Philips tech.Rev, 36, Nö, 11/12 . MODULATION· 309

I. Modulation of a sinusoidal carrier

Conventional amplitude modulation

The oldest and also the most obvious form of mod-ulation is what we shall refer to as conventional am-plitude modulation. In this form the pattern of theinformation signal is directly 'impressed' on the carrier(fig. 2a). In other words, the modulated carrier has an'envelope' in the shape of the information signal. If wesuppose that the carrier transmitter consists of an LCcircuit in which an electrical oscillation is generated bya transmitter tube, then the modulation can be effected,for instance, by varying the anode voltage of the tubein accordance with the information signal. Recoveringthe information signal from the modulated carrier atthe receiver end - the process of detection or demod-ulation - is a particularly simple matter in the case ofconventional amplitude modulation. A rectifier (diode),followed by an RC filter that passes the frequencies ofthe information signal but not those of the carrier,delivers the desired result (fig.2b). This is known asenvelope detection or peak detection.

Let the unmodulated carrier be A cos (wet + cp) andthe information signal be pet); then the modulatedsignal S(t) has the form:

S(t) = {C + p(t)} cos (wet + cp). (1)

The constant C has an essential function: it must belarge enough for C + pet) to be positive at all times,for only then will peak detection yield the originalsignal; see fig. 3. If the average value of pet) is zero,the value of C in the above method of modulation isequal to the average anode voltage. The requirementthat C + p shall always be positive mayalso beexpressed by stipulating that the modulation depth mshall not be greater than 1. The modulation depth isdefined by the relation (see fig. 4):

(C +P)max -(C; +P)mlnm= .

(C +P)max + (C +P)mln

pmax-Pmln2C +P~ax +Pmln .

(2)

Often pmln is equal to -Pmax, in which case m is equaltOPmax/C.

To determine the spectrum of Set), let us first assumethat pet) is sinusoidal:

pet) = a cos wpt.

For Set) we then find:

Set) = C cos (wet + cp) + la cos {(wc+ wp)t + cp}. + la cos {(wc - wp)t + cp}. (3)

p(f)

1S(f)

i

-t -t -f Q

Fig. 2. a) Unmodulated carrier (left), information signal p(t) andmodulated carrier S(t) in conventional amplitude modulation.The carrier is schematically represented by verticallines, with theenvelope of the peaks drawn as a solid line. b) Diagram of peakdetector in its simplest form: a diode D followed by a lowpassfilter RC.

-t -f -fFig. 3. Information signalp(t), modulated signal S(t) and detectedsignal (right) for the case where C in eq. (1) is too small, so thatC + p(t) now and then changes sign. In peak detection this leadsto 'folding over' of the parts of p(t) where C + p(t~ is negative.

C+p

t(C'PJ~: -f~:;~J_n__J

Pmin __~ V(C+P)min - -------------

OL____----:----f

Fig. 4. Illustrating the definition (2) of modulation depth. Amodulation depth of 100% (m = 1) is only just permissible.Then (C + P)mln = 0, so that C + p only just fails to changesign.

In this simple case the spectrum thus consists of threelines, at the frequencies Je -Jp, Je and Je +Jp, withJe = Wc/2n,fp = wp/2n. The vector diagram in fig. 5,which rotates with the carrier vector, shows the threecomponents of the signal Set) of eq. (3): a stationary

310 F. W. DE VRIJER

vector of amplitude C, and two vectors of amplitudeta that rotate in opposite directions at an angularvelocity CUp. The total vector sum does not rotate, butvaries only in amplitude, in accordance with eq. (1).

When expressions like those in eq. (3), consisting of a numberof cosine terms, are represented in a vector diagram, eachterm is regarded as the real part of an exponential given bycos 1p = Re exp (jljl), and the appropriate exponential functionsare divided by exp (jwct) and plotted as vectors in the complexplane. The effect of this division is to make the carrier vectorstationary. Movement of a vector indicates a frequency differencefrom the carrier.

A periodic but non-sinusoidal information signalcan be expanded in a Fourier series, and each com-ponent in Set) then gives rise to a sum frequency and adifference frequency relative to fe. The total spectrumthus has the character oî fig, 6: a centralline atfe withtwo symmetrically located sidebands. If, for example,we use a carrier of 35 000 Hz to transmit telephonyspeech signals (300-3400Hz), then the lower sidebandoccupies the band from 31 600 to 34 700 Hz, and theupper sideband the band from 35 300 to 38 400 Hz.

S

-t

Philips tech. Rev. 36, No. 11/12

-t

Fig. 8. Information signal pet) and modulated signal Set) in DSBmodulation.

Fig. 9. Vector diagram for DSB modulation with a sinusoidalinformation signal. The two sidebands rotate in opposite direc-tions at an angular velocity Wp. The point S corresponding to thevector sum oscillates between A and B.

ptt)Fig. 5. Vector diagram for conventional AM with a sinusoidal S(t)information signal. The vectors in the complex plane representthe exponentials whose real parts are the cosine terms in (3), butonly after division by exp (jwct), so that the carrier vector OCis stationary. The vectors of the two 'sideband signals' have thesame magnitude and rotate in opposite directions at an angularvelocity Wp. The total vector sum OS varies in magnitude butnot in direction.

Fig. 6. Spectrum of a modulated carrier in conventional AM,consisting of the carrier-wave component and two sidebands.

11

binfe -f

Fig. 7. Spectrum in double-sideband modulation. The carrier-wave component is suppressed, so that the spectrum only consistsof two sidebands.

e(f)" " n 11 n

V U v \J V

,-_ 7~ f-....I\

~111 / Tl. ',_ i- I),

1\\ t:"\\

~ ~1I\~ I r-I~I

I- I- I- I-

'- '- '- '- '-

Fig. 10. Peak detection (pd) and synchronous detection (sd) ofthe modulated signal (4), where the information signal changessign. C(t) carrier, pet) information signal, Set) modulated signal,R(t) reference signal. The (full-wave) rectification that takes placein peak detection, followed by filtering, gives the signal Si whichreproduces the positive parts of Pct) correctly but reverses thenegative parts. In synchronous detection, Set) is multiplied by asignal R(t) with the same frequency and phase as C(t). In thefigure R(t) is a square-wave signal; after filtering, a signal S2(t)is then obtained which also reproduces the negative parts of pet)correctly.

R(t)

Philips tech. Rev. 36, No. 11/12 MODULATION 311

Double-sideband modulation with suppressed carrier(DSB)

The component Ccos (wet + cp) in the modulatedsignal Set) is in a sense a nuisance and redundant; ittakes up a high proportion ofthe power, but carries noinformation. In conventional amplitude modulation,however, it cannot be left out, because, as we haveseen, the constant C must be sufficiently large to givefaithful peak detection.

We shall now discuss a method in which the mod-ulated signal has the form

Set) = pet) cos (wet + cp).The inconvenient unwanted component is thus elim-inated (fig. 7), provided pet) is on average equal tozero. In what follows we shall assume that this isinvariably the case, an assumption that is alwayspermissible for audio signals. This method is called'double-sideband suppressed-carrier modulation'(DSB-SC). For brevity we shall refer here simply toDSB modulation, although it is also amplitude mod-ulation, while on the other hand the same two side-bands occur as in conventional AM. A DSB-mod-ulated signal Set) is shown infig. 8, andfig. 9 gives thevector diagram for the case of a sinusoidal informationsignal.

fc-f",ax fc+f",ax-f

Fig. 11. Spectrum of the signal (5), i.e. the synchronous detectionsignal after the multiplication of S by R but before the lowpassfilter. The low-frequency part is identical with the spectrum ofpet) itself. The spectrum of pet) can be completely recovered byfiltering only ifthe maximum frequency fmB" of pet) is lower thanthe carrier frequency fe.

9ffJJlflA.t 0vvr;rFig. 12. Modulator for multiply-ing an arbitrary signal f(t) by asinusoidal signal g(t). Dl, D2,Da, D4 are diodes, lI(t) is theoutput signal. If the amplitudeof get) is made sufficiently large,then lI(t) is equal to gI(t)f(t),where gIet) is the square wavewith the phases of g(t). Right:the spectrum of lI(t) for the casewhere f(t) is a low-frequencysignal. The first band representsthe desired product.

