Therefore, thegeostationary orbit (GEO) systems ofAMSC and Celsat would not be permittedin this band. To qualify for a Big LEOlicense, the Commission proposed that theservice must be global (excluding thepoles) and that companies must meet

stringent financial standards.In October, 1994 the FCC issued its

final rules for MSS, closely followinglanguage of the January proposedrulemaking. However, it allowed theCDMA systems to share the entire16.5 MHz of downlink spectrum inS-band. The Commission gave the BigLEO applicants a November 16 deadlineto amend their applications to conform tothe new licensing rules.

On January 31, 1995 the FCC grantedlicenses to Iridium, Globalstar, andOdyssey but withheld its decision onEllipsat and Aries pending an evaluation oftheir financial qualifications. The lattercompanies finally received licenses in Junelast year, while in December TRWdropped its Odyssey system in favor ofpartnership with ICO, the internationalsubsidiary of Inmarsat which entered thecompetition in 1995.

Outside the United States, Iridium mustobtain access rights in each country whereservice is provided. The company expectsto have reached agreements with 90priority countries that represent 85% of itsbusiness plan by the start of service thismonth. Altogether, Iridium is seekingaccess to some 200 countries through anarduous negotiating process.

FINANCING

Iridium LLC was established by Motorolain December, 1991 to build and operatethe Iridium system, with Robert W. Kinzieas its chairman. In December, 1996Edward F. Staiano was appointed ViceChairman and CEO.

Iridium LLC, based in Washington, DC,is a 19-member international consortium ofstrategic investors representingtelecommuni-cation and industrialcompanies, including a 25 percent stake byits prime contractor, Motorola, Inc.

In August 1993, Motorola and IridiumLLC announced they had completed thefirst-round financing of the Iridium systemwith $800 million in equity. The secondround was completed in September, 1994,bringing the total to $1.6 billion. In July oflast year $800 million in debt financingwas completed. Iridium WorldCommunications, Ltd., a Bermudacompany, was formed to serve as a vehicle

3

for public investment in the Iridiumsystem. In June 1997 an initial $240million public offering was made on theNASDAQ Stock Exchange.

TECHNICAL DESCRIPTION

The Iridium constellation consists of 66satellites in near-polar circular orbitsinclined at 86.4° at an altitude of 780 km. The satellites are distributed into six planesseparated by 31.6° around the equator witheleven satellites per plane. There is alsoone spare satellite in each plane.

Starting on May 5, 1997, the entireconstellation was deployed within twelvemonths on launch vehicles from threecontinents: the U.S. Delta II, the RussianProton, and the Chinese Long March. Thefinal complement of five 700 kg (1500 lb)satellites was launched aboard a Delta IIrocket on May 17. With a satellite lifetimeof from 5 to 8 years, it is expected that thereplenishment rate will be about a dozensatellites per year after the second year ofoperation.

The altitude was specified to be withinthe range 370 km (200 nmi) and 1100 km(600 nmi). The engineers wanted aminimum altitude of 370 km so that thesatellite would be above the residualatmosphere, which would have diminishedlifetime without extensive stationkeeping,and a maximum altitude of 1100 km sothat the satellite would be below the VanAllen radiation environment, which wouldrequire shielding.

Each satellite covers a circular arearoughly the size of the United States with adiameter of about 4400 km, having anelevation angle of 8.2° at the perimeter andsubtending an angle of 39.8° with respectto the center of the earth. The coveragearea is divided into 48 cells. The satellitehas three main beam phased arrayantennas, each of which serves 16 cells.

The period of revolution isapproximately 100 minutes, so that a givensatellite is in view about 9 minutes. Theuser is illuminated by a single cell forabout one minute. Complex protocols arerequired to provide continuity ofcommunication seamlessly as handover ispassed from cell to cell and from satelliteto satellite. The communications linkrequires 3.5 million lines of software,

while an additional 14 million lines ofcode are required for navigation andswitching. As satellites converge near thepoles, redundant beams are shut off. Thereare approximately 2150 active beams overthe globe.

The total spectrum of 5.15 MHz isdivided into 120 FDMA channels, eachwith a bandwidth of 31.5 kHz and aguardband of 10.17 kHz to minimizeintermodulation effects and twoguardbands of 37.5 kHz to allow forDoppler frequency shifts. Within eachFDMA channel, there are four TDMAslots in each direction (uplink anddownlink). The coded data burst rate withQPSK modulation and raised cosinefiltering is 50 kbps (corresponding to anoccupied bandwidth of 1.26 × 50 kbps / 2= 31.5 kHz). Each TDMA slot has length8.29 ms in a 90 ms frame. The supportedvocoder information bit rate is 2.4 kbps fordigital voice, fax, and data. The totalinformation bit rate, with rate 3/4 forwarderror correction (FEC) coding, is 3.45 kbps(0.75 × (8.28 ms/90 ms) × 50 kbps =3.45 kbps), which includes overhead and source encoding, exclusive of FEC coding,for weighting of parameters in importanceof decoding the signal. The bit error ratio(BER) at threshold is nominally 0.01 but ismuch better 99 percent of the time.

The vocoder is analogous to a musicalinstrument synthesizer. In this case, the"instrument" is the human vocal tract. Instead of performing analogue-to-digitalconversion using pulse code modulation(PCM) with a nominal data rate of 64 kbps(typical of terrestrial toll-quality telephonecircuits), the vocoder transmits a set ofparameters that emulate speech patterns,vowel sounds, and acoustic level. Theresulting bit rate of 2.4 kbps is thuscapable of transmitting clear, intelligiblespeech comparable to the performance ofhigh quality terrestrial cellular telephones,but not quite the quality of standardtelephones.

The signal strength has a nominal 16 dBlink margin. This margin is robust forusers in exterior urban environments, but isnot sufficient to penetrate buildings. Satellite users will have to stand nearwindows or go outside to place a call. Handover from cell to cell within the fieldof view of an orbiting satellite is

imperceptible. Handover from satellite tosatellite every nine minutes mayoccasionally be detectable by a quarter-second gap.

Each satellite has a capacity of about1100 channels. However, the actualnumber of users within a satellite coveragearea will vary and the distribution of trafficamong cells is not symmetrical.

CALL ROUTING

The Iridium satellites are processingsatellites that route a call through thesatellite constellation. The system iscoordinated by 12 physical gatewaysdistributed around the world, although inprinciple only a single gateway would berequired for complete global coverage. Intersatellite links operate in Ka-band from23.18 to 23.38 GHz and satellite-gatewaylinks operate in Ka-band at 29.1 to 29.3GHz (uplink) and 19.4 to 19.6 GHz(downlink).

For example, a gateway in Tempe,Arizona serves North America and CentralAmerica; a gateway in Italy serves Europeand Africa; a gateway in India servessouthern Asia and Australia. There are 15regional franchise owners, some of whomshare gateway facilities. The constellationis managed from a new satellite networkoperations center in Lansdowne, Virginia.

As described by Craig Bond, Iridium'svice president for marketing development,the user dials a telephone number with thehandset using an international 13 digitnumber as one would do normally using astandard telephone. The user presses the"send" button to access the nearestsatellite. The system identifies the user'sposition and authenticates the handset atthe nearest gateway with the home locationregister (HLR).

Once the user is validated, the call issent to the satellite. The call is routedthrough the constellation and drops to thegateway closest to the destination. There itis completed over standard terrestrialcircuits.

For a call from a fixed location to ahandset, the process is reversed. After thecall is placed, the system identifies therecipient's location and the handset rings,no matter where the user is on the earth.

It is projected that about 95 percent ofthe traffic will be between a mobile

4

handset and a telephone at a fixed location. The remaining 5 percent of the trafficrepresents calls placed from one handset toanother handset anywhere in the world. Inthis case, the call "never touches theground" until it is received by the handsetof the intended recipient.

By comparison, a "bent pipe" satellitesystem, such as Globalstar, requires that asingle satellite see both the user and thenearest gateway simultaneously. Thusmany more gateways are needed. Forexample, in Africa Globalstar will requireabout a dozen gateways, while Iridium hasnone at all. Globalstar advocates wouldcounter that this is not a disadvantage,since their system places the complexity onthe ground rather than the satellite andoffers greater flexibility in building andupgrading the system.

HANDSET

The Iridium handsets are built by Motorolaand Kyocera, a leading manufacturer ofcellular telephones in Japan. Handsets willpermit both satellite access and terrestrialcellular roaming capability within the sameunit. The unit also includes a SubscriberIdentity Module (SIM) card. Majorregional cellular standards areinterchanged by inserting a CellularCassette. Paging options are available, aswell as separate compact Iridium pagers.

The price for a typical configurationwill be around $3,000. The handsets willbe available through service providers andcellular roaming partners. In June, Iridiumfinalized its 200th local distributionagreement.

Information on how to obtain Iridiumtelephones will be advertised widely. Customers will also be actively solicitedthrough credit card and travel servicesmemberships. Distribution of the handsetsand setup will typically be through salesrepresentatives who will interface with thecustomer directly. Rental programs willalso be available to give potentialcustomers the opportunity to try out thesystem on a temporary basis.

MARKET

Iridium has conducted extensive researchto measure the market. As described byIridium's Bond, the intended market can be

divided into two segments: the verticalmarket and the horizontal market.

The vertical market consists ofcustomers in remote areas who requiresatellites for their communications needsbecause they cannot access conventionalterrestrial cellular networks. This marketincludes personnel in the petroleum, gas,mining, and shipping industries. It alsoincludes the branches of the U.S. military. In fact, the U.S. government has built adedicated gateway in Hawaii capable ofserving 120,000 users so that it can accessthe Iridium system at a lower per minutecharge.

The horizontal market is represented bythe international business traveler. Thistype of customer wants to keep in contactwith the corporate office no matter wherehe or she is in the world. Althoughmindful of the satellite link, this customerdoesn't really care how the telephonesystem works, as long as it is alwaysavailable easily and reliably.

It has been consistently estimated thatthe total price for satellite service will beabout $3.00 per minute. This price isabout 25 percent to 35 percent higher thannormal cellular roaming rates plus longdistance charges. When using the roamingcellular capability, the price will be about$1.00 to $1.25 per minute.

The expected break-even market forIridium is about 600,000 customersglobally, assuming an undisclosed averageusage per customer per month. Thecompany hopes to recover its $5 billioninvestment within one year, or by thefourth quarter of 1999. Based onindependent research, Iridium anticipates acustomer base of 5 million by 2002.

PROBLEMS

As might be expected for a complexundertaking, the deployment of theconstellation and the manufacture of thehandsets has not been without glitches. Sofar, a total of seven spacecraft havesuffered in-orbit failures. In addition,Iridium has announced delays in thedevelopment of the handset software.

Of the 72 satellites launched, includingspares, one lost its stationkeeping fuelwhen a thruster did not shut off, one wasdamaged as it was released from a Delta II

launch vehicle, and three had reactionwheel problems. In July two moresatellites failed because of hardwareproblems. Delta II and Long Marchrockets, scheduled to begin a maintenanceprogram of launching additional spares,were retargeted to deploy sevenreplacement birds to the orbital planeswhere they are needed in August.

Investors are also nervous about finalsoftware upgrades to the handsets. Following alpha trials last month, betatesting of the units was scheduled tocommence within one week of theSeptember 23 commercial activation date. The Motorola handsets are expected to beavailable to meet initial demand, but thosemade by Kyocera may not be ready untillater. [Note added: On September 9,Iridium announced that the debut of fullcommercial service would be delayed untilNovember 1 because more time is neededto test the global system.]

The fifteen gateways have beencompleted. Equipment for the Chinagateway, the last one, was shippedrecently. Like a theatrical production, theplayers are frantically completing lastminute details as the curtain is about to goup and Iridium embarks upon the worldstage.

THE FUTURE

Iridium is already at work on its NextGeneration system (Inx). Planning thesystem has been underway for more than ayear. Although details have not beenannounced, it has been suggested that thesystem would be capable of providingbroadband services to mobile terminals. Inpart, it would augment the fixed terminalservices offered by Teledesic, whichMotorola is helping to build, and mightinclude aspects of Motorola's formerCelestri system. It has also been reportedthat the Inx terminal would provide greaterflexibility in transitioning between satelliteand cellular services and that the satellitepower level would be substantiallyincreased.

As customers sign up for satellitemobile telephony service, the utility andcompetitive advantage will becomeapparent. Information will flow morefreely, the world will grow still smaller,

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and economies around the world will bestimulated. There will also be a profoundeffect on geopolitics and culture. Just assatellite television helped bring down theBerlin Wall by the flow of pictures andinformation across internationalboundaries, the dawning age of globalpersonal communication amongindividuals will bring the world communitycloser together as a single family._______________________________

Dr. Robert A. Nelson, P.E., is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, MD, and isTechnical Editor of Via Satellite.

