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EC2353 -Antenna and wave propagation

Introduction

An antenna is an electrical conductor or system of conductors Transmission - radiates electromagnetic energy into space Reception - collects electromagnetic energy from space

In two-way communication, the same antenna can be used for transmission andreception

An antenna is a circuit element that provides a transition form a guided wave on atransmission line to a free space wave and it provides for the collection of

electromagnetic energy.

In transmit systems the RF signal is generated, amplified, modulated and appliedto the antenna

In receive systems the antenna collects electromagnetic waves that are cuttingthrough the antenna and induce alternating currents that are used by the receiver

CONCEPT OF VECTOR POTENTIAL

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Hertzian dipole

A simple practical antenna is a doublet or Hertzian dipole (see a figure below). It

is very short length of wire over which the current distribution can be assumed uniform.Maxwells equations show that such an antenna when energized by a high frequencycurrent is associated with an induction field which decreases inversely as square of the

distance and a radiation field which decreases inversely as distance only. The later is still

measurable at large distances from the doublet and is well-known radiation field used inradio communications

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DEFINITIONS

Radiation Intensity. In a given direction, the power radiated form an antenna perunit solid angle.

Directive Gain. In a given direction, 4 times the ratio of theradiation intensity inthat direction to the total power radiated by the antenna.

Directivity. The value of the directive gain in the direction of its maximum value. Power Gain. In a given direction, 4 times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter. NOTES: (1) When thedirection is not stated, the power gain is usually

taken to be thepower gain in the direction of its maximum value. (2) Power gaindoes not include reflection losses arising from mismatchof impedance.

Beamwidthis the angular separation of the half-power points of the radiatedpattern

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Bandwidthis the difference between the upper and lowercutoff frequenciesof,for example, afilter,acommunication channel,or asignal spectrum,and is

typically measured inhertz.In case of abasebandchannel or signal, the andwidthis equal to its upper cutoff frequency. Bandwidth in hertz is a centralconcept in

many fields, includingelectronics,information theory,radiocommunications,

signal processing,andspectroscopy GAINGain is an antenna property dealing with an antenna's ability to

direct its radiated power in a desired direction, or to receive

energy preferentially from a desired direction. However, gain isnot a quantity which can be defined in terms of physical quantities

such as the Watt, ohm or joule, but is a dimensionless ratio.

As a consequence, antenna gain results from the interaction of

all other antenna characteristics.Antenna characteristics of gain,beamwidth, and efficiency areindependent of the antenna's use for

either transmitting or receiving. Generally these characteristics are

more easilydescribed for the transmitting case, however, theproperties apply as well to receiving applications.

Radiation resistanceAn important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna. If I is the r.m.s (root mean square)antenna current and Rr is its radiation resistance, then the power radiated is I2Rr

watts where Rr is afictitiousresistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat. The larger the radiationresistance the larger the power radiated by the antenna. In contrast, for receiving

antenna its input impedance is important. The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable. The input impedance may or may not be equal to radiation resistance,though very often it does. In most case Rr may be calculated or it can be determined

experimentally.

Half-wavelength dipoleThis type of antenna is a special case where each wire is exactly one-quarter of

the wavelength, for a total of a half wavelength. The radiation resistance is about 73

ohms if wire diameter is ignored, making it easily matched to a coaxial transmissionline. The directivity is a constant 1.64, or 2.15 dB. Actual gain will be a little less due

to ohmic losses.

Folded dipoleA folded dipole is a dipole where an additional wire (/2) links the two ends of the

(/2) half wave dipole. The folded dipole works in the same way as a normal dipole,

but the radiation resistance is about 300ohmsrather than the 75 ohms which is

expected for a normal dipole. The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line.

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RECIPROCITY: An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniformand equal to its peak. The relationship between Le and L is given by:

Effective apertureThe power received by an antenna can be associated with collecting area. Every

antenna may be considered to have such a collecting area which is called its effectiveaperture A. If Pd is a power density at the antenna and Pr is received power, then:

Polarization is the direction of the electric field and is the same as the physicalattitude of the antenna

A vertical antenna will transmit a vertically polarized waveThe receive and transmit antennas need to possess the same polarization

Antenna Gain Relationship between antenna gain and effective area

G = antenna gain

Ae = effective areaf = carrier frequency

c = speed of light ( 3 108 m/s)

= carrier wavelength

Radiation Pattern Radiation pattern is an indication of radiated field strength around the antenna.