(4)

Fig. 10 shows in more detail why the signalof eq. (4)is not suitable for peak detection. Every time pet) goesthrough zero the phase of Set) rotates by 180°, andpeak detection is unable to sense this phase reversal.It can however be sensed with synchronous detection:Set) is multiplied bya synchronous reference signal R(t),which has the same frequency as the carrier [11. Fig. 10shows that with this method, after eliminating the r.f.components with a lowpass filter, the negative parts ofpet) are also faithfully reproduced.

Taking a sinusoidal signalof phase '1jJ for R(t), e.g.2 cos (wet + '1jJ), the multiplication gives:

R(t)S(t) = 2 cos (Wet + '1jJ) pet) COS (wet + cp) == pet) COS (2wet + cp + '1jJ) + pet) COS (cp - '1jJ). (5)

After elimination of the first high-frequency term, pet)is indeed obtained, but multiplied by cos (cp - '1jJ). Thereference signal must therefore be in phase with thecarrier ('1jJ = cp, cos (cp - '1jJ) = 1). Phase differenceslead to smaller output signals; in the worst case - aphase difference of 90° - the output signal is in factzero. Smal! phase differences, however, are not verytroublesome because the cosine only begins to differappreciably from 1 at larger values of cp - '1jJ. Fig. 1Jgives the spectrum of (5), the signal after multiplicationbut before the first term has been filtered out. It can beseen that the whole process can only be completelysuccessful if the information signal pet) contains nofrequencies higher than the carrier frequency fe.In both modulation and detection a particular signal

(p(t) or Set»~ has to be multiplied by a sinusoidal signal.Fig. 12 shows how this multiplication is often carriedout. Letf(t) be the first signal and get) the sinusoidalsignal: get) = sin wet. The signal get) is applied at highamplitude. In one half-cycle of get) both Dl and D 2

conduct while Da and D4 are biased off; the signalf(t)then arrives directly at the output. In the other half-cycle Da and D4 conduct while Dl and D2 are off, and

(1] Instead of 'synchronous' the term 'coherent' is sometimesused.

fft)

UJ

9ffJ-3

rnuft) -f

312 F. W. DE VRIJER Philips tech. Rev. 36, No. 11/12

Jet) arrives at the output with the opposite sign. Thesignal u(t) at the output is thuSj(t)gI(t), where gIet)is the square-wave function in fig. 12.Expansion of gIet)as a Fourier series yields for u(t):

4u(t) = j(t)gI(t) = - j(t){ sin wet + t sin 3 wet + ... }.

'TC

The first term gives the required result, the others canbe eliminated by a lowpass filter. Here again, theintended result can only be obtained provided Jet)contains no frequencies higher thanje (see the spectrumof u(t) in fig. 12).

DSB modulation compared with conventional AM

The quantitative advantage of the suppressed carrierin DSB modulation is that the peak power necessaryfor good transmission of a given information signal isfour times lower with DSB modulation than with con-ventional modulation. This follows immediately fromthe fact that the peak amplitude of the modulatedsignal in conventional amplitude modulation must beat least twice as great as in DSB; seefig. 13. In practiceit is especially important that this difference of 6 dB inpeak power [2] also occurs if a given signal-to-noiseratio after detection is to be achieved. This follows fromwhat has been said above, provided that the effect ofnoise or other interfering signals incident at the detectoris identical for synchronous and peak detection. Weshall now show that this is in fact the case.

We assume that the sideband amplitudes resultingfrom conventional AM or from DSB modulation witha sinusoidal signal are ta at the detector. We comparethis with the situation where the detector is affected byan interfering signal b cos wst, at a frequency Is in thefrequency band of the receiver. Fig. 14 gives the twovector diagrams for conventional modulation; in thesecond diagram the vector b rotates at an angularvelocity Ws- wc. Peak detection yields the variation inlength of the resultant vector OS. This is a cos wpt inthe 'signal' case, and supposing that b is much smallerthan the amplitude of the carrier, b cos (ws - we)t inthe 'noise' case. The signal-to-noise ratio after detec-tion is thus afb.

In DSB modulation with synchronous detection,multiplication by the reference signal 2 cos wet yields2a cos wpt cos- wet and 2b cos wst cos wet; the resultof the detection is the low-frequency component

a cos wpt and b cos (ws - We)t,

the same result as with peak detection.If the interference has the character of white noise,

the same reasoning applies to each Fourier componentof the noise. The high-frequency noise is converted intolow-frequency noise in the same way in both peak andsynchronous detection.

If the noise is in fact not much weaker than thesignal, the above reasoning remains valid for syn-chronous detection. For peak detection, however,complications arise that result in a relatively lowersignal-to-noise ratio.

rHigh-frequency white noise in a frequency band around js can

be described as two uncorrelated low-frequency noise signals,RI(t) and R2(t) of half the bandwidth, which DSB modulate two(suppressed) carriers at frequency le 'in quadrature' (quadraturemodulation, see p. 317):

N = RI(t) cos wet + R2(t) sin wet.

In the case of synchronous detection with reference signalcos wet the detected signal is proportional to RI(t) but insensitiveto R2(t), even when RI(t) and R2(t) are large.Peak detection in the presence of a carrier of amplitude A

likewise only yields RI(t) and not R2(t) if RI(t) and R2(t) aremuch smaller than A. If this is not the case, however, R2(t)starts to make a considerable indirect contribution. This followsfrom the fact that on detection - a nonlinear operation - noisecomponents with a frequency difference Ll constitute a low-frequency mixing product of frequency zl,

sinSff)

f -----.ai lItIHiHlfHlllllllllllltHHttH

conv AM DSB

Fig. 13. Peak power in conventional AM and DSB modulation.In conventional AM with 100% modulation depth the peakamplitude of the modulated signal S(t) is twice the maximum aof the information signal pCt), provided that the maximum andthe minimum of pet) are identical in absolute value. In DSBmodulation the peak amplitude is only a.

o

Q

Fig. 14. Vector diagrams for conventional AM. OC carrier.a) Sinusoidal information signal with amplitude a (a < OC);b) no information signal, but an interfering signal b cos wst atthe detector (b« OC). The vector b rotates at an angularvelocity Ws - Wc. Peak detection yields the variations in thelength of the vector sum OS. The amplitudes of the variationare a and b respectively.

Philips tech. Rev. 36, No. 11/12 MODULATION 313

Although DSB modulation has a 6-dB advantage inthe peak power required, it has the disadvantage thatthe detection is much more complicated. The receivermust contain a reference oscillator that is synchronouswith the unmodulated carrier. The phase informationis usually sent from the transmitter to the receiver inthe form of a pilot signal, independently of the mod-ulated signal. This is a signalof low amplitude with afixed frequency and phase relationship to the sup-pressed carrier. In the simplest case the frequency andphase are identical to those of the original carrier, butthis is not necessarily so. The phase may for examplebe shifted by 90°. There mayalso be a difference be-tween the pilot and carrier frequencies: however, thisshould be in the ratio of two (small) integers.

Briefly, the practical difference between DSB mod-ulation and conventional AM thus amounts to thefact that DSB modulation permits the use of a smallertransmitter, while conventional AM permits muchsimpler detection. In each application it is necessary todecide which carries the most weight. In broadcastsystems, for example, there is a single transmitter anda very large number of receivers. For this reason con-ventional AM is still used for (AM) broadcasting: theneed for a larger transmitter is of negligible importancecompared with the advantage of simple peak detection.

In two-way radio communication between fixedstations, between mobile units such as ships, aircraft,taxis and police cars, or between such units and a fixedstation, the situation is completely different. Here eachcommunicator has a transmitter, and therefore the sizeof the transmitter is very important and the advantageof carrier suppression predominates. Nevertheless,DSB modulation is not much used today, since anothermethod is available that offers much the same advan-tages but takes up less bandwidth. This method issingle-sideband modulation.

Single-sideband modulation (SSB)

The two sidebands of the DSB signal (fig. 7) eachcontain the complete information, and to economize onbandwidth it is obvious that one of them could besuppressed completely, e.g. by means of a filter. This isthe idea behind single-sideband modulation.

The suppression of a sideband has important conse-quences for the detection. With a sinusoidal informa-tion signal

pet) = a cos wpt,

the modulated signal after suppression of the upperside band is:

Set) = ta cos {(Wc - Wp)t + cp}.

Whereas in fig. 5 and fig. 9 the vector Set) changed inmagnitude but not direction, we now have the oppositesituation (fig. 15). The result of synchronous detectionwith R(t) = 4 cos (wet + 'Ifl) as reference signal isa cos (wpt + cp + 7fl). A phase error in the referencesignal thus produces a phase shift and not, as in DSBmodulation, a change in the amplitude of the detectedsignal. If the information signal is not sinusoidal, thenthe effect of a phase error is that all the Fourier com-ponents receive a phase shift but maintain their am-plitude. In DSB modulation a phase error had theeffect of reducing the whole signal.