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Via Satellite February, 1998

V-Band

Expansion of theSpectrum Frontier

by Robert A. Nelson

The settlement of the American west duringthe nineteenth century was bounded by anatural frontier: the Pacific Ocean. Forpioneers in the satellite industry, thereappears to be no analogous frontier in theelectromagnetic frequencies used forsatellite communications as the upperbound of frequencies is being pushed everhigher. On September 26, 1997, a dozencompanies submitted proposals to the U.S.Federal Communications Commission(FCC) for authorization to build satellitesystems that will exploit the frequencybands from 36 GHz to 51.4 GHz, whichincludes Q-band and V-band. These newsystems will supplement the manyKa-band broadband systems now invarious stages of development. Theproposed constellations span the full rangeof altitude regimes, including Low EarthOrbit (LEO), Medium Earth Orbit (MEO),and geostationary orbit (GEO). As historians have noted, the expansionof the American west was made possiblethrough the sudden advance oftechnology − the steamboat, the telegraph,and the railroad. Similarly, the focus onbroadband applications at higherfrequencies has been made possiblethrough technological change, includingprocessing satellites, sophisticatedswitching networks, low-noise amplifiers,modems, codecs, tracking antennas, andintelligent receivers. High frequencies, together with widebandwidths, permit the use of small Earthterminals and high data rates and thusmake satellite communication available tothe home, business, and mobile terminalfor diverse applications such as internetaccess, data retrieval, teleconferencing, andelectronic library research. Bary Bertiger, Corporate Vice Presidentand General Manager of the MotorolaSatellite Communication Group, describedthis capability as “global, instantaneous

infrastructure that will be equally availableat low cost to consumers in developingcountries and industrialized nations.Virtually any intellectual property, such asdocuments and computer software, can bedigitized and delivered via satellite insteadof being physically transported by hand ortransmitted over wires.” The development of these broadbandsatellite systems over the next few yearswill represent a communication revolution,notable both as a new stage ofdevelopment and as a lens to alter our viewof the world. Their existence will affectour very perception of how wecommunicate and the informationresources that we can access, just as theinvention of mechanical clocks in themiddle ages altered the public perceptionof time, the growth of high speed travelduring the twentieth century altered theperception of geographical distance, andthe exploration of space has altered theperception of our place in the universe.

FREQUENCY BANDS

The first band used for commercial satellitecommunication in the Fixed SatelliteService (FSS) was C-band (6/4 GHz,where the uplink frequency is given first).During the mid-1980s, Ku-band (14/12GHz) came into use. Due to its higherfrequency, this band is sensitive to rainfade but with higher power satellites it hasbecome popular because it permits smallerEarth station antennas. Mobile telephony systems such asMotorola's IRIDIUM and Loral/Qual-comm's GLOBALSTAR, both in theprocess of deployment, will use lowerfrequencies, which are desirable becausethey maximize the received carrier powerfor fixed satellite and handset antennagains. For example, IRIDIUM will use L-band (1.6 GHz) for both uplink anddownlink, while GLOBALSTAR will useL-band (1.6 MHz) for the uplink andS-band (2.5 GHz) for the downlink.Satellite systems in the emerging DigitalAudio Radio Service (DARS), such as CDRadio and AMRC, will use S-band in thevicinity of 2.3 GHz. In the early 1990s, a variety of systemswere designed for Ka-band (30/20 GHz)for broadband applications, such asMotorola's Millennium, Hughes’Spaceway, SS/Loral's Cyberstar, LockheedMartin's Astrolink, Echostar, GE*Star,KaStar, Morning Star, Net Sat 28, Orion,

and PanAmSat, which are all geostationaryconstellations, as well as the TeledesicLEO system. The practical use of suchhigh frequencies for communication wasfirst demonstrated by the NASA ACTSprogram. (The term K-band was originallygiven to the range 18 − 27 GHz, but after amolecular water vapor absorptionresonance was discovered at the center ofthe band at 22.3 GHz, the terms Ku band(12 − 18 GHz) and Ka band (27 − 40 GHz)were introduced to denote “under” and“above” K-band; however, the regime20 − 30 GHz for Ka-band is now commonusage.) The new systems will be at even higherfrequencies in the so-called Q-band (33 −50 GHz) and V-band (50 − 75 GHz) asdefined by the FCC in its Bulletin No. 70,July, 1997. The FCC also defines U-bandas 40 − 60 GHz, thus overlapping Q- andV-bands, and W-band as 75 − 110 GHzwith additional letter designations all theway up to 220 GHz. However,conventional usage seems to be convergingon the definition 40 − 50 GHz for V-band,which has also been called EHF; this trendwould suggest designating 30 − 40 GHz asQ-band, 50 − 60 GHz as U-band, and 60 −70 GHz as W-band if 10 − 20 GHzrepresents Ku-band, including both theFSS and BSS bands, and 20 − 30 GHzrepresents Ka-band.

ANTENNAS

Since the product of wavelength andfrequency is equal to the speed of light(3 × 108 m/s), the wavelength decreases asthe frequency increases. It is significant tonote that at V-band (50 GHz), the signalwavelength is only 6 millimeters. Bycomparison, at C-band (6 GHz) thewavelength is 50 millimeters (5 cm) and atL-band (1.6 GHz) the wavelength is about200 millimeters (20 cm). It is the verysmall wavelength that permits thefabrication of a high gain antenna with asmall physical aperture. Earth terminals that communicate withnongeostationary satellites will be requiredto have tracking and handover capability.A satellite in Medium Earth Orbit at analtitude of 10,000 km is visible for about2 hours. In Low Earth Orbit at an altitudeof 1000 km the maximum time in view isonly 15 minutes. The antennas, with gains on the order of50 dB, will be either mechanically-steered

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reflectors or electronically steered phasedarrays. The reflector antennas will betypical for business installations, while thephased arrays will find application in lowercapacity systems at residential sites ormobile terminals. The phased array antennas underdevelopment will represent a majorachievement in technology. The trackingrequirement will depend on advances inmicrocircuit state of the art more thanantenna design and it will be a challengefor the industry to offer them at attractiveprices.

RAIN

At high frequencies, rain attenuation is aserious problem. Physically, rainattenuation is due to scattering andabsorption of the microwave energy by therain. As the wavelength decreases andapproaches the size of a typical rain drop(approximately 1.5 mm), more scatteringand absorption occurs and the attenuationincreases. Also, as the rain rate increasesduring a heavy downpour, the size of therain drops, and hence the attenuation,increases. It is the rain rate, and not the annualrainfall, that determines availability. ThusSan Francisco and Seattle are in the samerain climate region because the probabilityof a given rain rate being exceeded is aboutthe same, despite the disparity in the totalannual rainfall. By way of example, for an availabilityof 99.95 percent or a total outage of 43.8hours per year in Washington, DC, themaximum rain rate is 22 mm/h. Thecorresponding specific rain attenuation isapproximately 0.05 dB/km at C-band, 1dB/km at Ku-band, 3 dB/km at Ka-band,and 9 dB/km at V-band. For a given rainattenuation allowance, the availability atV-band is simply not as high as at Ku-bandor even Ka-band. The problem may be mitigated byswitching to lower frequencies duringperiods of heavy rain. Thus dual payloadsatellites with both Ka-band and V-bandsteerable beams may be desirable from thepoint of view of engineering design.Nevertheless, customer awareness of therain fade issue will be necessary. For large, high capacity Earth stations,site diversity is used to overcome rain.Earth stations about 10 km apart andconnected by terrestrial microwave circuitswill see different rain cells, so that at least

one Earth station will maintain the satellitelink. For example, IRIDIUM uses thistechnique for its Ka-band mobile telephonygateways. Terrestrial systems can also beused for backup.

PROPOSED V-BAND SYSTEMS

Motorola was the first to explore the use ofnongeostationary satellites in the newfrequency regime. In September, 1996 thecompany submitted an application to theFCC for a Low Earth Orbit satelliteconstellation called M-Star to providebroadband services to businesses in the40 GHz band. The proposed constellationconsists of 72 satellites in circular orbits atan altitude of 1350 km and distributed in12 planes inclined at 47°. The M-Starsystem is designed to offer two types ofservice: voice and data transport to serviceproviders and business customers at2.048 Mbps and interconnection andbackhaul services at up to 51.84 Mbps. Last June, Motorola submitted anapplication for a Ka-band LEO systemcalled Celestri. The Celestri LEO systemwill comprise 63 satellites at an altitude of1400 km distributed into 7 orbital planesinclined at 48°. Services to be offeredinclude point-to-point symmetric transferat 64 kbps to 155 Mbps; point-to-pointasymmetric transfer with “bandwidth ondemand” up to 16 Mbps; broadcastservices; and interactive real-time responseservices. The market comprises residentialconsumers seeking work-at-home,entertainment, education, and securitycapabilities; small businesses purchasingfrom multimedia outlets; and largemultinational corporations seekingimproved customer awareness. TheCelestri system would augment therecently licensed Millennium Ka-bandsystem of four geostationary satellites andthe proposed M-Star system to form athree-tier LEO/GEO FDMA/TDMAcommunication architecture. Celestri is presently regarded as anumbrella designation for all three systems.The available data rates for the LEOcomponent is 2 Mbps on the uplink and 16Mbps on the downlink; the GEOcomponent provides a downlink data rateof 20 Mbps. Motorola has amended itsapplication to request authorization forboth V-band and Ka-band payloads on theCelestri satellites, and is considering theincorporation of the M-Star payload on the

Celestri bus. Celestri is entirely differentfrom IRIDIUM. Celestri will offerbroadband services for high speed datatransfer to fixed terminals, while IRIDIUMwill provide narrowband services for voicecommunication and messaging to mobileterminals. In order to connect the satellite systemto end-users, Motorola has developed arange of terminal sizes, which collectivelyare described by the broad term "CustomerPremises Equipment (CPE)". Thisequipment can be as large as a gatewaystation for telecommunications carriers andas small as a home unit that can bemounted on a roof. The home unit antennais a high gain phased array capable oftracking the LEO satellite and providingseamless handover from leading tofollowing satellites. According toMotorola spokesperson Robert Edwards,the projected cost of this unit is about$700, a surprisingly low estimate given theadvanced technology it represents. Three new V-band systems have beenproposed by Hughes. “The V-band filingspioneer new spectrum to keep the satellitemarket strong by advancing technologyinto the realm of new market demands formobile connectivity and increasedbandwidth,” said Wendy Greene,spokesperson for Hughes. The first is Expressway, a constellationof 14 geostationary satellites at 10 orbitallocations to provide global high-capacity,wideband satellite communications.Expressway will use 3 GHz of uplink anddownlink bandwidth in V-band and 500MHz of uplink and downlink bandwidth inKu-band. The V-band capacity will beused to serve high data rate users, such asmultinational companies, with spot beamsthat can be activated in response todemand. The Ku-band capacity will bedistributed through a series of largerbeams. A typical user terminal has a 2.5meter antenna and a 30 watt HPA. The satellite architecture uses a piece ofproven ACTS technology. On-boardTDMA, IF-switched processing facilitatesthe allocation of “bandwidth on demand”and the satellites are interconnected byoptical (laser) links. The data rates varyfrom T1 (1.544 Mbps) to OC-3 (155Mbps), a 100:1 ratio on an individualcarrier basis. The total capacity is 588,000equivalent T1 circuits. Expressway uses a “systems” approachto availability, seamlessly migrating trafficbetween its V-band and Ku-band capacity

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on an individual user basis. With a typicalallocation for rain fade of about 3 dB, theV-band availability will be around 98percent; higher availabilities are providedwith the satellite’s Ku-band capability. Expressway has been engineered tooptimize capacity. This system is intendedfor a “leased line” dedicated user. TheKu-band capacity will be used sparingly toenhance availability where needed duringperiods of rain, and will be allocateddepending on user level of service andpricing schedule. By comparison, the Hughes Ka-bandSpaceway system of eight geostationarysatellites is optimized to user terminal andavailability requirements. It is intended foroccasional access, such as to smallbusiness and residential consumers, andwill be priced by the bit. Spacewayinvolves substantial processing on thesatellite. The second component of the Hughessystem is Spacecast, which will consist ofsix geostationary satellites. Spacecast willoffer video and multimedia services atV-band and Ku-band. Using spot beams,the system will have multitaskingcapabilities for one-way transmission tosmall terminals for applications such ascorporate training and distance learning.The data rate to a 45 cm terminal would be26 Mbps and the data rate to a 1 meterterminal would be 155 Mbps. The third component of the Hughessystem is Starlynx. This is a hybridV-band constellation with fourgeostationary satellites (two satellites ineach of two orbital slots) and 20 MediumEarth Orbit satellites at an altitude of10,352 km. The MEO constellationconsists of four planes inclined at 55° withfive satellites per plane. Starlynx willprovide two-way data connectivity toportable terminals, such as notebook anddesktop computers, using small, flatantennas. The terminals can be eitherstationary or mobile. For stationaryterminals, the antenna size will be about30 cm × 30 cm and the data rates will beup to 2 Mbps, while for mobile terminalsthe antenna size will be about 60 cm ×60 cm and the data rates will be up to 8Mbps. PanAmSat, an independent companywith majority ownership by Hughes, hasasked the FCC for approval to launch a 12satellite geostationary constellation toprovide global digital services at V-band.The system, called V-Stream, is to be

deployed in 11 orbital slots, from 99° Wlongitude for North America to 124.5° Elongitude for the Pacific Rim. It will use3 GHz of spectrum in the 50/40 GHz bandand will include high powered spot beamswith onboard processing and intersatellitelinks at 33/23 GHz and/or 60 GHz. (The60 GHz frequency is particularlyappropriate for intersatellite links becausethe atmosphere is opaque in thisneighborhood due to resonance absorptionby molecular oxygen.) The V-Stream system will augmentPanAmSat's existing network of 16satellites providing C-band and Ku-bandservices; in addition, the company hasreceived FCC authorization to operate Ka-band satellites in nine orbital slots. TRW has requested FCC authorizationto launch and operate a system called theTRW Global EHF Satellite Network(GESN). The GESN system space segmentconsists of a hybrid constellation of fourgeostationary satellites and 15 MEOsatellites that will operate in 6 hour circularorbits at an altitude of 10,355 km. Thesatellites are distributed in three orbitalplanes inclined at 50° with five equallyspaced satellites per plane to ensure highelevation angle links (greater than 30°). The MEO component of theconstellation has an obvious similarity withTRW's former 12 satellite ODYSSEYsystem for mobile telephony, which wasabandoned in favor of a partnership withICO, and suggests that TRW may beplacing its commercial satellitedevelopment emphasis in a new direction. According to TRW’s Director ofTelecommunications Policy PeterHadinger, the requirements of a V-bandsystem certainly complement theexperience the company has gained in thesatellite arena. “This is really playing toour forté, in terms of the millimeter wavefrequency bands and the use of onboardsignal processing,” Hadinger says. Hebelieves TRW’s work on the Milstarproject and other military payloads willgive the company an advantage ontechnical development. The services to be offered on a globalbasis will be two-way point-to-pointwideband data connectivity, multimediadistribution services, and private networkservices. The GESN system applicationrequests the use 3 GHz of bandwidth ineach direction, specifically 47.2 to 50.2GHz for the uplink and 37.5 to 40.5 GHzfor the downlink.