Power radiated from a /2 dipole occurs at right angles to the antenna with nopower emitting from the ends of the antenna. Optimum signal strength occurs at

right angles or 180 from opposite the antenna

Radiation pattern Graphical representation of radiation properties of an antenna Depicted as two-dimensional cross section

Beam width (or half-power beam width) Measure of directivity of antenna

Reception pattern Receiving antennas equivalent to radiation pattern

Antenna Temperature

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( ) is a parameter that describes how much noise an antenna produces in a given

environment. This temperature is not the physical temperature of the antenna. Moreover,an antenna does not have an intrinsic "antenna temperature" associated with it; rather the

temperature depends on its gain pattern and the thermal environment that it is placed in.

To define the environment, we'll introduce a temperature distribution - this is thetemperature in every direction away from the antenna in spherical coordinates. Forinstance, the night sky is roughly 4 Kelvin; the value of the temperature pattern in thedirection of the Earth's ground is the physical temperature of the Earth's ground. This

temperature distribution will be written as . Hence, an antenna's temperature willvary depending on whether it is directional and pointed into space or staring into the sun.

For an antenna with aradiation patterngiven by , the noise temperature is

mathematically defined as:

This states that the temperature surrounding the antenna is integrated over the entire

sphere, and weighted by the antenna's radiation pattern. Hence, an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna; for a perfectly directional antenna (with a pencil beam), the antenna temperaturewill only depend on the temperature in which the antenna is "looking".

The noise power received from an antenna at temperature can be expressed in terms ofthebandwidth(B) the antenna (and its receiver) are operating over:

In the above,Kis Boltzmann's constant (1.38 * 10^-23 [Joules/Kelvin = J/K]). The

receiver also has a temperature associated with it ( ), and the total system temperature

(antenna plus receiver) has a combined temperature given by . This

temperature can be used in the above equation to find the total noise power of the system.

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics, because the resulting systems very much depend on each other.

A parameter often encountered in specification sheets for antennas that operate in certainenvironments is the ratio ofgainof the antenna divided by the antenna temperature (or

system temperature if a receiver is specified). This parameter is written as G/T, and has

units of dB/Kelvin [dB/K].

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end,that behaves as a dipole antenna. It is formed by a conductor in length. It is fed in

the lower end, which is near a conductive surface which works as a reflector (see

Effect of ground). The current in the reflected image has the same direction andphase that the current in the real antenna. The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space.

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Antenna arrayis a group of antennas or antenna elements arranged to provide the

desired directional characteristics. Generally any combination of elements can form anarray. However, equal elements in a regular geometry are usually used.

PATTERN MULTIPLICATIONThe pattern multiplication principle states that the radiation patterns of an array ofN

identical antennas is equal to the product of the element patternFe( )(pattern of one ofthe antennas) and the array patternFa( ), whereFa( )is the pattern obtained upon

replacing all of the actual antennas with isotropic sources.

LOOP ANTENNAThe small loop antenna is a closed loop as shown in Figure 1. These antennas

have low radiation resistance and high reactance, so that theirimpedanceis

difficult to match to a transmitter. As a result, these antennas are most often

used as receive antennas, where impedance mismatch loss can be tolerated.

The radius is a, and is assumed to be much smaller than a wavelength (a

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Figure 1. Small loop antenna.

Since the loop is electrically small, the current within the loop can be

approximated as being constant along the loop, so thatI= .

The fields from a small circular loop are given by:

The variation of the pattern with direction is given by , so that the

radiation pattern of a small loop antenna has the same power pattern as that of a

short dipole.However, the fields of a small dipole have the E- and H- fields

switched relative to that of a short dipole; the E-field is horizontally polarized

in the x-y plane.

The small loop is often referred to as the dual of the dipole antenna, because if

a small dipole had magnetic current flowing (as opposed to electric current as

in a regular dipole), the fields would resemble that of a small loop.