For audio signals such phase shifts, which implyrelative phase shifts between the components, arepermissible. This is because the human ear behavesrather like a detector that resolves the acoustic signalsinto Fourier components and records only the am-plitude. Speech remains intelligible even with con-tinuous slow changes in phase differences, whichmeans that a small difference in frequency between car-

Fig. IS. Vector diagram for lower-sideband modulation with asinusoidal information signalof angular frequency Wp. Thevector OS of the modulated signal Set) is constant in length,and rotates at an angular velocity -Wp. In upper-sideband modu-lation the angular velocity is Wp.

rier and reference signals is admissible. The pilot signalcan then be omitted and a stable local oscillator at thereceiver can provide the reference signal. The tolerancein the reference frequency for good speech intelligibilityis many tens of hertz. The ITU (International Tele-communication Union) standard for good telephony isa maximum deviation of 20 Hz. Such frequency shiftsare not permissible in the transmission of music.

There are also information signals for which even aconstant phase difference cannot be tolerated. In tele-vision signals, for example, the steepness of pulse edges- transitions between dark and light - are important,and the shape of a pulse edge is very sensitive to therelative phase relations of the Fourier components. Insuch cases it is essential to have a fixed phase relation-ship between the reference signal and the carrier, and apilot signal is therefore indispensable.

[2] A decibel (dB) is a logarithmic measure of power ratios.When the ratio is x the difference is said to be (10 log x) dB.A factor of 10 is a difference of 10 dB, a factor of 2 is veryclose to 3 dB.

314 Philipstech. Rev.36, No.llj12

An AM broadcasting transmitter built by Nederlandsche Seintoestellen-fabriek in 1925. The transmitter operated at a wavelength of 1050 metresand radiated a power of 500 watts.

Philips tech. Rev. 36, No. I I I 12 MODULATION 315

11will be evident that in two-way radio communica-tion, where intelligible speech is the main requirement,while it is very important to keep the equipment simple,SSB modulation has great advantages over conven-tional AM and DSB modulation. These may be sum-marized as follows. In the first place the required band-width is equal to that of the basic signal, i.e. at leasttwice as small as in DSB modulation and conventionalAM. In addition the peak power required for a givensignal-to-noise ratio is another 3 dB lower than in DSBmodulation - i.e. 9 dB lower than in conventionalAM - because the detector only receives half as muchnoise, as a result of the halved receiver bandwidth.If speech only is to be transmitted, the advantage

compared with conventional AM is in one respect evengreater. For the equipment it is often the mean power,not the peak power that is the important quantity; thelower the mean power the more compact the equip-ment can be. Now with a speech signal the mean poweris very much lower than the peak power (of the orderof 10 dB). Consequently the mean power transmittedin SSB and DSB modulation is JO dB lower than thepeak power. Jn conventional AM, on the other hand,this difference is no more than 6 dB; see fig. 16. Thenet result is thus an advantage of 9 + (l0 - 6) dB= 13 dB in the mean power required when SSB mod-ulation is compared with conventional AM. In suchcases a 100-W SSB transmitter is therefore as effectiveas a 2-kW AM transmitter.

Generation of an SSB signal

As already indicated, an SSB signal can be obtainedby first producing a OSB signal and then filtering outone sideband. This method is in fact used. Since, how-ever, the two bands are close together, very good filterperformance is required. We shall mention here twoother widely used methods, which avoid the use of anr. f. filter.

A block diagram of the first of these methods IS

shown injig. 17. It is based on the relation:

cos wpt cos wet ± sin wpt sin wef = cos (wc =f wp)t. (6)

The information signal pet) and the carrier C(t) aremultiplied together at two places: directly in MI, andin M2 after all the components have been shifted by90° in phase in PI and P2. MI and M2 are modulatorsof the type shown in fig. 12. The two multiplicationsyield two DSB signals, i.e. the first and second termsin (6), which, added together or subtracted from eachother, give the desired SSB signal.

This method is in practice only used for speechsignals, that is to say signals with a relatively narrowfrequency band. For these signals the required 90°phase shift of each Fourier component - the main

problem of the method - is still feasible, although the'ordinary' circuits used for this (with resistors, induc-tors and capacitors) are already fairly complicated.The 'transversal filters' discussed later (see p. 332) area modern alternative for such circuits.

The eperation that PI performs in the ideal case is known asa Hilbert transformation. The Hilbert transform pCt) ofa functionp(l) is:

+00pU) = _l_ I per) dr.

n J (-r-00

(7)

It can easily be shown from this definition that the transforma-tions of cos (wt + <p) and sin (wt + <p) give sin (wt + <p) and-cos (wt + <p). Since in addition the relation (7) between pet)and pet) is linear and additive, the transformation is in factequivalent to the operation of PI: the 90° rotation of eachFourier component. This notation allows the SSB signals of theinformation signal pCt) 10 be represented in a closed form:

upper-sideband signal: pCt) cos wet - jJ(t) sin wet,lower-sideband signal: pet) cos wet + p(l) sin wet.

The second method we shall discuss here, generallyknown as the Weaver method, is illustrated in the block

p(f) S(f) S(tJ

DSBSSB conv AM

Fig. 16.1n speech the average power ofthe information signalp(t)is roughly 10 dB lower than the peak power. In DSB and SSBmodulation this relationship is directly reflected in the modulatedsignal 5(t). In conventional AM with 100% modulation theaverage amplitude is however about half the peak amplitude, sothat the mean power is only 6 dB lower than the peak power.

coswpfp(f)

Fig. 17. Block diagram of a commonly used circuit for generatingan SSB signal, which does not require an r.f. filter; pet) informa-tion signal, C(l) carrier. MI, M2 multipliers. PI, P2 90° ph ase-shifters. Summation of the double-sideband signals from MI andM2 yields the lower-sideband signal, subtraction yields the upper-sideband signal.

316 F. W. DE VRIJER Philips tech. Rev.36, No. 11/12

diagram in fig. 18 tai, Here the information signal ismultiplied by cos wot in Ml and by sin wot in Ms',where Wo is a low frequency, in the centre of the fre-quency band of the information signal. Signals at thesum frequency are eliminated from the products byfilters F and F'. The remaining signals are multipliedin M2 and M2' by high-frequency signals cos (wc + wo)tand sin (wc + wo)t. Addition of the two products thusobtained gives the upper-sideband signal (frequencyWc + wp). To obtain the lower-sideband signal, thegenerator G2 must deliver the frequency Wc - Wo, andthe difference ofthe products obtained with M2 and M2'must be taken. This method does not require r.f. filtersand the components of pet) do not have to be alteredin phase.

In both methods the special combination of twoDSB signals completely eliminates one ofthe sidebandsin the ideal case. In practice a difference of 30 dB be-tween the wanted and the unwanted sidebands isreadily achieved. Often the resultant signal is passed toa final simple filter to give even greater suppression ofthe unwanted band.

Electronic problems such as those encountered herecan nowadays often be solved more readily by digitalprocessing of the signals.

Frequency-division multiplex (FDM)

Single-sideband modulation is very widely usedtoday in telephony. In the 1920s the rapid growth oftelephone communication created a need for a systemin which different speech signals could be transmittedsimultaneously along a single cable. This led to thedevelopment of the frequency-division multiplex sys-tem, FDM. In this system a number of speech signalsmodulate separate carriers in SSB in such a way thatthe modulated signals appear in adjacent separatebands of the frequency spectrum. They can then be

Fig. 18. The Weaver method used for generating an SSB signal.This avoids the use of r.f. filters and also a 90° phase shifter forthe components ofthe information signal pet). 01, 02 are the sineand cosine generators of wot and (wc + wo)t respectively. HereWo is the centre of the baseband. MI, MI', M2, M2' multipliers.F, F' filters. Addition of the signals from M2 and M2' yields theupper-sideband signal. The lower-sideband signal is obtained bycausing 02 to generate the frequency Wc - Wo instead ofWc + COoand taking the difference ofthe signals from M2 and M2'.

transmitted over a common cable, and separated fromeach other at the receiving end by means of filters [4l.