The system will use optical intersatellitelinks. The uplink supports a standardservice link (SSL) of 155.52 Mbps and awideband service link (WSL) of 1.5552Gbps The downlink supports a totalchannel rate, including data rate andoverhead, of either 317 Mbps (SSL) or3.17 Mbps (WSL). The modulation formatis OQPSK. These signal structures areused for both the GEO and MEO satellites. TRW is targeting large businesses andinternational carriers, not the residentialconsumer market. The user terminalantenna aperture is 1.5 to 2.2 meters andthe RF power is 12 to 30 watts for the SSL,while the antenna aperture is 2.2 to 2.5meters and the RF power is 100 W for theWSL. Terminals that operate through theMEO constellation will be required tomechanically track the satellites through a120° arc and will also be required to havedual tracking capability to achievetransparent handovers between leading andfollowing satellites. Recognizing thatmechanically steered reflector antennasmay be objectionable or impractical forsome users, TRW has indicated that it willwork with established manufacturers ofcommercial satellite terminals to developsmall, attractively priced, electronicallysteered, flat phased array antennas usingmonolithic microwave integrated circuit(MMIC) devices. Lockheed Martin's proposed GlobalQ/V-Band Satellite CommunicationsSystem will consist of 9 geostationarysatellites. It requests FCC authorization toprovide broadband services requiring 3GHz for the uplink in the range 47.2 − 50.2GHz and 3 GHz for the downlink in therange 39.5 − 42.5 GHz. This system will provide high data ratecommunication to provide infrastructure toareas not adequately served by terrestrialsystems. Through the use of both smalland large user terminals, it will provideinstant connectivity for the exchange ofdata at rates up to OC-3 (155 Mbps). Thiscapability will extend the services providedat Ka-band by Astrolink, which will beoptimized to provide switched dataservices at data rates from 64 kbps to2 Mbps. Astrolink is a Lockheed Martinstrategic venture. The coverage will be composed of 48transmit and receive beams serving userterminals and 8 transmit and receive beamsserving gateway Earth stations. Each beamhas a nominal half power beamwidth of0.3° and occupies 125 MHz of bandwidth.

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The transmission scheme utilizes aunique TDM architecture in whichredundant data bits are added to userchannels experiencing significant rainfading. Each 125 MHz downlink channelcontains a single 96.29 Mbps carrier.Ground terminals extract and buffer dataaddressed only to them. The bi-directionaluser terminals will have antenna diametersas small as 45 cm with a transmit gain of44.8 dB. A terminal of this size will have atraveling wave tube amplifier (TWTA)with an output power of 4 watts and for aminimum elevation angle of 30° willsupport a maximum information uplinkdata rate of 384 kbps. Larger antennas will be used for lowerelevation angles and high rain rate regions.A 2.4 meter reflector with a transmit gainof 59.3 dB and an output power of 12 wattswill support uplink data rates up to9.216 Mbps. The target availability for theallocated rain margin is 98%. Interferenceto adjacent satellites is mitigated byinteractive power control with thespacecraft. The Loral Space and Communicationssystem, called CyberPath, consists of 10geostationary satellites. Loral seeks 1 GHzof spectrum for the uplink and 1 GHz ofspectrum for the downlink. Data ratesbegin at 16 kbps. Higher data rates, suchas 6 Mbps, are available on demand forvideo and data transmission. Trunkingdata rates up to 90 Mbps are also available.The CyberPath system capacity is17.9 Gbps. Each satellite uses on-boarddemodulation and decoding and ATM-likeswitching to achieve connectivity amongthe 100 V-band spot beams and the twointer-satellite links. Data are routedaccording to the packet header using aTDM/FDM/CDMA format. The subscriber Earth station, ranging insize from 0.5 to 3.0 meters, is selected toachieve the desired availability in rain. Itmay be installed at the home, business, orgovernment facility and are expected toinitially cost $1500 installed. The Earthstation is connected via the subscriber'scomputer to home or office equipmentutilizing the multimedia services. The linkis designed to have an availability of99.5%, reflecting a larger rain allowancethan most other systems. GE American Communications seeksauthorization for a constellation of 11geostationary satellites in nine orbitallocations. The global broadband system,

called GE*StarPlus, would offerconnectivity for data-based applications atrates up to 155 Mbps. The system woulduse 3 GHz for both uplink and downlink inthe 50/40 GHz V-band and 500 MHzwithin Ku-band. The system will useoptical intersatellite links. Each satellite payload receives uplinksignals, demodulates them, and routesthem to 20 V-band and 8 Ku-band spotbeams and one Ku-band hemispheric beamwith dual circular polarizations. The proposed GE*Starplus systemwould serve a diverse market for high-datarate communications that previously reliedon less suitable telephone network lines,such as for the transport of medical images,desktop publishing, and academicinformation. Users will be able to changelocations easily without requiringconnection to wire-based data services.Each satellite will have an estimatedcapacity of 40,000 equivalent T1 circuits. Spectrum Astro has designed a 25satellite, 50/40 GHz V-band system calledAster that will consist of five clusters ofcollocated geostationary satellites. Thecluster approach will enable the companyto build up its system in conformance withmarket demand. Each of the satellites produces 48 spotbeams 0.5° in diameter, 8 elliptical 1° ×1.5° regional beams, and 2 steerable 0.8°beams. The spot beams and regionalbeams divide the required 2 GHz ofbandwidth in each direction. Service isoffered at data rates of 155 Mbps andhigher through terminals in the range from4 m to 7 m. Lower data rates from 2 Mbpsto 51 Mbps are available through terminalsin the 1.2 m to 5 m range. SpectrumAstro’s system will be available to homes,businesses, medical clinics, educationalinstitutions, government agencies, andlaboratories. CAI Satellite Communications, Inc.intends to launch a single V-bandgeostationary satellite that has the ability toprovide high quality two-way video, voice,and data services to business andresidential customers in the contiguousUnited States (CONUS). The satellitewould be collocated with a Ka-bandsatellite proposed by CAI's affiliate, CAIData Systems, Inc., at 93°, 95°, or 102° Wlongitude. The company seeks 1 GHz of spectrumfrom 49.2 to 50.2 GHz for Earth-to-spaceand 1 GHz of spectrum from 40.5 to 41.5GHz for space-to-Earth. This system will

complement CAI's existing terrestrialMMDS “wireless cable” system operatingin the 2 GHz band to provide subscriberswith a greater variety of video andinteractive services. Orbital Sciences is proposing a sevensatellite broadband system from MEOcalled Orblink. The satellites will operateat an altitude of 9000 km in a singleequatorial plane and will be equally spacedby 51.4°, forming a "wireless ring" aroundthe Earth. Two primary services will be offered:service to large gateways for digital trunksand “bandwidth on demand” for high-speed data users. Each satellite will beable to simultaneously accommodate 20gateway users at 1.244 Gbps each and upto 4000 wideband users at 10 to 51 Mbpseach. Orbcomm requests the bands 47.7 to48.7 GHz for user to satellite, 37.5 to 38.5GHz for satellite to user, and 65.0 to 71.0GHz for intersatellite links, all using dualcircular polarization. Pentriad, a system developed by DenaliTelecom, LLC, is proposed as aninternational system to provide broadbandmulticasting and Direct To Home (DTH)services in the northern hemisphere. Themain capacity of the Pentriad satellitesystem would be utilized for broadbandservices to telecommunications carriers. Itemploys a unique constellation of nineoperational satellites in highly ellipticalorbits distributed into three orbital planesplus three in-orbit spares and one groundspare. Pentriad proposes to use 2 GHz of V-band (near 50 GHz) for the uplink and 2GHz of Q-band (near 40 GHz) and 200MHz of Ku-band (near 12 MHz) for thedownlink. The Pentriad satellites have“bent pipe” transponders that relay, but donot process, data from one ground locationto another. The basic channel data rate is155 Mbps, which can be subdivided toprovide slower rates down to 10 Mbps orgrouped together to provide higher rates upto 3.875 Gbps. Teledesic is proposing a 72-satellitesystem called V-Band Supplement (VBS)to augment its already ambitious 288satellite Ka-band system (down from theoriginal 840 satellite constellation). LEO One has asked for additionalspectrum at 40 GHz for its 48 satellite“Little LEO” constellation for tracking andmessaging. Globalstar plans to launch an 80satellite V-band constellation called GS-40

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to expand its mobile telephony system. Inaddition, it plans to launch 64 Low EarthOrbit satellites and four geostationarysatellites that will operate at 2 GHz.

ANOTHER GOLD RUSH

V-band spectrum was not the only territoryon which companies rushed to stakeclaims. Additional new proposals at 2GHz meeting the FCC September 26deadline, contemporaneous with theV-band deadline, include a 16 satelliteMedium Earth Orbit constellationproposed by Boeing for navigation servicesto airlines, a 96 satellite constellationcalled Macrocell to expand andcomplement the IRIDIUM 66 satelliteconstellation, and a 26 satelliteconstellation to expand the capacity of the17 satellite Ellipso system. In addition to the new filings, threeletters of intent asking spectrum at 2 GHzwere submitted by ICO GlobalCommunications for its 10 satellite MEOmobile telephony system, TMICommunications for CanSat-M3 tosupplement its operational MSat-1 satellitethat provides two-way voice, tracking, andpaging services, and INMARSAT for its 4satellite Horizons system that will providedata, voice, and videoconferencingcapabilities to portable computers.

CROWDED SKIES

The first geostationary satellite, SYNCOMIII, was successfully launched in 1964.Since that time approximately 250satellites have been launched into GEO, ofwhich about 170 are operational. Roughlyanother 80 satellites are on order toincrease or replace services at C-band andKu-band. About 165 "Big LEO" satellitesare planned for mobile telephony andanother 200 "Little LEO" satellites areplanned for messaging and data gathering.In Ka-band, about 70 geostationarysatellites have been proposed in addition tothe 288 satellite Teledesic LEOconstellation. To these we now addanother 250 satellites at S-band and nearly300 more at Q- and V-bands. The totalnumber of new satellites is staggering andis in excess of 1300 satellites. Not everyproposed system will be approved, funded,built, and supported by the market.However, it is clear that there is anenormous growth ahead in satellite

hardware and services. The true frontier isnowhere in sight.__________________________________Dr. Robert A. Nelson, P.E. is president ofSatellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, Maryland.

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Via Satellite, November 1999

The GlobalPositioning System

A National Resource

by Robert A. Nelson

On a recent trip to visit the JetPropulsion Laboratory, I flew fromWashington, DC to Los Angeles on a newBoeing 747-400 airplane. Thegeographical position of the plane and itsrelation to nearby cities was displayedthroughout the flight on a video screen inthe passenger cabin. When I arrived inLos Angeles, I rented a car that wasequipped with a navigator. Thenavigator guided me to my hotel inPasadena, displaying my position on amap and verbally giving me directionswith messages like “freeway exit aheadon the right followed by a left turn.”When I reached the hotel, it announcedthat I had arrived at my destination.Later, when I was to join a colleague fordinner, I found the restaurant listed in amenu and the navigator took me there.

This remarkable navigation capabilityis made possible by the GlobalPositioning System (GPS). It wasoriginally designed jointly by the U.S.Navy and the U.S. Air Force to permitthe determination of position and time formilitary troops and guided missiles.However, GPS has also become the basisfor position and time measurement byscientific laboratories and a widespectrum of applications in a multi-billion dollar commercial industry.Roughly one million receivers aremanufactured each year and the totalGPS market is expected to approach $ 10billion by the end of next year. The storyof GPS and its principles of measurementare the subjects of this article.