While the short dipole has a capacitive impedance (imaginary part of

impedance is negative), the impedance of a small loop is inductive (positive

imaginary part). The radiation resistance (and ohmic loss resistance) can be

increased by adding more turns to the loop. If there areNturns of a small loop

antenna, each with a surface area S(we don't require the loop to be circular at

this point), the radiation resistance for small loops can be approximated (in

Ohms) by:

For a small loop, the reactive component of the impedance can be determined

by finding the inductance of the loop, which depends on its shape (then

X=2*pi*f*L). For a circular loop with radius aand wire radiusp, the reactive

component of the impedance is given by:

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Small loops often have a low radiation resistance and a highly inductivecomponent to their reactance. Hence, they are most often used as receive

antennas. Exaples of their use include in pagers, and as field strength probes

used in wireless measurements.

Loop antennaA loopantennahas a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor. All planar loops aredirectional antennas with a sharp null, and have a radiation pattern similar to thedipoleantenna.However, the large and small loops have different orientations with respect to

their radiation pattern.

Small loopsA loop is considered asmall loopif it is less than 1/4 of a

wavelength in circumference. Most directional receiving loops are about 1/10 of a

wavelength. The small loop is also called themagnetic loopbecause it is more sensitivie

to themagnetic componentof the electromagnetic wave. As such, it is less sensitive tonear field electric noise when properly shielded. The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor.

Since the small loop is small with respect to a wavelength, thecurrent around the antenna is nearly completely in phase. Therefore, waves approaching

in the plane of the loop will cancel, and waves in the axis perpendicular to the plane of

the loop will be strongest. This is the opposite mechanism as the large loop.

Large loopsThe (large) loop antenna is similar to a dipole, except that the

ends of the dipole are connected to form a circle, triangle () or square. Typically a loop is

a multiple of a half or full wavelength incircumference.A circular loop gets higher gain(about 10%) than the other forms of large loop antenna, as gain of this antenna is directly

proportional to the area enclosed by the loop, but circles can be hard to support in a

flexible wire, making squares and triangles much more popular. Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane. The largeloop has its strongest signal in the plane of the loop, and nulls in the axis perpendicular tothe plane of the loop. This is the opposite orientation to the small loop.

AM loopsAM loops are loops tuned for theAM broadcastingband.

Because of the extremely long wavelength, an AM loop may have multiple turns of wire

and still be less than 1/10 of a wavelength. Typically these loops are tuned with a

capacitor, and may also be wound around aferriterod to increaseaperture.

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain,

but have a sharp null in the axis perpendicular to their highest gain. Therefore, when

using a loop for direction finding, the plane of the antenna is rotated until the signaldisappears. As planar loops have a 180 degree symmetry, other methods must be used to

determine if the signal is in front or behind the loop.

Frequently, a dipole and a loop are used together, to obtain acombinedcardioidradiation pattern with a sharp null on only one side.

Uniform linear array

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Slot antennasare used typically at frequencies between 300 MHz and

24 GHz. These antennas are popular because they can be cut out of whateversurface they are to be mounted on, and haveradiation patternsthat are roughly

omnidirectional (similar to a linear wire antenna, as we'll see). The polarization

is linear. The slot size, shape and what is behind it (the cavity) offer design

variables that can be used to tune performance.

Consider an infinite conducting sheet, with a rectangular slot cut out of

dimensions aand b, as shown in Figure 1. If we can excite some reasonable

fields in the slot (often called the aperture), we have an antenna.

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Figure 1. Rectangular Slot antenna with dimensions aand b.

To gain an intuition about slot antennas, first we'll learn Babinet's principle (put

into antenna terms by H. G. Booker in 1946). This principle relates the radiated

fields and impedance of an aperture or slot antenna to that of the field of its

dual antenna. The dual of a slot antenna would be if the conductive materialand air were interchanged - that is, the slot antenna became a metal slab in

space. An example of dual antennas is shown in Figure 2:

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Hence, if we know the fields from one antenna we know the fields of the other

antenna. Hence, since it is easy to visualize the fields from adipole antenna,the

fields and impedance from a slot antenna can become intuitive if Babinet's

principle is understood.