The carrier frequencies are multiples of 4 kHz. Thesmallest FDM group standardized by the CCITT(Comité Consultatif International de Télégraphie etTéléphonie) consists of 12 channels, which are lowersidebands (LSB) at the carrier frequencies 64, 68,72, ... 108 kHz. The complete band thus goes from 60to 108 kHz and is 48 kHz wide ('basic group'). Tohandle large volumes of telephone traffic severalbasic groups with LSB each in turn modulate aseparate carrier. A 'supergroup' consists of five basicgroups (60 channels) at carrier frequencies of 420,468, ... 612 kHz. The lowest basic group is thuslocated in the band from 312 kHz (420 - 108) to360 kHz (420 - 60), the second is in the band from 360to 408 kHz, and so on. The total band goes from 312 to552 kHz and is 240 kHz wide. There are also 'mastergroups' (five 'supergroups' consisting of 300 channelsfrom 812 to 2044 kHz) and 'supermaster groups' (three'master groups' consisting of 900 channels from 8516to 12388 kHz). Other groupings are also in use.

With such wide frequency bands it is necessary totake into account the frequency dependence of theattenuation in the transmission channel. In ordernevertheless to obtain a flat transmission characteristicfor the whole of the frequency band in use, some bandshave to be given more amplification at repeaters or atthe receiving end than others ('equalization'). To beable to determine at any given moment what the equal-ization characteristic and the overall gain should be, anumber of pilot frequencies are transmitted at varyingspacings within the band. These might also be used forsynchronous detection, but there is generally no needfor this since detection with stable local oscillatorsgives adequate results.

The transmission of so many signals by frequency-division multiplexing over a single transmission pathrequires very good linearity from all the amplifiers(repeaters), modulators and other equipment if inter-ference is to be avoided from signals at sum and dif-ference frequencies (caused by 'intermodulation' and'cross-modulation').

Related methods of amplitude modulation

In DSB modulation the frequency band used is atleast twice as wide as is necessary for the transmissionof a given baseband. To make more efficient use ofavailable bandwidths it is possible, instead of eliminat-ing one sideband as in SSB modulation, to transmittwo independent information signals in the two side-bands. In 'ISB' (independent-sideband) modulation,SSB methods are used to transmit one information

Philips tech. Rev. 36, No. 11/12 MODULATION 317

signal in the upper sideband and the other in the lowerside band of the same carrier. The practical significaneeof using the same carrier is mainly that only one pilotsignal and one reference oscillator are necessary todetect both signals. Separation of the two signals in thereceiver, however, calls for a very selective filter. Theseparation can also be effected by reversing the circuitof fig. 18 (the Weaver method); the circuits must thenbe very accurately balanced. ISB modulation is some-times used in fixed radio links (p. 357) for the simul-taneous transmission of different speech or telegraphsignals.

As we have seen on page 311, the output signal insynchronous detection is zero if the reference phase

IIIII

--- ------ S(t}

Fig. 19. Vector diagram for quadrature amplitude modulationQAM). As in DSB modulation, the signals pet) cos wet andq(t) sin wet change only in length in the vector diagram and notin direction, but they change independently, so that the vectorsum Set) generally changes both in length and direction.

II,,-----i---~-...-----

I I \I I \I MI \I \I \I \" ,

-f

Fig. 20. Vestigial-sideband modulation (VSB). The VSB signalis a conventionally modulated signal (dashed line) which haspassed through a filter whose amplitude-response characteristicis shown by the solid line. The filter transmission is 50% at le;the characteristic is symmetrical with respect to point M.

o A

Q

o

Fig. 21. Vector diagrams a) for conventional AM, ö) for VSBmodulation. Because of the symmetry of the filter in VSBmodulation (fig. 20), the length of CP + CQ in (b) is the sameas CP in (a), and DC in (b) is half DC in (a). The relations betweenthe variation AB in the length of the vector sum OS and thecarrier amplitude DC are thus the same in VSB modulation asin conventional AM, so that peak detection produces much thesame result. -

differs by 90° from that of the carrier. This gives yetanother way of transmitting two signals in the side-bands of a single carrier. If for simplicity we takecp = 0 in eq. (4), then our original modulated signal ispet) cos wct. We now add a signal that is 90° out ofphase and is modulated by another informationsignal, q(t):

Set) = pet) cos Wct+ q(t) sin wct.

This is shown by the vector diagram in fig. 19. Thetotal signal now varies not only in amplitude, as before,but also in phase. As can easily be shown, synchronousdetection with cos Wct as reference signal yields thesignal pet), while synchronous detection with sin Wctas reference signal yields q(t). Small phase errors, notserious with DSB modulation, now lead however tocrosstalk between pand q.

An example of this quadrature amplitude 'modulation(QAM), as it is called, is found in colour television.The video information consists of a brightness signaland two colour signals. The colour signals are in quad-rature on a subcarrier, that is to say a carrier that formspart of the signal transmitted on the main carrier.

Finally, there is another method, used in televisionand in other forms of communication, for modulatingthe main carrier. During the development of mono-chrome television it was decided - as in the case ofsound broadcasting because of the large number ofreceivers - to adopt a method in which peak detectioncould be used. At the same time it was also desirableto be economical of bandwidth. This resulted in thevestigial-sideband system (VSB). In this system a con-ventionally modulated signal is passed through a filterwith the amplitude-response characteristic shown infig·20.

Fromfig. 21 it can easily be seen that peak detectionnow gives about the same results as in conventionalamplitude modulation. Fig. 21a again shows the vectordiagram for conventional AM; the two componentsCP and CQ from the lower and upper sidebands rotatein opposite senses at an angular velocity Wp; the result-ant CS varies only in amplitude, and peak detectionyields the variation AB in amplitude of the total vectorOS (CA = CB = 2CP). Fig. 2Ib is the vector diagramfor VSB modulation. The resultant OS of the carrierOC and the components CP and CQ from the lowerand upper sideband now vary in phase as well. Owingto the symmetry of the filter the sum of the lengths CPand CQ in (b), however, is equal to the length CP in (a),so that the detected variation AB in the amplitude _of

[3J D. K. Weaver Jr., Proc. IRE 44, 1703, 1956.[4J See for example H. N. Hansen, Philips tech. Rev. 26, 206;

1965.

318 F. W. DE VRIJER Philips tech. Rev. 36, No. 11/12

OS is half that in (a). Since the carrier is also halved, themodulation depth remains unchanged. If the filter hasa sharp cut-off, the vector CP in (b) is zero at higherjj,and the vector point Q rotates around the dashed circle.The phase variations - negligible when the modulationdepth is sufficiently small- result in some distortion.In television these variations are generally tolerable,although a correction is sometimes made at the trans-mitter to compensate for the distortion. However,synchronous detection is steadily replacing peak detec-tion in television receivers, and this distortion is notencountered with synchronous detection; the referencesignal is obtained by sharply filtering out the carrier.

Frequency and phase modulation

Amplitude modulation may be described as the sub-stitution of a function of time, e.g. C + pet), for theconstant A in the expression for the carrier

C(t) = A cos (wet + ep).

In frequency and phase modulation the situation is notso straightforward since variations in phase and varia-tions in frequency are inseparably related [51. This canbe seen immediately if the constant epin (8) is replacedby a function of time, ep(t). The result is a waveform ofthe type shown in fig. 22, and it can be seen that thefrequency - considered as the number of periods ofSet) per second - also fluctuates. To investigate thisfurther we must first take a closer look at the conceptof 'frequency' in this new situation.

A carrier of the type in fig. 22 can generally berepresented by

Set) .:_ A cos wet),

.."

where A is a constant and dW/dt is greater than zero.When, in a certain time interval !::..t, a whole number ofperiods of Set) have elapsed, this number divided by!:l.t is the 'mean frequency' over !:l.t. The number ofperiods elapsed is the number of times that W hasincreased by 2n, i.e. !:l.7p/2n, and the mean frequency isthus (1/2n)!:l.w/!:l.t. This expression can also be usedwhen the number of periods that have elapsed in !:l.tisnot an integer. The value to which this mean frequencyapproaches for !::..t -+ 0 is called the instantaneous fre-quency f-«:

. 1!:l.7p 1 dWfm=hm -- =--.

tH~O 2n!:l.t 2n dt

The corresponding instantaneous angular frequency Wm

is equal to d7p/dt.In the case of an unmodulated carrier the instantane-

ous angular frequency is of course equal to the angular

frequency Wc of the carrier. In the case of a fluctuatingphase ep(t) we have:

7p = wet + ep(t), (10)

Wm = Wc+ dep/dt. (ll)

With a given information signal p(t) the terms phasemodulation and frequency modulation are now used asfollows. If the phase cfo(t) in (10) varies in proportionto pet), we have phase modulation. The instantane-ous frequency then varies in proportion to dp/dt from(11). Conversely, we have frequency modulation whenthe deviations in the instantaneous frequency are pro-portional to p(t); in that case dep/dt is proportional topet) and the phase thus varies in proportion to [pát,

(8)

Frequency modulation is therefore not the substitution of avariable such as Wc + ap(t) for the constant Wc in (8). Thiswould lead to ridiculous results. If we assume for instance thatp(t) is periodic: p(t) = cos wpt, then we would find:

1j! = (wc + a cos wpt)t + rp = wet + at cos wpt + rp. (12)

Fig. 23 shows the variation of tp as given by (12). This is a com-pletely unusable form of modulation: the variation of tp, andhence of S, eventually becomes too violent.