EARLY METHODS OFNAVIGATION The shape and size of the earth hasbeen known from the time of antiquity.The fact that the earth is a sphere waswell known to educated people as long

ago as the fourth century BC. In his bookOn the Heavens, Aristotle gave twoscientifically correct arguments. First,the shadow of the earth projected on themoon during a lunar eclipse appears to becurved. Second, the elevations of starschange as one travels north or south,while certain stars visible in Egypt cannotbe seen at all from Greece. The actual radius of the earth wasdetermined within one percent byEratosthenes in about 230 BC. He knewthat the sun was directly overhead atnoon on the summer solstice in Syene(Aswan, Egypt), since on that day itilluminated the water of a deep well. Atthe same time, he measured the length ofthe shadow cast by a column on thegrounds of the library at Alexandria,which was nearly due north. Thedistance between Alexandria and Syenehad been well established by professionalrunners and camel caravans. ThusEratosthenes was able to compute theearth’s radius from the difference inlatitude that he inferred from hismeasurement. In terms of modern unitsof length, he arrived at the figure ofabout6400 km. By comparison, the actualmean radius is 6371 km (the earth is notprecisely spherical, as the polar radius is21 km less than the equatorial radius of6378 km). The ability to determine one’s positionon the earth was the next major problemto be addressed. In the second century,AD the Greek astronomer ClaudiusPtolemy prepared a geographical atlas, inwhich he estimated the latitude andlongitude of principal cities of theMediterranean world. Ptolemy is mostfamous, however, for his geocentrictheory of planetary motion, which wasthe basis for astronomical catalogs untilNicholas Copernicus published hisheliocentric theory in 1543. Historically, methods of navigationover the earth's surface have involved theangular measurement of star positions todetermine latitude. The latitude of one’sposition is equal to the elevation of thepole star. The position of the pole star onthe celestial sphere is only temporary,however, due to precession of the earth'saxis of rotation through a circle of radius23.5° over a period of 26,000 years. Atthe time of Julius Caesar, there was nostar sufficiently close to the north

celestial pole to be called a pole star. In13,000 years, the star Vega will be nearthe pole. It is perhaps not a coincidencethat mariners did not venture far fromvisible land until the era of ChristopherColumbus, when true north could bedetermined using the star we now callPolaris. Even then the star’s diurnalrotation caused an apparent variation ofthe compass needle. Polaris in 1492described a radius of about 3.5° about thecelestial pole, compared to 1° today. Atsea, however, Columbus and hiscontemporaries depended primarily onthe mariner’s compass and deadreckoning. The determination of longitude wasmuch more difficult. Longitude isobtained astronomically from thedifference between the observed time of acelestial event, such as an eclipse, and thecorresponding time tabulated for areference location. For each hour ofdifference in time, the difference inlongitude is 15 degrees. Columbus himself attempted toestimate his longitude on his fourthvoyage to the New World by observingthe time of a lunar eclipse as seen fromthe harbor of Santa Gloria in Jamaica onFebruary 29, 1504. In his distinguishedbiography Admiral of the Ocean Sea,Samuel Eliot Morrison states thatColumbus measured the duration of theeclipse with an hour-glass anddetermined his position as seven hoursand fifteen minutes west of Cadiz, Spain,according to the predicted eclipse time inan almanac he carried aboard his ship.Over the preceding year, while his shipwas marooned in the harbor, Columbushad determined the latitude of SantaGloria by numerous observations of thepole star. He made out his latitude to be18°, which was in error by less than halfa degree and was one of the best recordedobservations of latitude in the earlysixteenth century, but his estimatedlongitude was off by some 38 degrees. Columbus also made legendary use ofthis eclipse by threatening the nativeswith the disfavor of God, as indicated bya portent from Heaven, if they did notbring desperately needed provisions tohis men. When the eclipse arrived aspredicted, the natives pleaded for theAdmiral’s intervention, promising tofurnish all the food that was needed.

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New knowledge of the universe wasrevealed by Galileo Galilei in his bookThe Starry Messenger. This book,published in Venice in 1610, reported thetelescopic discoveries of hundreds of newstars, the craters on the moon, the phasesof Venus, the rings of Saturn, sunspots,and the four inner satellites of Jupiter.Galileo suggested using the eclipses ofJupiter’s satellites as a celestial clock forthe practical determination of longitude,but the calculation of an accurateephemeris and the difficulty of observingthe satellites from the deck of a rollingship prevented use of this method at sea.Nevertheless, James Bradley, the thirdAstronomer Royal of England,successfully applied the technique in1726 to determine the longitudes ofLisbon and New York with considerableaccuracy. Inability to measure longitude at seahad the potential of catastrophicconsequences for sailing vesselsexploring the new world, carrying cargo,and conquering new territories.Shipwrecks were common. On October22, 1707 a fleet of twenty-one shipsunder the command of Admiral SirClowdisley Shovell was returning toEngland after an unsuccessful militaryattack on Toulon in the Mediterranean.As the fleet approached the EnglishChannel in dense fog, the flagship andthree others foundered on the coastalrocks and nearly two thousand menperished. Stunned by this unprecedented loss,the British government in 1714 offered aprize of £20,000 for a method todetermine longitude at sea within a half adegree. The scientific establishmentbelieved that the solution would beobtained from observations of the moon.The German cartographer Tobias Mayer,aided by new mathematical methodsdeveloped by Leonard Euler, offeredimproved tables of the moon in 1757.The recorded position of the moon at agiven time as seen from a referencemeridian could be compared with itsposition at the local time to determine theangular position west or east. Just as the astronomical methodappeared to achieve realization, theBritish craftsman John Harrison provideda different solution through his inventionof the marine chronometer. The story of

Harrison’s clock has been recounted inDava Sobel’s popular book, Longitude. Both methods were tested by seatrials. The lunar tables permitted thedetermination of longitude within fourminutes of arc, but with Harrison'schronometer the precision was only oneminute of arc. Ultimately, portions of theprize money were awarded to Mayer’swidow, Euler, and Harrison. In the twentieth century, with thedevelopment of radio transmitters,another class of navigation aids wascreated using terrestrial radio beacons,including Loran and Omega. Finally, thetechnology of artificial satellites madepossible navigation and positiondetermination using line of sight signalsinvolving the measurement of Dopplershift or phase difference.

TRANSIT

Transit, the Navy Navigation SatelliteSystem, was conceived in the late 1950sand deployed in the mid-1960s. It wasfinally retired in 1996 after nearly 33years of service. The Transit system wasdeveloped because of the need to provideaccurate navigation data for Polarismissile submarines. As related in anhistorical perspective by BradfordParkinson, et al. in the journal Navigation(Spring 1995), the concept was suggestedby the predictable but dramatic Dopplerfrequency shifts from the first Sputniksatellite, launched by the Soviet Union inOctober, 1957. The Doppler-shiftedsignals enabled a determination of theorbit using data recorded at one siteduring a single pass of the satellite.Conversely, if a satellite's orbit werealready known, a radio receiver's positioncould be determined from the sameDoppler measurements. The Transit system was composed ofsix satellites in nearly circular, polarorbits at an altitude of 1075 km. Theperiod of revolution was 107 minutes.The system employed essentially thesame Doppler data used to track theSputnik satellite. However, the orbits ofthe Transit satellites were preciselydetermined by tracking them at widelyspaced fixed sites. Under favorableconditions, the rms accuracy was 35 to100 meters. The main problem withTransit was the large gaps in coverage.

Users had to interpolate their positionsbetween passes.

GLOBAL POSITIONINGSYSTEM

The success of Transit stimulated boththe U.S. Navy and the U.S. Air Force toinvestigate more advanced versions of aspace-based navigation system withenhanced capabilities. Recognizing theneed for a combined effort, the DeputySecretary of Defense established a JointProgram Office in 1973. TheNAVSTAR Global Positioning System(GPS) was thus created. In contrast to Transit, GPS providescontinuous coverage. Also, rather thanDoppler shift, satellite range isdetermined from phase difference. There are two types of observables.One is pseudorange, which is the offsetbetween a pseudorandom noise (PRN)coded signal from the satellite and areplica code generated in the user’sreceiver, multiplied by the speed of light.The other is accumulated delta range(ADR), which is a measure of carrierphase. The determination of position may bedescribed as the process of triangulationusing the measured range between theuser and four or more satellites. Theranges are inferred from the time ofpropagation of the satellite signals. Foursatellites are required to determine thethree coordinates of position and time.The time is involved in the correction tothe receiver clock and is ultimatelyeliminated from the measurement ofposition. High precision is made possiblethrough the use of atomic clocks carriedon-board the satellites. Each satellite hastwo cesium clocks and two rubidiumclocks, which maintain time with aprecision of a few parts in 1013 or 1014

over a few hours, or better than 10nanoseconds. In terms of the distancetraversed by an electromagnetic signal atthe speed of light, each nanosecondcorresponds to about 30 centimeters.Thus the precision of GPS clocks permitsa real time measurement of distance towithin a few meters. With post-processed carrier phase measurements, aprecision of a few centimeters can beachieved.

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The design of the GPS constellationhad the fundamental requirement that atleast four satellites must be visible at alltimes from any point on earth. Thetradeoffs included visibility, the need topass over the ground control stations inthe United States, cost, and sparingefficiency. The orbital configuration approved in1973 was a total of 24 satellites,consisting of 8 satellites plus one spare ineach of three equally spaced orbitalplanes. The orbital radius was 26,562km, corresponding to a period ofrevolution of 12 sidereal hours, withrepeating ground traces. Each satellitearrived over a given point four minutesearlier each day. A common orbitalinclination of 63° was selected tomaximize the on-orbit payload mass withlaunches from the Western Test Range.This configuration ensured between 6and 11 satellites in view at any time. As envisioned ten years later, theinclination was reduced to 55° and thenumber of planes was increased to six.The constellation would consist of 18primary satellites, which represents theabsolute minimum number of satellitesrequired to provide continuous globalcoverage with at least four satellites inview at any point on the earth. Inaddition, there would be 3 on-orbitspares. The operational system, as presentlydeployed, consists of 21 primarysatellites and 3 on-orbit spares,comprising four satellites in each of sixorbital planes. Each orbital plane isinclined at 55°. This constellationimproves on the “18 plus 3” satelliteconstellation by more fully integratingthe three active spares.

SPACE SEGMENT

There have been several generationsof GPS satellites. The Block I satellites,built by Rockwell International, werelaunched between 1978 and 1985. Theyconsisted of eleven prototype satellites,including one launch failure, thatvalidated the system concept. The tensuccessful satellites had an averagelifetime of 8.76 years. The Block II and Block IIA satelliteswere also built by RockwellInternational. Block II consists of ninesatellites launched between 1989 and

1990. Block IIA, deployed between 1990and 1997, consists of 19 satellites withseveral navigation enhancements. InApril 1995, GPS was declared fullyoperational with a constellation of 24operational spacecraft and a completedground segment. The 28 Block II/IIAsatellites have exceeded their specifiedmission duration of 6 years and areexpected to have an average lifetime ofmore than 10 years. Block IIR comprises 20 replacementsatellites that incorporate autonomousnavigation based on crosslink ranging.These satellites are being manufacturedby Lockheed Martin. The first launch in1997 resulted in a launch failure. Thefirst IIR satellite to reach orbit was alsolaunched in 1997. The second GPS 2Rsatellite was successfully launchedaboard a Delta 2 rocket on October 7,1999. One to four more launches areanticipated over the next year. The fourth generation of satellites isthe Block II follow-on (Block IIF). Thisprogram includes the procurement of 33satellites and the operation and support ofa new GPS operational control segment.The Block IIF program was awarded toRockwell (now a part of Boeing).Further details may be found in a specialissue of the Proceedings of the IEEE forJanuary, 1999.

CONTROL SEGMENT

The Master Control Station for GPS islocated at Schriever Air Force Base inColorado Springs, CO. The MCSmaintains the satellite constellation andperforms the stationkeeping and attitudecontrol maneuvers. It also determines theorbit and clock parameters with a Kalmanfilter using measurements from fivemonitor stations distributed around theworld. The orbit error is about 1.5meters. GPS orbits are derived independentlyby various scientific organizations usingcarrier phase and post-processing. Thestate of the art is exemplified by the workof the International GPS Service (IGS),which produces orbits with an accuracyof approximately 3 centimeters withintwo weeks. The system time reference is managedby the U.S. Naval Observatory inWashington, DC. GPS time is measuredfrom Saturday/Sunday midnight at the

beginning of the week. The GPS timescale is a composite “paper clock” that issynchronized to keep step withCoordinated Universal Time (UTC) andInternational Atomic Time (TAI).However, UTC differs from TAI by anintegral number of leap seconds tomaintain correspondence with therotation of the earth, whereas GPS timedoes not include leap seconds. Theorigin of GPS time is midnight onJanuary 5/6, 1980 (UTC). At present,TAI is ahead of UTC by 32 seconds, TAIis ahead of GPS by 19 seconds, and GPSis ahead of UTC by 13 seconds. Only1,024 weeks were allotted from the originbefore the system time is reset to zerobecause 10 bits are allocated for thecalendar function (1,024 is the tenthpower of 2). Thus the first GPS rolloveroccurred at midnight on August 21, 1999.The next GPS rollover will take placeMay 25, 2019.