Note that thepolarizationof the two antennas are reversed. That is, since the

dipole antenna on the right in Figure 2 is vertically polarized, the slot antenna

on the left will be horizontally polarized.

Duality Example

As an example, consider a dipole similar to the one shown on the right in

Figure 2. Suppose the length of the dipole is 14.4 centimeters and the width is 2

centimeters, and that the impedance at 1 GHz is 65+j15 Ohms. The fields fromthe dipole antenna are given by:

What are the fields from a slot at 1 GHz, with the same dimensions as the

dipole?

Using Babinet's principle, the impedance can be easily found:

The impedance of the slot for this case is much larger, and while the dipole's

impedance is inductive (positive imaginary part), the slot's impedance is

capacitive (negative imaginary part). The E-fields for the slot can be easily

found:

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We see that the E-fields only contain a phi (azimuth) component; the antenna istherefore horizontally polarized.

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher

frequencies (I've heard of horns operating as high as 140 GHz). They often

have a directionalradiation patternwith a highgain, which can range up to 25

dB in some cases, with 10-20 dB being typical. Horns have a wide impedance

bandwidth,implying that theinput impedanceis slowly varying over a wide

frequency range (which also implies low values forS11orVSWR). The

bandwidth for practical horn antennas can be on the order of 20:1 (for instance,

operating from 1 GHz-20 GHz), with a 10:1 bandwidth not being uncommon.

The gain often increases (and thebeamwidthdecreases) as the frequency of

operation is increased. Horns have very little loss, so thedirectivityof a horn is

roughly equal to its gain.

Horn antennas are somewhat intuitive and not relatively simple to manufacture.

In addition, acoustic horns also used in transmitting sound waves (for example,

with a megaphone). Horn antennas are also often used to feed a dish antenna, or

as a "standard gain" antenna in measurements.

Popular versions of the horn antenna include the E-plane horn, shown in Figure

1. This horn is flared in the E-plane, giving the name. The horizontal dimension

is constant at w.

Figure 1. E-plane horn.

Another example of a horn is the H-plane horn, shown in Figure 2. This horn is

flared in the H-plane, with a constant height for the waveguide and horn of h.

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Figure 2. H-Plane horn.

The most popular horn is flared in both planes as shown in Figure 3. This is a

pyramidal horn, and has widthBand heightAat the end of the horn.

Figure 3. Pyramidal horn.

Horns are typically fed by a section of a waveguide, as shown in Figure 4. The

waveguide itself is often fed with ashort dipole,which is shown in red in

Figure 4. A waveguide is simply a hollow, metal cavity. Waveguides are used

to guide electromagnetic energy from one place to another. The waveguide in

Figure 4 is a rectangular waveguide of width band height a, with b>a. The E-

field distribution for the dominant mode is shown in the lower part of Figure 1.

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Figure 4. Waveguide used as a feed to horn antennas.

Reflector AntennaTo increase thedirectivityof an antenna, a fairly intuitive solution is to use a

reflector. For example, if we start with a wire antenna (lets say ahalf-wave

dipoleantenna), we could place a conductive sheet behind it to direct radiation

in the forward direction. To further increase the directivity, a corner reflector

may be used, as shown in Figure 1. The angle between the plates will be 90

degrees.

Figure 1. Geometry of Corner Reflector.

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The radiation pattern of this antenna can be understood by using image theory,

and then calculating the result via array theory. For ease of analysis, we'll

assume the reflecting plates are infinite in extent. Figure 2 below shows the

equivalent source distribution, valid for the region in front of the plates.

Figure 2. Equivalent sources in free space.

The dotted circles indicate antennas that are in-phase with the actual antenna;

the x'd out antennas are 180 degrees out of phase to the actual antenna.

Assume that the original antenna has an omnidirectional pattern given by .Then the radiation pattern (R) of the "equivalent set of radiators" of Figure 2

can be written as:

The above directly follows from Figure 2 and array theory (kis thewave

number.The resulting pattern will have the same polarization as the original

vertically polarized antenna. The directivity will be increased by 9-12 dB. The

above equation gives the radiated fields in the region in front of the plates.

Since we assumed the plates were infinite, the fields behind the plates are zero.