We shall now confine ourselves for the moment tothe case in which the information signal is sinusoidaland the phase ep(t) is given by:

cp(t) = Cf.cos wpt. (13)

In the vector diagram (fig. 24) the vector of the mod-ulated signal,

Set) = A cos (wet + a cos wpt), (14)

(9) maintains a constant amplitude A, but the phase angleoscillates to and fro around the carrier vector. Theangular amplitude a of this motion is known as themodulation index. The instantaneous angular frequencywmis:

Wm = Wc - Cf.Wpsin wpt.

The frequency deviation Sf, i.e. the amplitude of thevariation in instantaneous frequency, is thus given by:

!:l.f = ajp. (15)

Since the instantaneous frequency oscillates to andfro between the values [« +!:l.f and [« -!:l.J, theobvious conclusion might seem to be that the requiredbandwidth is 2!:l.J, and is thus directly proportional tothe degree ofmodulation (which is equal to !:l.f or to Cf.,depending on whether frequency or phase modulationis under consideration). Because ofthis it was originallythought that in those cases where a low degree of mod-ulation was considered sufficient, frequency or phasemodulation could be used to save bandwidth, since it

Philips tech. Rev. 36, No. 11/12 MODULATION 319

-fFig. 22. Carrier modulated in phase and in frequency. Modulationof this type can be obtained by varying é in (8) as a function oftime. The duration of a complete period, and hence the fre-quency, then varies as well.

lJ'

rIII

o 1/fp -f

IIII

III

IIII

,-... -1IIIIII

Fig. 23. The argument 1p(t) = wet + '" of S(t) (see eq. 9), as afunction of t, when Wc is replaced by a constant plus a periodicfunction.

///

///////

-,\\ -,\\

",-,"\ -,

\\,,

Fig. 24. Vector diagram for frequency or phase modulation.OC vector of the unrnodulated carrier. OS, the vector of themodulated signal, does not change in length but its directionvaries periodically. The angular amplitude ex of this movementis the 'modulation index'.

follows from (15) that 2t::,.j is smaller. than the 2jprequired by conventional AM, if a is less than 1. Thisconclusion is not correct; as we shall presently see, FMalways requires a frequency band at least as wide asthat for AM.The usefulness of FM does not therefore lie in any

saving of bandwidth, but on the contrary in the pos-sibility it offers of using an a greater than 1. At a givencarrier amplitude A, that is to say at a given transmitterpower, the modulation amplitude in conventional AMis limited to tA, and in DSB and SSBmodulation to A.From equations (13) and (14) and fig. 24 it is evidentthat in FM the admissible degree of modulation (a) isnot limited by the transmitter power in such a simpleway. This means that at a given transmitter power amuch better signal-to-noise ratio can generally beobtained than with AM. This does however use up abandwidth of at least 2t::,.j, which increases with thea-value selected. We shall presently examine in moredetail what the bandwidth actually is and the extent towhich the signal-to-noise ratio can be improved com-pared with AM.The great virtue of FM really lies in the fact that the

zero crossings of the signal contain all the information.Small additive interferences such as noise - smallvertical displacements of Set) in fig. 22 - cause onlyslight shifts in the zero crossings; those due to thesignal can be made much greater by choosing a suf-ficiently large a. Multiplicative interference (amplitudevariations) have no effect at all on the zero crossings, atleast as long as the amplitude does not fall to zero.This also applies at small values of a. In FM, therefore,the information is well protected from unintentionalamplitude variations. This is the second importantadvantage of FM.

Modulation and detection

To modulate a carrier in frequency or in phase it isonly necessary to vary the capacitance ofthe frequency-determining Le circuit in the oscillator or of a phase-shifting filter after the oscillator. This is what is donein practice, with the aid of solid-state 'varactor diodes',which have a voltage-sensitive capacitance. Because ofthe insensitivity of FM to amplitude errors, there areno special requirements for the linearity of the outputamplifier. For this reason an FM transmitter can besimpler than an AM transmitter - an important advan-tage in mobile installations.The detector of an FM signal must deliver a current

or voltage that follows the variations in the instantane-ous frequency. Many methods have been developed forthis, two of which will be mentioned here. In the first

[5] See for example Balth. van der Pol, Proc. IRE 18,1194,1930.

320 Phi!ips tech. Rev. 36, No. 11/12

Relay station in a microwave link. Traffic is sent simultaneously in bothdirections. The information is sent on a frequency-modulated carrier; thewavelength is between 3 and 15 centimetres. The parabolic reflectors directthe signals into a beam with an aperture of about I", A link ofthis kind cancarry up to 2700 simultaneous telephone conversations per carrier infrequency-division multiplex (FD M). The capacity can be increased byusing more than one carrier.

method, the signal is directly applied to a circuit thatconverts the frequency variations into amplitude varia-tions. The simplest example is a tuned circuit, with theside of the resonance curve covering the required fre-quency range; seefig. 25. The resultant AM signal canbe demodulated by a peak detector. FM detection doesnot therefore need to be much more complicated thanordinary AM detection. To ensure linear detection,however, the amplitude-frequency response should besufficiently linear. In this respect the side of a tuned-circuit response is not the ideal solution. More refinedcircuits, like the Foster-Seeley detector and the ratio

detector, use coupled tuned circuits. An additionaladvantage of the ratio detector is that it is relativelyinsensitive to amplitude variations in the input signal.

In the second method the zero crossings of the signalare converted into electrical pulses of constant shapeand amplitude, and the pulse train thus obtained isthen electronically integrated over short periods. Theresultant signal is proportional to the instantaneousfrequency.

rn all FM detection methods, amplitude variationsare removed before detection by clipping the signalpeaks in an amplitude Limiter.

Philips tech. Rev. 36, No. 11/12 MODULATION 321

A

1

Fig. 25. Amplitude-frequency characteristic of a tuned circuit.The side of the response curve can be used in frequency de-modulation to convert frequency variations into amplitude varia-tions.

p'

Fig. 26. Vector diagrams for conventional AM and for FM takinginto account only the first-order sidebands. In both cases thevectors of the sideband signals rotate in opposite directions at anangular velocity Wp. The point S corresponding to the vectorsum OS moves to and fro along the line of the carrier vector oein AM, but in this first-order approximation it moves perpen-dicular to oe in FM.

a=2

a=1

-20 -10 0 10 20_n

Fig. 27. Spectra of signals modulated in frequency or in phaseby a sinusoidal information signal; ex is the modulation index.The amplitude of the component of frequency Je ± nJp is pro-portional to !Jn(ex)!, the absolute value of the Bessel functionof the nth order of ex.

Bandwidth

When the instantaneous frequency fm changes slowlyat a given frequency deviation tsf, in other words whenthe signal frequency fp is small and the modulationindex (J. therefore large, the instantaneous frequency is'quasi-steady-state'. To a good approximation, we arethen only concerned with the frequencies that lie be-tween the maximum and the minimum of fm, so thatthe bandwidth is indeed 2Ój For small values of (J.

(a < 1) this is certainly not the case. To determine thebandwidth correctly we have to expand the modulatedsignal (14) as a Fourier series. In principle the result isan infinitely broad spectrum, because there is a com-ponent for every angular frequency Wc ± nwp (n in-teger). Its amplitude is equal to the absolute value ofthe Besselfunction of the nth order of a, IJn(a)l.