SIGNAL STRUCTURE

The satellite position at any time iscomputed in the user’s receiver from thenavigation message that is contained in a50 bps data stream. The orbit isrepresented for each one hour period by aset of 15 Keplerian orbital elements, withharmonic coefficients arising fromperturbations, and is updated every fourhours. This data stream is modulated by eachof two code division multiple access, orspread spectrum, pseudorandom noise(PRN) codes: the coarse/acquisition C/Acode (sometimes called the clear/accesscode) and the precision P code. The Pcode can be encrypted to produce asecure signal called the Y code. Thisfeature is known as the Anti-Spoof (AS)mode, which is intended to defeatdeception jamming by adversaries. TheC/A code is used for satellite acquisitionand for position determination by civilreceivers. The P(Y) code is used bymilitary and other authorized receivers. The C/A code is a Gold code ofregister size 10, which has a sequencelength of 1023 chips and a chipping rateof 1.023 MHz and thus repeats itselfevery 1 millisecond. (The term “chip” isused instead of “bit” to indicate that thePRN code contains no information.) TheP code is a long code of length 2.3547 x1014 chips with a chipping rate of 10

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times the C/A code, or 10.23 MHz. Atthis rate, the P code has a period of38.058 weeks, but it is truncated on aweekly basis so that 38 segments areavailable for the constellation. Eachsatellite uses a different member of theC/A Gold code family and a differentone-week segment of the P codesequence. The GPS satellites transmit signals attwo carrier frequencies: the L1component with a center frequency of1575.42 MHz, and the L2 componentwith a center frequency of 1227.60 MHz.These frequencies are derived from themaster clock frequency of 10.23 MHz,with L1 = 154 x 10.23 MHz and L2 =120 x 10.23 MHz. The L1 frequencytransmits both the P code and the C/Acode, while the L2 frequency transmitsonly the P code. The second P codefrequency permits a dual-frequencymeasurement of the ionospheric groupdelay. The P-code receiver has a two-sigma rms horizontal position error ofabout 5 meters. The single frequency C/A code usermust model the ionospheric delay withless accuracy. In addition, the C/A codeis intentionally degraded by a techniquecalled Selective Availability (SA), whichintroduces errors of 50 to 100 meters bydithering the satellite clock data. Throughdifferential GPS measurements, however,position accuracy can be improved byreducing SA and environmental errors. The transmitted signal from a GPSsatellite has right hand circularpolarization. According to the GPSInterface Control Document, thespecified minimum signal strength at anelevation angle of 5° into a linearlypolarized receiver antenna with a gain of3 dB (approximately equivalent to acircularly polarized antenna with a gainof 0 dB) is - 160 dBW for the L1 C/Acode, - 163 dBW for the L1 P code, and -166 dBW for the L2 P code. The L2signal is transmitted at a lower powerlevel since it is used primarily for theionospheric delay correction.

PSEUDORANGE

The fundamental measurement in theGlobal Positioning System ispseudorange. The user equipmentreceives the PRN code from a satelliteand, having identified the satellite,

generates a replica code. The phase bywhich the replica code must be shifted inthe receiver to maintain maximumcorrelation with the satellite code,multiplied by the speed of light, isapproximately equal to the satellite range.It is called the pseudorange because themeasurement must be corrected by avariety of factors to obtain the true range. The corrections that must be appliedinclude signal propagation delays causedby the ionosphere and the troposphere,the space vehicle clock error, and theuser’s receiver clock error. Theionosphere correction is obtained eitherby measurement of dispersion using thetwo frequencies L1 and L2 or bycalculation from a mathematical model,but the tropospheric delay must becalculated since the troposphere isnondispersive. The true geometricdistance to each satellite is obtained byapplying these corrections to themeasured pseudorange. Other error sources and modelingerrors continue to be investigated. Forexample, a recent modification of theKalman filter has led to improvedperformance. Studies have also shownthat solar radiation pressure models mayneed revision and there is some newevidence that the earth’s magnetic fieldmay contribute to a small orbit periodvariation in the satellite clockfrequencies.

CARRIER PHASE

Carrier phase is used to performmeasurements with a precision thatgreatly exceeds those based onpseudorange. However, a carrier phasemeasurement must resolve an integralcycle ambiguity whereas thepseudorange is unambiguous. The wavelength of the L1 carrier isabout 19 centimeters. Thus with a cycleresolution of one percent, a differentialmeasurement at the level of a fewmillimeters is theoretically possible. Thistechnique has important applications togeodesy and analogous scientificprograms.

RELATIVITY

The precision of GPS measurements isso great that it requires the application ofAlbert Einstein’s special and generaltheories of relativity for the reduction of

its measurements. Professor CarrollAlley of the University of Maryland oncearticulated the significance of this fact ata scientific conference devoted to timemeasurement in 1979. He said, “I think itis appropriate ... to realize that the firstpractical application of Einstein’s ideas inactual engineering situations are with usin the fact that clocks are now so stablethat one must take these small effects intoaccount in a variety of systems that arenow undergoing development or areactually in use in comparing timeworldwide. It is no longer a matter ofscientific interest and scientificapplication, but it has moved into therealm of engineering necessity.” According to relativity theory, amoving clock appears to run slow withrespect to a similar clock that is at rest.This effect is called “time dilation.” Inaddition, a clock in a weaker gravitationalpotential appears to run fast incomparison to one that is in a strongergravitational potential. This gravitationaleffect is known in general as the “redshift” (only in this case it is actually a“blue shift”). GPS satellites revolve around theearth with a velocity of 3.874 km/s at analtitude of 20,184 km. Thus on accountof the its velocity, a satellite clockappears to run slow by 7 microsecondsper day when compared to a clock on theearth’s surface. But on account of thedifference in gravitational potential, thesatellite clock appears to run fast by 45microseconds per day. The net effect isthat the clock appears to run fast by 38microseconds per day. This is anenormous rate difference for an atomicclock with a precision of a fewnanoseconds. Thus to compensate forthis large secular rate, the clocks aregiven a rate offset prior to satellite launchof- 4.465 parts in 1010 from their nominalfrequency of 10.23 MHz so that onaverage they appear to run at the samerate as a clock on the ground. The actualfrequency of the satellite clocks beforelaunch is thus 10.22999999543 MHz. Although the GPS satellite orbits arenominally circular, there is always someresidual eccentricity. The eccentricitycauses the orbit to be slightly elliptical,and the velocity and altitude vary overone revolution. Thus, although theprincipal velocity and gravitational

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effects have been compensated by a rateoffset, there remains a slight residualvariation that is proportional to theeccentricity. For example, with an orbitaleccentricity of 0.02 there is a relativisticsinusoidal variation in the apparent clocktime having an amplitude of 46nanoseconds. This correction must becalculated and taken into account in theGPS receiver. The displacement of a receiver on thesurface of the earth due to the earth’srotation in inertial space during the timeof flight of the signal must also be takeninto account. This is a third relativisticeffect that is due to the universality of thespeed of light. The maximum correctionoccurs when the receiver is on theequator and the satellite is on the horizon.The time of flight of a GPS signal fromthe satellite to a receiver on the earth isthen 86 milliseconds and the correction tothe range measurement resulting from thereceiver displacement is 133nanoseconds. An analogous correctionmust be applied by a receiver on amoving platform, such as an aircraft oranother satellite. This effect, asinterpreted by an observer in the rotatingframe of reference of the earth, is calledthe Sagnac effect. It is also the basis fora laser ring gyro in an inertial navigationsystem.

GPS MODERNIZATION

In 1996, a Presidential DecisionDirective stated the president wouldreview the issue of Selective Availabilityin 2000 with the objective ofdiscontinuing SA no later than 2006. Inaddition, both the L1 and L2 GPS signalswould be made available to civil usersand a new civil 10.23 MHz signal wouldbe authorized. To satisfy the needs ofaviation, the third civil frequency, knownas L5, would be centered at 1176.45MHz, in the Aeronautical RadioNavigation Services (ARNS) band,subject to approval at the World RadioConference in 2000. According to KeithMcDonald in an article on GPSmodernization published in theSeptember, 1999 GPS World, with SAremoved the civil GPS accuracy wouldbe improved to about 10 to 30 meters.With the addition of a second frequencyfor ionospheric group delay corrections,the civil accuracy would become about 5

to 10 meters. A third frequency wouldpermit the creation of two beatfrequencies that would yieldone-meter accuracy in real time. A variety of other enhancements areunder consideration, including increasedpower, the addition of a new militarycode at the L1 and L2 frequencies,additional ground stations, more frequentuploads, and an increase in the number ofsatellites. These policy initiatives aredriven by the dual needs of maintainingnational security while supporting thegrowing dependence on GPS bycommercial industry. When theseupgrades would begin to be implementedin the Block IIR and IIF satellitesdepends on GPS funding. Besides providing position, GPS is areference for time with an accuracy of 10nanoseconds or better. Its broadcast timesignals are used for national defense,commercial, and scientific purposes. Theprecision and universal availability ofGPS time has produced a paradigm shiftin time measurement and dissemination,with GPS evolving from a secondarysource to a fundamental reference initself. The international community wantsassurance that it can rely on theavailability of GPS and continued U.S.support for the system. The RussianGlobal Navigation Satellite System(GLONASS) has been an alternative, buteconomic conditions in Russia havethreatened its continued viability.Consequently, the European Union isconsidering the creation of a navigationsystem of its own, called Galileo, toavoide relying on the U.S. GPS andRussian GLONASS programs. The Global Positioning System is avital national resource. Over the pastthirty years it has made the transitionfrom concept to reality, representingtoday an operational system on which theentire world has become dependent.Both technical improvements and anenlightened national policy will benecessary to ensure its continued growthinto the twenty-first century.__________________________

Dr. Robert A. Nelson, P.E. is presidentof Satellite Engineering ResearchCorporation, a satellite engineeringconsulting firm in Bethesda, Maryland.He is Via Satellite’s Technical Editor.

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Via Satellite, February 2000

The InternationalSystem of Units (SI)Its History and Use inScience and Industry

by Robert A. Nelson

On September 23, 1999 the MarsClimate Orbiter was lost during anorbit injection maneuver when thespacecraft crashed onto the surfaceof Mars. The principal cause of themishap was traced to a thrustercalibration table, in which Britishunits instead of metric units wereused. The software for celestialnavigation at the Jet PropulsionLaboratory expected the thrusterimpulse data to be expressed innewton seconds, but LockheedMartin Astronautics in Denver,which built the orbiter, provided thevalues in pound-force seconds,causing the impulse to be interpretedas roughly one-fourth its actualvalue. The failure was magnified bythe loss of the companion spacecraftMars Polar Lander due to anunknown cause on December 3. The incident renews acontroversy that has existed in theUnited States since the beginningof the space program regarding theuse of metric or British units ofmeasurement. To put the issue intoperspective, this article reviews thehistory of the metric system and itsmodern version, the InternationalSystem of Units (SI). The originand evolution of the metric units,and the role they have played in theUnited States, will be summarized.Technical details and definitionswill be provided for reference.Finally, the use of metric units inthe satellite industry will beexamined.