This result is found by writing the modulated signal (14) inthe form

Set) = A cos wet cos (ex cos wpt) - A sin wet sin (ex cos wpt),

substituting in this the following series for cos (ex cos wpt) andsin (ex cos wpt), the Jacobi series:

cos (excos wpt) = Jo(ex) - 2h(ex) cos 2wpt + 2J4(ex) cos 4wpt ... ,sin (excos wpt) = 2h(ex) cos wpt - 2h(ex) cos 3wpt + ...

and then replacing each product of coscosr or sin wet and cosnwptby a term at the sum frequency and a term at the differencefrequency. A term with a negative, sign can be taken care of byan extra phase term of 180°.

If the Fourier series is discontinued after the terms of the firstorder, we obtain a simple parallel with AM. The result obtainedand the expression for AM (eq. 3) with rp = 0 are respectively:

Set) = AJo(ex) cos Wet- Alt(ex) sin (wc + wp)t-- Ah(ex) sin (wc - wp)t, (FM)

Set) = e cos wet + ta cos (wc + Wp)t + ta cos (Wc- wp)t. (AM)

Fig. 26 shows the corresponding vector diagrams. Because ofthe differences in the phases of the sideband components, theresultant of the vector sum in FM moves up and down along theverticalline p' Q' and not along the horizontal line PQ as in AM.In the first case we have mainly a rotation of the vector sum,and in the second a change in length. When the terms of higherorder are included, the straight line p' Q' becomes a circular are(fig. 24).

Fig. 27 shows the spectra for a = 1, a = 2, a = 3and a = 20. These illustrate two important facts. Inthe first place, at a given IX the components for which nexceeds a particular value can be neglected. In thesecond place, the larger the value of a the more com-ponents have to be taken into account. Neglecting com-ponents implies signal distortion. It is therefore neces-sary to compromise between a strong signal (implyingstrong modulation), a narrow bandwidth and lowdistortion. Fig. 28 gives curves of a as a function of nfor several values of the distortion t5. This quantity isdefined by the rule that all components in the spectrumwhose amplitude IJn(a)1 is less than t5 are suppressed.

322 F. W. DE VRIJER Philips tech. Rev. 36, No. 11/12

30r---------.---------.-------~

ex

I

O.11L-----2.J...._----l..3--L-L-J._J_L...LJ10.,..-------l20---l30

---nFig. 28. a as a function of /I for ·some values of c5 = IJ,,(a)l.This indicates how large the frequency deviation /),1 (= alp) ata' given bandwidth B (= 2/l/p) can be before the distortion c5exceeds a particular limit. At a distortion c5 all Fourier com-ponents are cut off whose amplitude is smaller than c5 timesthat of the unmodulated carrier.

Fig. 28 shows, for example, that at a permitted distor-tion of 10-a, three components on either side of thecarrier are sufficient for a modulation index of a = 0.2,whereas as many as seven are required for a = 2.

For small values of a (a « 1) all components can bedisregarded except for those of the zero and first orders(n = 0 and 1). The bandwidth is then equal to that forconventional AM, i.e. 2fp. FM therefore requires at:least as much bandwidth as AM, and in general muchmore.

The spectrum for a = 20 in fig. 27 illustrates the factthat at large values of a the components can soon bedisregarded when n becomes greater than a. The band-width is then approximately equal to 2afp, and there-fore approximately equal to twice the frequency devia-tion (see eq. 15), in accordance with the prediction forthis quasi-steady-state situation.

Summarizing, the bandwidth B is equal to 2fp forsmall IX, and to 26.f for large a. In intermediate casesthe usual rule of thumb is:

B = 2(6.f + fp).

So far we have only considered a sinusoidal signal.If the information signal is built up from a large num-ber of Fourier components, the FM signal, unlike anAM signal, cannot be obtained by superposition oftheFM signals of the components ('FM is not linear').Sidebands also occur at all possible combinations offrequencies. In this case, however, there is again a veryuseful rule of thumb for the bandwidth, known asCarson's rule:

B = 2(!:if + fmax). (16)

Here fmax is the maximum frequency of the basebandand !:if is the frequency deviation of the total mod-ulated signal (i.e. 1/2n times the maximum of Idep/dtIin (11)).

Signal-to-noise ratio

We shall first consider the situation where a carrier(amplitude A, frequency fc) enters the detector togetherwith a small sinusoidal interfering signalof amplitude band frequency fc + fn, where j], is a low frequency. Inthe vector diagram (fig. 29) the interfering vector brotates at an angular velocity COn. For phase detectionthe interference corresponds to a signalof frequency fnfrom the base band and modulation index IXn. Weassume that b is much smaller than A; then an = blA.If in addition the carrier is phase-modulated by asignalof frequency fp and modulation index IX, theratio of the signal to the interference is:

a/an = «Alb.

Now Alb happens to be equal to the signal-to-noiseratio in AM with 100% modulation depth. After phasedetection the signal-to-noise ratio is thus IX timesgreater than in AM.

In frequency detection the interference correspondsto a signal with a frequency deviation !:ifn, given by

!:ifn = as f«. (17)

After detection the ratio of the signal 6.f to the inter-ference !:ifn is therefore:

6.f afp (afp') A6.fn = anfn = fn b'

In this case the factor of improvement compared withAM is thus greater the closer the interfering frequencyfc + [« lies to fc. The reason for this is that the fre-quency excursions 6.fn of the interference are propor-tional to fn (see 17). This also implies that if the FMtransmission channel contains white noise - a flatspectrum of uncorrelated interference vectors (b and anindependent of fn) - the low-frequency amplitude-noise spectrum after detection will be peaked ('trian-

Philips tech. Rev. 36, No. 11/12 MODULATION 323

gular noise'); the power spectrum is then parabolic(fig·30).We now consider an information signalof frequency

fp from a baseband O:fmax,and an FM transmissionchannel of bandwidth B (fig. 31). We let the frequencydeviation I1F of the signal be as large as the bandwidthallows. For simplicity we assume that B is much largerthanfmax, so that I1F ~ tB, and thus independent offp. After detection the signal contains low-frequencynoise originating from high-frequency noise from thewhole band B. A filter eliminates the low-frequency

Fig. 29. Vector diagram for phase or frequency modulation, withan interfering signal b cos (wc + Wn)t at the detector. For phasedetection the interference corresponds to a signalof modulationindex IXn.

Fig.30. 'Triangular noise'. In.frequency detection the frequencydeviation !:;,./n = IXn/n of an interfering signal is detected. Whitenoise before the detector can be regarded as uncorrelated inter-fering vectors b (see fig. 29), where b, and hence IXn, are inde-pendent of In. The low-frequency amplitude-noise signal (!:;,./n) atthe output of the FM detector is thus proportional to In, and thenoise-power spectrum (11) is proportional to/112•

o fmaxB

Fig. 31. Baseband O-/max and transmission channel of band widthB. Assuming that B is much larger than Imax, the maximum fre-quency deviation !:;,.P is very nearly equal to tB.

noise at frequencies above fmax. For the case of whitenoise in the FM channel we now calculate the ratio ofthe detected (low-frequency) noise power (N) in thebaseband to the detected signal power (S). The low-frequency noise power is the sum of contributions fromthe subbands dfn. We put b2 = ndfn; apart from aconstant factor, n is the noise power per Hz of band-width before the detector. We then find:

r-:= (A:F)2 f fn

2dfn

o

n/max3- 3(AI1F)2·

For AM detection we would have:Ima.

N = L:b2 = _!__ f náf« = nfmax.

S A2 A2 A2o

The improvement factor in the ratio ofthe signal powerto the noise power, SIN, in FM as compared with AMis thus 3(I1Flfmax)2 = 30:02•Here 0:0is the permissiblemodulation index at the highest frequency of the infor-mation signal. If, for example, 0:0is equal to 5, thenSIN in FM is 75 times greater than in AM.

Information theory shows that the signal-to-noise ratio afterthe detector, (SIN)o, can be improved by increasing the bandwidthof the channel combined with an appropriate signal treatment.The theoretically possible improvement, for not unduly smallvalues of (SIN)!, is given by the relation

(SIN)o Ri (SIN)lBlfmax.

Here (SIN)l is the ratio of the signal power in the channel to thenoise power generated in the channel. In FM the improvementis proportional to (Bllmax)2, as has just been demonstrated. Thus,FM gives an improvement of SIN when a larger bandwidth isused, but the improvement is far from what is theoretically pos-sible.

Pre-emphasis

We assume now that the information signal pet) isnot a pure sine wave but nearly sinusoidal, and that thefrequency fp varies slowly to and fro in the basebandO-fmax with unchanging amplitude (fig. 32a). Withphase modulation (fig. 32b), 0:is then constant and I1fis proportional to fp. The highest value of 11J, atfmax,must not exceed the maximum I1Fset by the bandwidthof the channel. At lower frequencies I1f is smaller andoptimum use is therefore not made ofthe channel band-width. Frequency modulation (fig.32c) does makeoptimum use of the channel bandwidth if I1f - whichhere is everywhere the same - is made equal to I1F.With normal audio signals, e.g. music, the power

decreases in general with rising frequency. To make

324

optimum use of the transmission channel over thewhole baseband in frequency modulation, the signalsat the higher frequencies are amplified with respect tothose with lower frequencies before modulation (pre-

ptt)

1Q O~------------------~---o -fp max

ex

I

1--__ ~--:L1:.;f-------J1 L1FIII1I

FM

O~ _J _

o -fpFig.32. When the information signal varies in frequency whilemaintaining a constant amplitude (a), exis constant and l:!.fproportional to fp in phase modulation (b), whereas l:!.f is con-stant and exinversely proportional to fp in frequency modulation(c). Phase modulation does not therefore make optimum use ofthe bandwidth (2l:!.F) of the transmission channel at all frequen-cies, whereas FM does.

F. W. DE VRIJER Philips tech. Rev. 36, No. 11/12

emphasis), in such a way that the spectrum of the newinformation signal q(t) becomes approximately flat.After modulation the reverse operation (de-emphasis)is applied to restore the original relationship betweenthe components. Fig. 33 shows some simple examplesof pre-emphasis and de-emphasis circuits used in FMradio, together with the pre-emphasis obtained. Athigh frequencies the pre-emphasis is proportional toJp; at the higher frequencies it therefore really amountsto transmitting pet) with "phase modulation (seefig. 32b). In this way an additional improvement ofthesignal-to-noise ratio is obtained.

Threshold effect

As long as the amplitude b of the interfering signalis smaller than A in fig.29, the phase variations itproduces are limited to the interval ± n/2; the resultantoscillates backwards and forwards in the vector dia-gram. The situation becomes entirely different as soonas the interference becomes stronger than the signal(b > A); the resultant then rotates r61. Whereas in thefirst case the zero in the signal Set) only shifted back-wards and forwards, in the second case the signal Set)completes one period more or less than the carrier atevery rotation of the resultant, so that there is oneextra or one less zero. In the first case the phase of thetotal signal approximately follows the phase of theoriginal signal; in the second case it follows that of theinterference signal. Within the detector band it is thusthe stronger of two FM signals that is received; theweaker, distorted beyond recognition, is audible asnoise. If the strength ratio changes, there is only anarrow transition region in which both signals are un-recognizable. In mobile telephone communication, forexample, this is an important consideration (p. 360).In the case of one signal, distorted by noise, this

effect sets a limit to the usefulness of increasing thefrequency deviation and thebandwidth. If the band-width is increased, so alsois the noise power at the de-tector. The vector diagramin fig. 34 shows the noiseof the detector schematic-ally as the area of a circle of

mdB~----------------~16

14

q(t) 12-+

10

8

6

4

2

O~--~~~----~~.0.1

QocP(l+jwRC) (r-«:R)

R

~P(XQ(1+jwRCr1 --- .. Fp

Fig. 33. Pre-emphasis and de-emphasis circuits and the pre-emphasis obtained for two valuesof the product RC. The quanti-ties Pand Q are the complexamplitudes of p(t) and q(t) as afunction of w.

Philips tech. Rev. 36, No. 11/12 MODULATION 325

radius b. When the modulation index (J. is increased,the growth of the bandwidth results in a larger 'noisecircle'. When b approaches the carrier amplitude A,the threshold is reached at which any further increasein frequency deviation has an adverse effect.

The situation is summarized in fig. 35. For FM andAM (with synchronous detection) the figure gives thesignal-to-noise power ratio (S/N)o after detection, in alog-log plot as a function of (Sc/N)j, which is the ratio,before detection, of the carrier power to the noisepower in a bandwidth equal to that of the basebandsignal. In AM (curve AM) the two quantities arealways identical (A 2/"Lb2 in fig. 34). At not too smallvalues of (Sc/N)i the value of (S/N)o in FM (curveFMl) is higher than in AM by a fixed factor (a number

Fig. 34. Threshold effect. If (X and hence the frequency deviationand bandwidth are increased to improve the signal-to-noise ratio,the total noise power at the detector also increases. This impliesthat the 'noise circle' (radius b) becomes larger. If b is no longersmall compared with A, the threshold has been reached at whicha further increase of a leads to a worse result.

(dB) //,.

/ FM2

////I//

(dB)

Fig.35. Ratio of low-frequency signal power to low-frequencynoise power after the detector, (S/ N)o, as a function of the ratioof the carrier power to the r.f, noise power in a band with thesarne bandwidth as the base band signal at the detector, (Se/N)l.In AM with synchronous detection both quantities are identical.For large values of (Se/N)i, FM is better than AM by a constantnumber of decibels; at the threshold Dl the advantage diminishes,and below D2, FM is worse than AM (curve FMI). With a largerfrequency deviation (and bandwidth) the curve for large (Se/N)ishifts upward (FM2), but the thresholds shift to the right.

of decibels that is independent of (SclN)j). If thedistance from the transmitter to the receiver is nowincreased, (Sc/N)i decreases because A in fig. 34 be-comes smaller and therefore b becomes relatively larger.When b approaches A, the advantage of FM (after thethreshold Dl) is reduced. When the threshold D2 isreached, FM in fact becomes worse than AM. Inpractice Dl would be 10 to 12 dB and Dz 6 to 8 dB.If the frequency deviation and the bandwidth are in-creased in FM, the gain with FM is greater (curve FMz),but on decreasing (Sc/N)i the thresholds are reachedearlier because the noise circle was initially larger.

Threshold extension

It may sometimes be necessary to work with weak signals, forexample in reception of signals from a communication satelliteowing to the very limited power that the satellite can deliver, orin communication between distant stations that lie in each other'sEarth shadow, orwhen the cornrnunication is brought about by thescatteringofradio signals from inhomogeneities in the troposphereor ionosphere. In such cases the following method may be used toextend the thresholds in fig. 35. Fig. 36a gives a block diagram ofa conventional FM receiver, if the connection indicated by thedashed line is disregarded for the moment. The radio-frequencyFM signal S of carrier amplitude A and modulation index (Xl

(fig. 36b) is converted in the mixer M by the local oscillator Lainto an intermediate-frequency signal S'. The relations in thevector diagram remain unchanged. The i.f. filter FI determinesthe bandwidth ofthe transmission channel, and hence at the sametime the radius bI ofthe noise circle in fig. 36b. The FM detector Dsenses the freq uency variations due to signal and noise, and thedetected signal is limited in bandwidth by the lowpass filter F2,

r.f if f.fifM

- - - - - - --+ - - - - - - _.g

Fig.36. a) Circuit for 'threshold extension'. M mixer, La localoscillator, FI i.f. filter, D detector, F2 low-frequency filter. Inordinary FM reception (no dashed line) the deviation of thei.f. signal S' is the same as that of the r.f. signal S. By meansof the dashed connection the signalof the local oscillator is madeto follow the input signal S in frequency, thus reducing the devia-tion of S'. The response of FI can then be narrowed. The noisecircle becomes smaller and the distance to the threshold becomeslarger. b) Modulation index and noise circle before (al, bl) andafter (a2, b2) the threshold extension.

[6] See for example J. van Slooten, Philips tech. Rev. 22, 352,1960/61.

326 F. W. DE VRIJER Philips tech. Rev. 36, No. 11/12

which removes all signals of frequency greater than j;nax (themaximum frequency of the information signal).

Let the modulation index al be so large that the bandwidth itrequires causes b, to approach closely to A; the threshold is thenreached. The connection indicated by the dashed line in fig. 36arepresents feedback that introduces the desired threshold ex-tension. La now oscillates at a frequency that depends on theinstantaneous value of the signal from F2, in such a way that theinstantaneous frequency of S is followed. Consequently the fre-quency swing of S' becomes smaller, so that in fig. 36b the signalis now represented by, say, a2. This does not cause any change inthe noise (at least if S was not filtered before M). However, thefilter Fi can now be made so narrow that S' is only just accepted.As a result the noise is reduced, say to the circle of radius b2 infig. 36b. Thus, while preserving the signal-to-noise ratio, thethreshold has been effectively extended. In this way it is possiblein practice to shift the threshold in fig. 35 by 6 to 10 dB towardsthe left. There are limits, however, to the process. Narrowing ofF, implies frequency narrowing and hence a delay in the controlloop. In the long run LO follows the signal S with a delay suchthat the frequency deviation of S' remains too large for F1.