ORIGIN OF THE METRICSYSTEM

The metric system was one ofmany reforms introduced in Franceduring the period between 1789and 1799, known as the FrenchRevolution. The need for reform inthe system of weights andmeasures, as in other affairs, had

long been recognized. No otheraspect of applied science affects thecourse of human activity so directlyand universally. Prior to the metric system, therehad existed in France a disorderlyvariety of measures, such as forlength, volume, or mass, that werearbitrary in size and variable fromone town to the next. In Paris theunit of length was the Pied de Roiand the unit of mass was the Livrepoids de marc. These units couldbe traced back to Charlemagne.However, all attempts to imposethe “Parisian” units on the wholecountry were fruitless, as they wereopposed by the guilds and nobleswho benefited from the confusion. The advocates of reform soughtto guarantee the uniformity andpermanence of the units of measureby taking them from propertiesderived from nature. In 1670, theabbe Gabriel Mouton of Lyonsproposed a unit of length equal toone minute of arc on the earth’ssurface, which he divided intodecimal fractions. He suggested apendulum of specified period as ameans of preserving one of thesesubmultiples. The conditions required for thecreation of a new measurementsystem were made possible by theFrench Revolution, an event thatwas initially provoked by a nationalfinancial crisis. In 1787 King LouisXVI convened the Estates General,an institution that had last met in1614, for the purpose of imposingnew taxes to avert a state ofbankruptcy. As they assembled in1789, the commoners, representingthe Third Estate, declaredthemselves to be the onlylegitimate representatives of thepeople, and succeeded in havingthe clergy and nobility join them inthe formation of the NationalAssembly. Over the next two years,they drafted a new constitution. In 1790, Charles-Maurice deTalleyrand, Bishop of Autun,presented to the National Assemblya plan to devise a system of unitsbased on the length of a pendulumbeating seconds at latitude 45°. Thenew order was envisioned as an

“enterprise whose result shouldbelong some day to the wholeworld.” He sought, but failed toobtain, the collaboration ofEngland, which was concurrentlyconsidering a similar proposal bySir John Riggs Miller. The two founding principleswere that the system would bebased on scientific observation andthat it would be a decimal system.A distinguished commission of theFrench Academy of Sciences,including J. L. Lagrange and PierreSimon Laplace, considered the unitof length. Rejecting the secondspendulum as insufficiently precise,the commission defined the unit,given the name metre in 1793, asone ten millionth of a quarter of theearth’s meridian passing throughParis. The proposal was acceptedby the National Assembly onMarch 26, 1791. The definition of the meterreflected the extensive interest ofFrench scientists in the figure of theearth. Surveys in Lapland byPierre Louis Maupertuis in 1736and in France by Nicolas Lacaillein 1740 had refined the value of theearth’s radius and establisheddefinitively that the shape of theearth is oblate. Additional meridianarcs were measured in Peru in1735 – 1743 and at the Cape ofGood Hope in 1751. To determine the length of themeter, a new survey was conductedby the astronomers Jean BaptisteDelambre and P.F.A. Mechainbetween Dunkirk, in France on theEnglish Channel, and Barcelona,Spain, on the coast of theMediterranean Sea. This work wasbegun in 1792 and completed in1798, enduring the hardshipsof the “reign of terror” and theturmoil of revolution. We nowknow that the quadrant ofthe earth is 10 001 966 meters (inthe WGS 84 model) instead ofexactly 10 000 000 meters asoriginally planned. The principalsource of error was the assumedvalue of the earth’s flattening usedin correcting for oblateness. The unit of volume, the pinte(later renamed the litre), was

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defined as the volume of a cubehaving a side equal to one-tenth ofa meter. The unit of mass, thegrave (later renamed thekilogramme), was defined as themass of one pinte of distilled waterat the temperature of melting ice. Inaddition, the centigrade scale fortemperature was adopted, withfixed points at 0 °C and 100 °Crepresenting the freezing andboiling points of water (nowreplaced by the Celsius scale). The work to determine theunit of mass was assigned toAntoine-Laurent Lavoisier, thefather of modern chemistry, andRene-Just Hauy. In a tragedysymbolic of the period, Lavoisierwas guillotined by a revolutionarytribunal in 1794. The measure-ments were completed by LouisLefevre-Gineau and GiovanniFabbroni in 1799. However, theyfound that they could not coolliquid water to exactly 0 °C andthat the maximum density occurs at4 °C, not at 0 °C as had beensupposed. Therefore, the definitionof the kilogram was amended tospecify the temperature ofmaximum density. We now knowthat the intended mass was 0.999972 kg, i.e., 1000.028 cm3 insteadof exactly 1000 cm3 for the volumeof 1 kilogram of pure water at 4 °C. On August 1, 1793 the NationalConvention, which by then ruledFrance, issued a decree adoptingthe preliminary definitions andterms. The “methodical” nomen-clature, specifying multiples andfractions of the units by Greek andLatin prefixes, was chosen in favorof the “common” nomenclature,involving separate names. A new calendar was establishedby a law of October 5, 1793. Itsorigin was designated retroactivelyas September 22, 1792 tocommemorate the overthrow of themonarchy and the inception of theRepublic of France. The FrenchRevolutionary Calendar consistedof twelve months of thirty dayseach, concluded by a five or six dayholiday. The months were givenpoetic names that suggested theprevailing seasons. Each month

was divided into three ten-dayweeks, or decades. The day itselfwas divided into decimal fractions,with 10 hours per day, 100 minutesper hour, and 100 seconds perminute. The calendar waspolitically, rather than scienti-fically, motivated, since it wasintended to weaken the influence ofChristianity. It was abolished byNapoleon in 1806 in return forrecognition by the Church of hisauthority as emperor of France.Although the calendar reformremained in effect for twelve years,the new method of keeping the timeof day required the replacement ofvalued clocks and timepieces andwas never actually used in practice. The metric system was officiallyadopted on April 7, 1795. Thegovernment issued a decree (Loi du18 germinal, an III) formalizing theadoption of the definitions andterms that are in use today. A brassbar was made to represent theprovisional meter, obtained fromthe survey of Lacaille, and aprovisional standard for thekilogram was derived. A scientific conference was heldfrom 1798 to 1799 that includedrepresentatives of the Netherlands,Switzerland, Denmark, Spain, andthe Italian states, as well as France,to validate the computations anddesign prototype standards.Permanent standards for the meterand kilogram made from platinumwere constructed. The full lengthof the meter bar represented theunit. These standards weredeposited in the Archives of theRepublic. They became official byan act of December 10, 1799. During the Napoleonic era,several regressive acts were passedthat temporarily revived oldtraditions. Thus in spite of itsauspicious beginning, the metricsystem was not quickly adopted inFrance. Although the systemcontinued to be taught in theschools, lack of funds prevented thedistribution of secondary standards.Finally, after a three year transitionperiod, the metric system becamecompulsory throughout France asof January 1, 1840.

REACTION IN THE UNITEDSTATES

The importance of a uniformsystem of weights and measureswas recognized in the UnitedStates, as in France. Article I,Section 8, of the U.S. Constitutionprovides that Congress shall havethe power “to coin money ... andfix the standard of weights andmeasures.” However, although theprogressive concept of decimalcoinage was introduced, the earlyAmerican settlers both retained andcultivated the customs and tools oftheir British heritage, including themeasures of length and mass. Incontrast to the French Revolution,the “American Revolution” was nota revolution at all, but was rather awar of independence. In 1790, the same year thatTalleyrand proposed metric reformin France, President GeorgeWashington referred the subject ofweights and measures to hisSecretary of State, ThomasJefferson. In a report submitted tothe House of Representatives,Jefferson considered twoalternatives: if the existingmeasures were retained they couldbe rendered more simple anduniform, or if a new system wereadopted, he favored a decimalsystem based on the principle of theseconds pendulum. As it waseventually formulated, Jeffersondid not endorse the metric system,primarily because the metric unit oflength could not be checkedwithout a sizable scientificoperation on European soil. The political situation at the turnof the eighteenth century also madeconsideration of the metric systemimpractical. Although France underLouis XVI had supported thecolonies in the war with England,by 1797 there was manifesthostility. The revolutionary climatein France was viewed by theexternal world with a mixture ofcuriosity and alarm. The NationalConvention had been replaced bythe Directory, and French officialswho had been sympathetic to theUnited States either had been

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executed or were in exile. Inaddition, a treaty negotiated withEngland by John Jay in 1795regarding settlement of theNorthwest Territories and tradewith the British West Indies wasinterpreted by France as evidenceof an Anglo-American alliance.France retaliated by permitting herships to prey upon Americanmerchant vessels and FederalistPresident John Adams prepared fora French invasion. Thus in 1798,when dignitaries from foreigncountries were assembled in Paristo learn of France’s progress withmetrological reform, the UnitedStates was not invited. A definitive investigation wasprepared in 1821 by Secretary ofState John Quincy Adams that wasto remove the issue from furtherconsideration for the next 45 years.He found that the standards oflength, volume, and mass usedthroughout the 22 states of theUnion were already substantiallyuniform, unlike the disparatemeasures that had existed in Franceprior to the French Revolution.Moreover, it was not at all evidentthat the metric system would bepermanent, since even in France itsuse was sporadic and, in fact, theconsistent terminology had beenrepealed in 1812 by Napoleon.Therefore, if the metric systemfailed to win support in earlyAmerica, it was not for want ofrecognition. Serious consideration of themetric system did not occur againuntil after the Civil War. In 1866,upon the advice of the NationalAcademy of Sciences, the metricsystem was made legal by theThirty-Ninth Congress. The Actwas signed into law on July 28 byPresident Andrew Johnson.

TREATY OF THE METER

A series of internationalexpositions in the middle of thenineteenth century enabled theFrench government to promote themetric system for world use.Between 1870 and 1872, with aninterruption caused by the Franco-Prussian War, an international

meeting of scientists was held toconsider the design of newinternational metric standards thatwould replace the meter andkilogram of the French Archives.A Diplomatic Conference on theMeter was convened to ratify thescientific decisions. Formalinternational approval was securedby the Treaty of the Meter, signedin Paris by the delegates of 17countries, including the UnitedStates, on May 20, 1875. The treaty established theInternational Bureau of Weightsand Measures (BIPM). It alsoprovided for the creation of anInternational Committee forWeights and Measures (CIPM) torun the Bureau and the GeneralConference on Weights andMeasures (CGPM) as the formaldiplomatic body that would ratifychanges as the need arose. TheFrench government offered thePavillon de Breteuil, once a smallroyal palace, to serve asheadquarters for the Bureau inSevres, France near Paris. Thegrounds of the estate form a tinyinternational enclave within Frenchterritory. The first three kilograms weremade in 1880 and one was chosenas the international prototype. In1884 an additional 40 kilogramsand 30 meter bars were obtained.They were all manufactured from aan alloy of 90 percent platinum and10 percent iridium by Johnson,Mathey and Company of London.The original meter and kilogram ofthe French Archives in theirexisting states were taken as thepoints of departure. The standardswere intercompared at theInternational Bureau. A particularmeter bar, number 6, became theinternational prototype. Theremaining standards weredistributed to the signatories. Thework was approved by the FirstGeneral Conference on Weightsand Measures in 1889. The United States receivedmeters 21 and 27 and kilograms 4and 20. On January 2, 1890 theseals to the shipping cases formeter 27 and kilogram 20 were

broken in an official ceremony atthe White House with PresidentBenjamin Harrison presiding. Thestandards were deposited in theOffice of Weights and Measures ofthe U.S. Coast and GeodeticSurvey.

U.S. CUSTOMARY UNITS

The U.S. customary units were tiedto the British and French units by avariety of indirect comparisons. Troy weight was the standardfor the minting of coins. Congresscould be ambivalent aboutnonuniformity in standards fortrade, but it could not toleratenonuniformity in its standards formoney. Therefore, in 1827 a brasscopy of the British troy pound of1758 was secured by Ambassadorto England and former Secretary ofthe Treasury, Albert Gallatin. Thisstandard was kept in thePhiladelphia mint and lesser copieswere made and distributed to othermints. The troy pound of thePhiladelphia mint was virtually theprimary standard for commercialtransactions until 1857 andremained the standard for coinsuntil 1911. The semi-official standards usedin commerce for a quarter centurymay be attributed to FerdinandHassler, who was appointedsuperintendent of the newlyorganized Coast Survey in 1807. In1832 the Treasury Departmentdirected Hassler to construct anddistribute to the states standards oflength, mass, and volume, andbalances by which masses might becompared. As the standard oflength, Hassler adopted theTroughton scale, an 82-inch brassbar made by Troughton of Londonfor the Coast Survey that Hasslerhad brought back from Europe in1815. The distance between the27th and 63rd engraved lines on asilver inlay scale down the centerof the bar was taken to be equal tothe British yard. The standard ofmass was the avoirdupois pound,derived from the troy pound of thePhiladelphia mint by the ratio 7000grains to 5760 grains. It wasrepresented by a brass knob weight

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that Hassler constructed andmarked with a star. Thus it hascome to be known as the “star”pound. The system of weights andmeasures in Great Britain had beenin use since the reign of QueenElizabeth I. Following a reformbegun in 1824, the imperialstandard avoirdupois pound wasmade the standard of mass in 1844and the imperial standard yard wasadopted in 1855. The imperialstandards were made legal by anAct of Parliament in 1855 and arepreserved in the Board of Trade inLondon. The United Statesreceived copies of the Britishimperial pound and yard, whichbecame the official U.S. standardsfrom 1857 until 1893. When the metric system wasmade lawful in the United States in1866, a companion resolution waspassed to distribute metricstandards to the states. TheTreasury Department had in itspossession several copies derivedfrom the meter and kilogram of theFrench Archives. These includedthe “Committee” meter andkilogram, which were an iron endstandard and a brass cylinder withknob copied from the Frenchprototypes, that Hassler hadbrought with him when heimmigrated to the United States in1805. He had received them as agift from his friend, J.G. Tralles,who was the Swiss representativeto the French metric convocation in1798 and a member of itscommittee on weights andmeasures. Also available were the“Arago” meter and kilogram,named after the French physicistwho certified them. They werepurchased by the United States in1821 through Albert Gallatin, thenminister to France. The Committeemeter and the Arago kilogram wereused as the prototypes for brassmetric standards that weredistributed to the states. In 1893, under a directive fromThomas C. Mendenhall,Superintendent of StandardWeights and Measures of the Coastand Geodetic Survey, the U.S.

customary units were redefined interms of the metric units. Theprimary standards of length andmass adopted were prototype meterNo. 27 and prototype kilogram No.20 that the United States hadreceived in 1889 as a signatory tothe Treaty of the Meter. The yardwas defined as 3600/3937 meterand the avoirdupois pound-masswas defined as 0.453 592 427 7kilogram. The conversion for masswas based on a comparisonbetween the British imperialstandard pound and theinternational prototype kilogramperformed in 1883. Thesedefinitions were used by theNational Bureau of Standards (nowthe National Institute of Standardsand Technology) from its foundingin 1901 until 1959. On July 1,1959 the definitions were fixed byinternational agreement among theEnglish-speaking countries to be1 yard = 0.9144 meter and1 pound-mass = 0.453 592 37kilogram exactly. The definition ofthe yard is equivalent to therelations 1 foot = 0.3048 meter and1 inch = 2.54 centimeters exactly. The derived unit of force in theBritish system is the pound-force(lbf), which is defined as theweight of one pound-mass (lbm) ata hypothetical location where theacceleration of gravity has thestandard value 9.806 65 m/s2

exactly. Thus, 1 lbf = 0.453 592 37kg x 9.806 65 m/s2 = 4.448 Napproximately. The slug (sl) is themass that receives an accelerationof one foot per second squaredunder a force of one pound-force.Thus 1 sl = (1 lbf)/(1 ft/s2) =(4.448 N)/(0.3048 m/s2) = 14.59 kg= 32.17 lbm approximately.