Applications; magnetic recording of video signals

In the foregoing the emphasis has been placed on thepossibility of obtaining a better signal-to-noise ratiowith FM than with AM. This is of great importance inmany forms of telecommunication. The insensitivity toamplitude variations is another great advantage, forexample in microwave links and mobile installations.We shall not consider the use of FM in telecommunica-tion further now, but will return to it at some length inthe final section.

Another example of an application is to be found infrequency-analog measurement and control systemswhere quantities in a physical process to be telemeteredor used in a remote-control system are converted intothe frequency of an electrical signal, to protect theinformation from transmission interference [7].

In this section we shall confine ourselves to anexample of the use of modulation for inforrnationstorage: the magnetic recording of video signals. Thereason for using FM here is its insensitivity to ampli-tude variations; there is no question of any gain insignal-to-noise ratio.

An audio signalon a gramophone disc or audiomagnetic tape is recorded directly in the baseband.This cannot be done with a video signal, because theratio of the highest to the lowest frequency is too great.The ratio that can be handled by a magnetic tape is ofthe order of 1000. This is given by the minimum andmaximum wavelengths of the magnetic variations onthe tape, which in their turn are determined respectivelyby the gap length of the head and the size of the headitself (fig. 37). At a maximum frequency of 5 MHz- the upper limit of the video signal (seefig· 38) - thelowest frequency would therefore be 5 kHz, and this isnot low enough.

Ns N N 5-vFig. 37. Magnetic head Hand tape··;r.-of a tape recorder, schematic.The interaction between the coil C and the tape magnetizationtakes place via the lines of force through the head. The interactionbecomes very poor when the wavelength J. on the tape becomessmaller than the gap length lor greater than the head itself.

y

o

Fig.38. Video baseband spectrum. The video signal consists ofthe luminance signal Y and the chrominance signal C (coloursignaion a subcarrier at 4.43 M Hz) [8].

Dr

T

OrFig. 39. Video tape recorder with two moving heads in the VCR,schematic. Left: the tape T follows a helical line around thedrum Dr. The heads HI and Hz rotate on the disc D along thegap G. Right: drum and tape developed into a plane. Each por-tion of track from one edge of the tape to the other correspondsto one television field period (1/50 s). The pitch of the tracks is0.187 mm, the tape speed 14.3 cm/s, the head-over-tape speed8.1 mis.

Modulation is the remedy here: by shifting the video-frequency band towards higher frequencies, we reducethe frequency ratio while preserving the bandwidth.Tn particular, FM is the best method here because thesignal amplitude at the highest frequencies (the shortestwavelengths) depends closelyon the distance betweenhead and tape and on the tape quality, and conse-quently can show considerable unintended variations.

The move to higher frequencies has to be paid for bya higher tape speed relative to the head. In tape recor-ders for use in the home (VCR, video cassette recorders)the video baseband cut-off is at 3 MHz, and a tapespeed of 8.1 mis relative to the head is used; this is

[7] D. Gossel, Philips tech. Rev. 34, 288, 1974.[8] Colour-television systems are discussed in F. W. de Vrijer,

Philips tech. Rev. 27, 33, 1966.

Philips tech. Rev. 36, No. J 1/12 MODULATION 327

_-_~,. <,, ........

J ,

I ", " ,,, ,,{:

(8.5MHz)

(10MHz)

Fig. 40. The spectrum available with magnetic tape (schematicallyindicated by dashed curve) - which may differ slightly from tapeto tape - is so limited that it can barely contain at the same timetwo sidebands of the first order,!e ± fmnx (fmnx, the width of thebaseband, is 5 MHz in a professional video tape recorder). Inthis diagram the choice of 8.5 MHz for the 'carrier frequency'fe is somewhat arbitrary.

- ------w

-----g

-ts

-tFig. 41. Instantaneous frequency fm of the modulated signal as afunction of time during a picture line period, for the case where awhite, a grey and a black area are side by side in the picture. Thetable below gives the values of fm for 'white' (w), 'black' (b) and'top sync' (ts), the passed bandwidth fmnx of the video signal,the maximum peak-to-peak frequency deviation 2tlJ, the mod-ulation index Ol: = tlflfmnx and the head-over-tape speed h inbroadcast equipment and in VCR.

Broadcast VCR

fm white 9.30 MHz 4.4 MHzblack 7.80 MHz 3.5 MHztop sync 7.16 MHz 3.0 MHz

fmn" 5.0 MHz 3.0 MHz2!lf 2.14 MHz 1.4 MHzOl: 0.21 0.23v 41.1 mis 8.1 mis

",..-- .....,. ...... ...... ........ ......4.43MHz

4.07 8.50MHz

-f0.36 4.79

Fig. 42. FM spectrum at a 'carrier frequency' of 8.50 MHz and abaseband signalof 4.43 MHz, the frequency of the colour sub-carrier. Since in practice negative frequencies are equivalent topositive ones, lower sidebands with negative frequencies arefound 'folded back' into the spectrum of positive frequencies.In the present case the third lower sideband comes into the bandused (shown dashed) and would cause interference there if Ol: werenot so small.

achieved by means of two moving heads (fig. 39). Inprofessional equipment used for broadcasting the base-band goes up to 5 MHz; the head/tape speed of41.1 mis is obtained with four moving heads.The available bandwidth is unfortunately so small

that it is barely able to contain the 2/max part (10 MHzin professional equipment) of the 2/max + 2Ll/band-width required according to Carson (fig. 40). Thuslittle remains for 2Llf, the maximum peak-to-peak fre-quency deviation; seefig. 41. The modulation index ctis therefore much smaller than 1, so that there is nosignal-to-noise improvement.A very small ct in the situation illustrated in fig. 40 is

also required for other reasons. Since the 'carrier fre-quency' le is not much greater than half the bandwidth- unlike the case in FM broadcasting, for example -'folded lower sidebands of higher order' enter the fre-quency band used, and would give rise to interferencèif ct was not so small. In this respect the subcarrier ofthe colour signal (fig. 38), which is always present ata fairly large amplitude, is especially troublesome; seefig. 42. A further danger comes from the nonlinearityof the recording process. This gives rise to higher har-monics of the carrier in the read-out signal (at fre-quencies 2/e, 3/e, ... ), which are also frequency-mod-ulated, and whose lower sidebands may enter the bandin use. For this reason again ct must be small.

In fact the process of magnetically recording video signals isvery difficult to analyse. In the first place the 'carrier frequency'does not have such a distinct meaning as it has in FM broad-casting, because the video signal, and hence the instantaneousfrequency fm, have no obvious mean: it is lower in the darkerareas than in the light areas of the picture. Here fe can best beregarded as the mean of fm over suitably chosen short periods.

In the second place the situation is complicated by the factthat the. available frequency band (fig. 40) is very limited, is notflat and is different for every magnetic tape. In particular, devia-tions from the normal FM situation arise because the upper side-band is attenuated more than the lower sideband. The magnitudeof this effect depends both on the baseband frequency (whichmay have values from 0 tofmn,,) and on the 'carrier frequency' fe.These deviations, however, are partly overcome by a VSB-typeeffect arising as a result of the sloping band edge (see figs. 20 and21). In any case, these effects are least pronounced at the lowfrequencies of the baseband signal, the frequencies to whichthe eye is most sensitive.

In the video cassette player, as stated earlier, thebaseband signal is limited to about 3 MHz. The coloursubcarrier is therefore suppressed. The colour informa-tion in this case is carried in QAM on a separate carrierat about 560kHz. The frequency band for this informa-tion is below the band used for the brightness signal.At these low frequencies the amplitude variationsresulting from 'band flutter' are sufficiently small forthis form of amplitude modulation.

328 Philips tech. Rev. 36, No. 11/12

RO 150 communications receiver for frequencies between 0.2 MHz and30 MHz (wavelengths between 10 and 1500 m). The tuning is electronic;the coarse tuning is by stepping switches and thefine tuning is continuousover intervals of 100 kHz. The tunedfrequency is displayed digitally. Thereceiver can detect various types of amplitude modulation: conventionalAM, AM with suppressed carrier, upper-sideband and lower-sidebandmodulation. In addition a separate module permits the reception of AMwith two independent sidebands ([SB), and of frequency-shift keying andfacsimile.