ELECTROMAGNETISM

The theories of electricity andmagnetism developed and maturedduring the early 1800s asfundamental discoveries were madeby Hans Christian Oersted,Andre-Marie Ampere, MichaelFaraday, and many others. Thepossibility of making measure-ments of terrestrial magnetism interms of mechanical units, that is,

in “absolute measure,” was firstpointed out by Karl FriedrichGauss in 1833. His analysis wascarried further to cover all electro-magnetic phenomena by WilhelmWeber, who in 1851 discussed amethod by which a complete set ofabsolute units might be developed. In 1861 a committee of theBritish Association for theAdvancement of Science, thatincluded William Thomson (laterLord Kelvin), James ClerkMaxwell, and James Prescott Joule,undertook a comprehensive studyof electrical measurements. Thiscommittee introduced the conceptof a system of units. Fourequations were sufficient todetermine the units of charge q,current I, voltage V, and resistanceR. These were either Coulomb’sforce law for charges or Ampere’sforce law for currents, the relationbetween charge and currentq = I t, Ohm’s law V = I R, and theequation for electrical workW = V q = I 2 R t, where t is time. A fundamental principle wasthat the system should be coherent.That is, the system is founded uponcertain base units for length, mass,and time, and derived units areobtained as products or quotientswithout requiring numericalfactors. The meter, gram, andmean solar second were selected asbase units. In 1873 a secondcommittee recommended acentimeter-gram-second (CGS)system of units because in thissystem the density of water isunity. Two parallel systems of unitswere devised, the electrostaticand electromagnetic subsystems,depending on whether the law offorce for electric charges or forelectric currents was taken asfundamental. The ratio of theelectrostatic to the electromagneticunit of charge or currentwas a fundamental experimentalconstant c. The committee also conductedresearch on electrical standards. Itissued a wire resistance standard,the “B.A. unit,” which soonbecame known as the “ohm.” The

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idea of naming units after eminentscientists was due to Sir CharlesBright and Latimer Clark. At the time, electricity andmagnetism were essentially twodistinct branches of experimentalphysics. However, in a series ofpapers published between 1856 and1865, Maxwell created a unifiedtheory based on the field conceptintroduced by Faraday. Hepredicted the existence ofelectromagnetic waves andidentified the “ratio of the units” cwith the speed of light. In 1888, Heinrich Hertz verifiedMaxwell’s prediction by generatingand detecting electromagneticwaves at microwave frequencies inthe laboratory. He also greatlysimplified the theory by eliminatingunnecessary physical assumptions.Thus the form of Maxwell’sequations as they are known tophysicists and engineers today isdue to Hertz. (Oliver Heavisidemade similar modifications andintroduced the use of vectors.) Inaddition, Hertz combined theelectrostatic and electromagneticCGS units into a single systemrelated by the speed of light c,which he called the “Gaussian”system of units. The recommendations of theB.A. committees were adopted bythe First International ElectricalCongress in Paris in 1881. Five“practical” electrical units weredefined as certain powers of 10 ofthe CGS units: the ohm, farad,volt, ampere, and coulomb. In1889, the Second Congress addedthe joule, watt, and a unit ofinductance, later given the namehenry. In 1901, the Italian engineerGiovanni Giorgi demonstrated thatthe practical electrical units and theMKS mechanical units could beincorporated into a single coherentsystem by (1) selecting the meter,kilogram, and second as the baseunits for mechanical quantities;(2) expanding the number of baseunits to four, including one of anelectrical nature; and (3) assigningphysical dimensions to thepermeability of free space µ0, with a

numerical value of 4π x 10−7 in a“rationalized” system or 10−7 in an“unrationalized” system. (The term“rationalized,” due to Heaviside,concerned where factors of 4πshould logically appear in theequations based on symmetry.) Thelast assumption implied that themagnetic flux density B andmagnetic field H, which are relatedin vacuum by the equationB = µ0 H, are physically distinctwith different units, whereas in theGaussian system they are of thesame character and aredimensionally equivalent. Ananalogous situation occurs for theelectric fields D and E that arerelated by D = ε0 E, where ε0 is thepermittivity of free space given byc2 = 1 / µ0 ε0 . In 1908, an InternationalConference on Electrical Units andStandards held in London adoptedindependent, easily reproducibleprimary electrical standards forresistance and current, representedby a column of mercury and asilver coulombmeter, respectively.These so-called “international”units went into effect in 1911, butthey soon became obsolete with thegrowth of the national standardslaboratories and the increasedapplication of electrical measure-ments to other fields of science. With the recognition of the needfor further international coopera-tion, the 6th CGPM amended theTreaty of the Meter in 1921 tocover the units of electricity andphotometry and the 7th CGPMcreated the Consultative Committeefor Electricity (CCE) in 1927. Bythe 8th CGPM in 1933 there was auniversal desire to replace the“international” electrical units with“absolute” units. Therefore, theInternational ElectrotechnicalCommission (IEC) recommendedto the CCE an absolute system ofunits based on Giorgi’s proposals,with the practical electrical unitsincorporated into a comprehensiveMKS system. The choice of thefourth unit was left undecided. At the meeting of the CCE inSeptember 1935, the delegate fromEngland, J.E. Sears, presented a

note that set the course for futureaction. He proposed that theampere be selected as the base unitfor electricity, defined in terms ofthe force per unit length betweentwo long parallel wires. The unitcould be preserved in the form ofwire coils for resistance andWeston cells for voltage bycalibration with a current balance.This recommendation wasunanimously accepted by the CCEand was adopted by the CIPM. Further progress was halted bythe intervention of World War II.Finally, in 1946, by authority givento it by the CGPM in 1933, theCIPM officially adopted the MKSpractical system of absoluteelectrical units to take effectJanuary 1, 1948.

TEMPERATURE

The concepts of temperature and itsmeasurement have evolved alongtwo parallel paths. On one hand,there has been the steady advancesince the early eighteenth centuryof mercury, alcohol, and resistancethermometers and the developmentof practical scales of temperaturebased on arbitrary fixed points. Onthe other hand, there has been thegrowth of gas thermometry and thedefinition of an absolute measureof temperature based on itsinterpretation in terms ofthermodynamic processes. The first reliable mercury-in-glass thermometers wereconstructed by the Germaninstrument maker Gabriel DanielFahrenheit in the period between1708 and 1724. He defined theFahrenheit scale by taking as fixedpoints the freezing point of watermixed with salt at 0 °F and thenormal temperature of the humanbody at 96 °F (now known to benearly 3° higher). The resultingfreezing and boiling points of purewater were 32 °F and 212 °F , with180° between them. In 1730,R.A.F. de Reaumer proposeddividing the same interval into 80°using an alcohol thermometer. Thisscale was widely used in Franceuntil the Revolution.

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Another mercury thermometerscale was invented by JosephDelisle in 1732. Delisle took theboiling point of water as 0° andworked downward to 150° as thefreezing point. In 1741 theSwedish astronomer AndersCelsius recalibrated the Delislethermometer with a centigradetemperature scale, having aninterval of 100° between the fixedpoints, again with the boiling pointat 0 °C but with the freezing pointdefined as 100 °C. By 1745, thebotanist Carl Linnaeus, a colleagueof Celsius, adopted a similar scale,but inverted it so that the freezingand boiling points are at 0 °C and100 °C, respectively, as iscustomary today. This centigradescale of temperature was adopted inFrance in 1794 during the creationof the metric system. The notion of an absolutetemperature scale based on athermodynamic process is due tothe French physicist GuillaumeAmontons, who is credited with theinvention of the air thermometer in1699. According to Amontons, thetemperature could be defined asproportional to the pressure of theair. In 1854 William Thomson(Lord Kelvin) proposed a definitionof temperature in terms of themacroscopic notion of heat or workaccording to the theory of an idealreversible heat engine, derived bythe French engineer Sadi Carnot.The ratio of the thermodynamictemperatures can be defined as theratio of the heat taken in to thatgiven out by a reversible heatengine operating in a Carnot cyle,so that T1/T2 = Q1/Q2. Thedefinition of thermodynamictemperature is thus independent ofthe working substance. Theresearch of James Clerk Maxwell,Ludwig Boltzmann, and J. WillardGibbs provided an equally validmicroscopic interpretation oftemperature as a measure of theenergy distribution of the particlesin the system. The Carnot cycle defines onlythe ratio of temperatures; todetermine the unit of temperature it

is also necessary to specify thetemperature difference betweentwo fixed points. Historically,these fixed points have been eitherthe freezing and boiling points ofwater in a relative scale, or thetriple point of water with respect toabsolute zero in a thermodynamicscale. Such a temperature scale canbe realized by means of an idealgas, whose equation of state isgiven by p V = n R T = N k T,where p is the pressure, V is thevolume, T is the thermodynamictemperature, and R is the universalgas constant. The number of molesis n = m/M = N/N0, where m is themass, M is the molar mass, N is thenumber of particles, and N0 isAvogadro's number. Theconnection between themacroscopic and microscopicviewpoints is thus made byBoltzmann's constant through therelation k = R/N0. The First General Conference ofWeights and Measures in 1889adopted the constant volumehydrogen scale based on fixedpoints at the freezing point (0 °C)and the boiling point (100 °C) ofwater at standard pressure. Thetemperature derived from themeasured pressure was corrected tothermodynamic temperature by aJoule-Thomson pourous-plugexperiment. By extrapolation of thedata, it was found that thethermodynamic temperature T,defined by the ideal gas equation ofstate, was related to the centigradetemperature tC by the approximaterelation T = tC + 273. The mercury thermometer wasselected as a secondary standard.Mercury-in-glass thermometers,made by Tonnelot of Paris oflead-free hard glass and carefullyannealed, were distributed to theparticipants. The United Statesreceived six of these thermometersas temperature standards for therange 0 °C to 100 °C to accompanyprototype meters 21 and 27 andprototype kilograms 4 and 20. In1948 the Ninth General Conferenceon Weights and Measures renamedthe centigrade scale as the Celsiusscale, with the unit degree Celsius.

INTERNATIONAL SYSTEMOF UNITS (SI)

By 1948 the General Conferenceon Weights and Measures wasresponsible for the units andstandards of length, mass,electricity, photometry,temperature, and ionizing radiation.At this time, the next major phasein the evolution of the metricsystem was begun. It was initiatedby a request of the InternationalUnion of Pure and Applied Physics“to adopt for international use apractical international system ofunits.” Thus the 9th CGPMdecided to define a complete list ofderived units. Derived units hadnot been considered previouslybecause they do not requireindependent standards. Also, theCGPM brought within its provincethe unit of time, which had been theprerogative of astronomers. The work was started by the10th CGPM in 1954 and wascompleted by the 11th CGPM in1960. During this period there wasan extensive revision andsimplification of the metric unitdefinitions, symbols, andterminology. The kelvin andcandela were added as base unitsfor thermodynamic temperatureand luminous intensity, and in 1971the mole was added as a seventhbase unit for amount of substance. The modern metric system isknown as the International Systemof Units, with the internationalabbreviation SI. It is founded onthe seven base units, summarized inTable 1, that by convention areregarded as dimensionallyindependent. All other units arederived units, formed coherently bymultiplying and dividing unitswithin the system without the useof numerical factors. Some derivedunits, including those with specialnames, are listed in Table 2. Forexample, the unit of force is thenewton, which is equal to akilogram meter per second squared,and the unit of energy is the joule,equal to a newton meter. Theexpression of multiples andsubmultiples of SI units is

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facilitated by the use of prefixes,listed in Table 3. (Additionalinformation is available on theInternet at the websites of theInternational Bureau of Weightsand Measures at http//www.bipm.frand the National Institute ofStandards and Technology athttp://physics.nist.gov/cuu.)

METRIC STANDARDS

One must distinguish a unit, whichis an abstract idealization, and astandard, which is the physicalembodiment of the unit. Since theorigin of the metric system, thestandards have undergone severalrevisions to reflect increasedprecision as the science ofmetrology has advanced. The meter. The internationalprototype meter standard of 1889was a platinum-iridium bar with anX-shaped cross section. The meterwas defined by the distancebetween two engraved lines on thetop surface of the bridge instead ofthe distance between the end faces.The meter was derived from themeter of the French Archives in itsexisting state and reference to theearth was abandoned. The permanence of theinternational prototype was verifiedby comparison with threecompanion bars, called “checkstandards.” In addition, there werenine measurements in terms of thered line of cadmium between 1892and 1942. The first of thesemeasurements was carried out byA. A. Michelson using theinterferometer which he invented.For this work, Michelson receivedthe Nobel Prize in physics in 1907. Improvements in monochro-matic light sources resulted in anew standard based on a well-defined wavelength of light. Asingle atomic isotope with an evenatomic number and an even massnumber is an ideal spectral standardbecause it eliminates complexityand hyperfine structure. Also,Doppler broadening is minimizedby using a gas of heavy atoms in alamp operated at a low temperature.Thus a particular red-orange

krypton-86 line was chosen, whosewavelength was obtained by directcomparison with the cadmiumwavelength. In 1960, the 11thCGPM defined the meter as thelength equal to 1 650 763.73wavelengths of this spectral line. Research on lasers at theBoulder, CO laboratory of theNational Bureau of Standardscontributed to another revision ofthe meter. The wavelength andfrequency of a stabilized helium-neon laser beam were measuredindependently to determine thespeed of light. The wavelengthwas obtained by comparison withthe krypton wavelength and thefrequency was determined by aseries of measurements traceable tothe cesium atomic standard for thesecond. The principal source oferror was in the profile of thekrypton spectral line representingthe meter itself. Consequently, in1983 the 17th CGPM adopted anew definition of the meter basedon this measurement as “the lengthof the path traveled by light invacuum during a time interval of1/299 792 458 of a second.” Theeffect of this definitionis to fix the speed of lightat exactly 299 792 458 m/s. Thusexperimental methods previouslyinterpreted as measurements of thespeed of light c (or equivalently,the permittivity of free space ε0)have become calibrations of length. The kilogram. In 1889 theinternational prototype kilogramwas adopted as the standard formass. The prototype kilogram is aplatinum-iridium cylinder withequal height and diameter of3.9 cm and slightly rounded edges.For a cylinder, these dimensionspresent the smallest surface area tovolume ratio to minimize wear. Thestandard is carefully preserved in avault at the International Bureau ofWeights and Measures and is usedonly on rare occasions. It remainsthe standard today. The kilogramis the only unit still defined interms of an arbitrary artifact insteadof a natural phenomenon. The second. Historically, theunit of time, the second, was

defined in terms of the period ofrotation of the earth on its axis as1/86 400 of a mean solar day.Meaning “second minute,” it wasfirst applied to timekeeping inabout the seventeenth century whenpendulum clocks were inventedthat could maintain time to thisprecision. By the twentieth century,astronomers realized that therotation of the earth is not constant.Due to gravitational tidal forcesproduced by the moon on theshallow seas, the length of the dayis increasing by about1.4 milliseconds per century. Theeffect can be measured bycomparing the computed paths ofancient solar eclipses on theassumption of uniform rotationwith the recorded locations on earthwhere they were actually observed.Consequently, in 1956 the secondwas redefined in terms of theperiod of revolution of the earthabout the sun, as represented by theTables of the Sun computed at theend of the nineteenth century by theastronomer Simon Newcomb of theU.S. Naval Observatory inWashington, DC. The second wasdefined to be 1/31 556 925.974 7 ofthe tropical year 1900. Theoperational significance of thisdefinition was to adopt the linearcoefficient in Newcomb’s formulafor the mean longitude of the sun todetermine the unit of time. The rapid development ofatomic clocks soon permitted yetanother definition. Accordingly, in1967 the 13th CGPM defined thesecond as “the duration of9 192 631 770 periods of theradiation corresponding to thetransition between the two groundstates of the cesium-133 atom.”This definition was based onobservations of the moon, whoseephemeris is tied indirectly to theapparent motion of the sun, andwas equivalent to the previousdefinition within the limits ofexperimental uncertainty. The ampere. The unit of electriccurrent, the ampere, is defined asthat constant current which, ifmaintained in each of two parallel,

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infinitely long wires with aseparation of 1 meter in vacuum,would produce a force per unitlength between them equal to 2 x10-7 N/m. This formal definitionserves to establish the value of theconstant µ0 as 4π x 10−7 N/A2

exactly. Although the base unit forelectricity is the ampere, theelectrical units are maintainedthrough the volt and the ohm. In the past, the practicalrepresentation of the volt was agroup of Weston saturatedcadmium-sulfate electrochemicalstandard cells. A primarycalibration experiment involved themeasurement of the force betweentwo coils of an “ampere balance” todetermine the current, while thecell voltage was compared to thepotential difference across a knownresistance. The ohm was represented by awire-wound standard resistor. Itsresistance was measured against theimpedance of an inductor or acapacitor at a known frequency.The inductance can be calculatedfrom the geometrical dimensionsalone. From about 1960, aso-called Thompson-Lampardcalculable capacitor has been used,in which only a singlemeasurement of length is required. Since the early 1970s, the volthas been maintained by means ofthe Josephson effect, a quantummechanical tunneling phenomenondiscovered by Brian Josephson in1962. A Josephson junction may beformed by two superconductingniobium films separated by anoxide insulating layer. If theJosephson junction is irradiated bymicrowaves at frequency f and thebias current is progressivelyincreased, the current-voltagecharacteristic is a step function, inwhich the dc bias voltage increasesdiscontinuously at discrete voltageintervals equal to f / KJ , whereKJ = 2 e / h is the Josephsonconstant, h is Planck’s constant,and e is the elementary charge. The ohm is now realized by thequantum Hall effect, acharacteristic of a two-dimensionalelectron gas discovered by Klaus

von Klitzing in 1980. In a devicesuch as a silicon metal-oxide-semiconductor field-effecttransistor (MOSFET), the Hallvoltage VH for a fixed current Iincreases in discrete steps as thegate voltage is increased. The Hallresistance, or RH = VH / I , isequal to an integral fraction of thevon Klitzing constant, given byRK = h / e2 = µ0 c / 2 α , where α isthe fine structure constant. Inpractice, RK can be measured interms of a laboratory resistancestandard, whose resistance isobtained by comparison with theimpedance of a calculablecapacitor, or it can be obtainedindirectly from α. A new method to determine therelation between the mechanicaland electromagnetic units that hasshown much promise is by meansof a “watt balance,” which hasgreater precision than an ordinaryampere balance. In this experiment,a current I is passed through a testcoil suspended in the magneticfield of a larger coil so that theforce F balances a known weightmg. Next the test coil is movedaxially through the magnetic fieldand the velocity v and inducedvoltage V are measured. By theequivalence of mechanical andelectrical power, F v = V I. Themagnetic field and apparatusgeometry drop out of thecalculation. The voltage V ismeasured in terms of the Josephsonconstant KJ while the current I iscalibrated by the voltage across aresistance known in terms of thevon Klitzing constant RK. Theexperiment determines KJ

2 RK (andthus h), which yields KJ if RK isassumed to be known in terms ofthe SI ohm. The Josephson and quantumHall effects provide highly uniformand conveniently reproduciblequantum mechanical standards forthe volt and the ohm. For thepurpose of practical engineeringmetrology, conventional values forthe Josephson constant and the vonKlitzing constant were adopted byinternational agreement startingJanuary 1, 1990. These values are

KJ-90 = 483 597.9 GHz/V andRK-90 = 25 812.807 Ω exactly. Thebest experimental SI values,obtained as part of an overall leastsquares adjustment of thefundamental constants completedin 1998, differ only slightly fromthese conventional values. The kelvin. From 1889 until1927, the national referencestandard of temperature for theUnited States comprised a set ofsixteen mercury-in-glassthermometers. In 1927, the CIPMadopted an InternationalTemperature Scale (ITS-27) basedon six reproducible equilibriumstates that agreed withthermodynamic temperatureswithin the limits of measurement.The platinum resistancethermometer, the platinumrhodium/platinum thermocouple,and the optical pyrometer wereused for interpolation over threetemperature ranges. This scale wasmodified in 1948 and clarified in1960. The Tenth General Conferenceon Weights and Measures in 1954adopted the absolute temperaturescale with a single fixed point,where the three phases of water(solid, liquid, and gas) coexist, withthe unit “degree Kelvin,” laterrenamed simply kelvin. The unit ofthermodynamic temperature, thekelvin, is defined as the fraction1/273.16 of the thermodynamictemperature of the triple point ofwater. The effect of this definitionis to make the temperature of thetriple point to be 273.16 K, whichcorresponds to 0.01 °C. TheCelsius scale is defined by therelation tC = T − 273.15 exactly.Although the values of thethermodynamic and Celsiustemperatures differ, the units areequivalent. Thus the degreeCelsius, with symbol °C, is equal tothe kelvin, with symbol K. A new International PracticalTemperature Scale (IPTS-68) with13 equilibrium states was adoptedin 1968 and was amended in 1975.This scale, however, was found todeviate from the thermodynamictemperature in certain regions and

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thus was replaced by theInternational Temperature Scale of1990 (ITS-90). By implication, the intervalbetween the freezing and boilingboiling points of water at standardpressure is no longer rigorously100 °C, since thermodynamictemperature is defined by a singlefixed point. Since 1968, when therevised International PracticalTemperature Scale was adopted,evidence has indicated that thedefinition of the kelvin leads to thevalue 99.975 °C for the boilingpoint, instead of exactly 100 °C asoriginally intended. The correctvalue for the triple point wouldhave been 273.22 K.

METRIC UNITS ININDUSTRY

The International System of Units(SI) has become the fundamentalbasis of scientific measurementworldwide. It is also used foreveryday commerce in virtuallyevery country of the world but theUnited States. Congress has passedlegislation to encourage use of themetric system, including the MetricConversion Act of 1975 and theOmnibus Trade andCompetitiveness Act of 1988, butprogress has been slow. The space program should havebeen the leader in the use of metricunits in the United States andwould have been an excellentmodel for education. Burt Edelson,Director of the Institute for AppliedSpace Research at GeorgeWashington University and formerAssociate Administrator of NASA,recalls that “in the mid-‘80s, NASAmade a valiant attempt to convert tothe metric system” in the initialphase of the international spacestation program. However, hecontinued, “when the time came toissue production contracts, thecontractors raised such a hue cryover the costs and difficulties ofconversion that the initiative wasdropped. The international partnerswere unhappy, but their concernswere shunted aside. No one eversuspected that a measurement

conversion error could cause afailure in a future space project.” Economic pressure to competein an international environment is astrong motive for contractors to usemetric units. Barry Taylor, head ofthe Fundamental Constants DataCenter of the National Institute ofStandards and Technology and U.S.representative to the ConsultativeCommittee on Units of the CIPM,expects that the greatest stimulusfor metrication will come fromindustries with global markets.“Manufacturers are movingsteadily ahead on SI for foreignmarkets,” he says. Indeed, mostsatellite design technical literaturedoes use metric units, includingmeters for length, kilograms formass, and newtons for force,because of the influence ofinternational partners, suppliers,and customers.

CONCLUSION

As we begin the new millennium,there should be a renewed nationaleffort to promote the use of SImetric units throughout industry,and to assist the general public inbecoming familiar with the systemand using it regularly. The schoolshave taught the metric system inscience classes for decades. It istime to put aside the customaryunits of the industrial revolutionand to adopt the measures ofprecise science in all aspects ofmodern engineering and commerce,including the United States spaceprogram and the satellite industry.____________________________Dr. Robert A. Nelson, P.E. ispresident of Satellite EngineeringResearch Corporation, a satelliteengineering consulting firm inBethesda, Maryland. He is ViaSatellite’s Technical Editor.

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Table 1. SI Base Units

Quantity UnitName Symbol

length meter mmass kilogram kgtime second selectric current ampere Athermodynamic temperature kelvin Kamount of substance mole molluminous intensity candela cd

Table 2. Examples of SI Derived Units

Quantity UnitSpecial Name Symbol Equivalent

plane angle radian rad 1solid angle steradian sr 1angular velocity rad/sangular acceleration rad/s2

frequency hertz Hz s-1

speed, velocity m/sacceleration m/s2

force newton N kg m/s2

pressure, stress pascal Pa N/m2

energy, work, heat joule J kg m2/s2, N mpower watt W kg m2/s3, J/spower flux density W/m2

linear momentum, impulse kg m/s, N sangular momentum kg m2/s, N m selectric charge coulomb C A selectric potential, emf volt V W/A, J/Cmagnetic flux weber Wb V sresistance ohm Ω V/Aconductance siemens S A/V, Ω-1

inductance henry H Wb/Acapacitance farad F C/Velectric field strength V/m, N/Celectric displacement C/m2

magnetic field strength A/mmagnetic flux density tesla T Wb/m2, N/(A m)Celsius temperature degree Celsius °C Kluminous flux lumen lm cd srilluminance lux lx lm/m2

radioactivity becquerel Bq s-1

Table 3. SI Prefixes

Factor Prefix Symbol Factor Prefix Symbol

1024 yotta Y 10-1 deci d1021 zetta Z 10-2 centi c1018 exa E 10-3 milli m1015 peta P 10-6 micro µ1012 tera T 10-9 nano n109 giga G 10-12 pico p106 mega M 10-15 femto f103 kilo k 10-18 atto a102 hecto h 10-21 zepto z101 deka da 10-24 yocto y