The directivity will be the highest when dis a half-wavelength. Assuming the

radiating element of Figure 1 is ashort dipolewith a pattern given by ,

the fields for this case are shown in Figure 3.

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Figure 3. Polar and azimuth patterns of normalized radiation pattern.

The radiation pattern, impedance and gain of the antenna will be influenced by

the distance dof Figure 1. The input impedance is increased by the reflector

when the spacing is one half wavelength; it can be reduced by moving the

antenna closer to the reflector. The lengthLof the reflectors in Figure 1 are

typically 2*d. However, if tracing a ray travelling along the y-axis from the

antenna, this will be reflected if the length is at least . The height of the

plates should be taller than the radiating element; however since linear antennasdo not radiate well along the z-axis, this parameter is not critically important.

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna, commonly

known as a satellite dish antenna. Examples of this dish antenna are shown in the

following Figures.

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Figure 1. The "big dish" of Stanford University.

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Figure 2. A random "direcTV dish" on a roof.

Parabolic reflectors typically have a very highgain(30-40 dB is common) and lowcross

polarization.They also have a reasonable bandwidth, with thefractional bandwidth

being at least 5% on commercially available models, and can be very wideband in the

case of huge dishes (like the Stanford "big dish" above, which can operate from 150

MHz to 1.5 GHz).

The smaller dish antennas typically operate somewhere between 2 and 28 GHz. The

large dishes can operate in the VHF region (30-300 MHz), but typically need to be

extremely large at this operating band.

The basic structure of a parabolic dish antenna is shown in Figure 3. It consists of a feed

antenna pointed towards a parabolic reflector. The feed antenna is often ahorn antenna

with a circular aperture.

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Figure 3. Components of a dish antenna.

Unlike resonant antennas like thedipole antennawhich are typically approximately a

half-wavelength long at the frequency of operation, the reflecting dish must be much

larger than a wavelength in size. The dish is at least several wavelengths in diameter, but

the diameter can be on the order of 100 wavelengths for very high gain dishes (>50 dB

gain). The distance between the feed antenna and the reflector is typically several

wavelenghts as well. This is in contrast to thecorner reflector,where the antenna is

roughly a half-wavelength from the reflector.

In the next section, we'll look at the parabolic dish geometry in detail and why a parabola

is a desired shape.To start, let the equation of a parabola with focal lengthFcan be written in the

(x,z) plane as:

This is plotted in Figure 1.

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Figure 1. Illustration of parabola with defining parameters.

The parabola is completely described by two parameters, the diameterDand

the focal lengthF. We also define two auxilliary parameters, the vertical height

of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ). These parameters are related to each other by the following

equations:

To analyze the reflector, we will use approximations from geometric optics.

Since the reflector is large relative to a wavelength, this assumption is

reasonable though not precisely accurate. We will analyze the structure viastraight line rays from the focal point, with each ray acting as a plane wave.

Consider two transmitted rays from the focal point, arriving from two distinct

angles as shown in Figure 2. The reflector is assumed to be perfectly

conducting, so that the rays are completely reflected.

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Figure 2. Two rays leaving the focal point and reflected from the parabolicreflector.

There are two observations that can be made from Figure 2. The first is that

both rays end up travelling in the downward direction (which can be

determined because the incident and reflected angles relative to the normal of

the surface must be equal). . The rays are said to be collimated. The second

important observation is that the path lengths ADE and ABC are equal. This

can be proved with a little bit of geometry, which I won't reproduce here. These

facts can be proved for any set of angles chosen. Hence, it follows that:

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction.

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant.

As a result of these observations, it follows the distribution of the field on the

focal plane will be in phase and travelling in the same direction. This gives rise

to the parabolic dish antennas highly directionalradiation pattern.This is why

the shape of the dish is parabolic.

Finally, by revolving the parabola about the z-axis, a paraboloid is obtained, as

shown below.

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For design, the value of the diameterDshould be increased to increase the gain

of the antenna. The focal lengthFis then the only free parameter; typical

values are commonly given as the ratioF/D, which usually range between 0.3and 1.0. Factors affecting the choice of this ratio will be given in the following

sections.

In the next section, we'll look at gain calculations for a parabolic reflector

antenna.

The fields across the aperture of the parabolic reflector is responsible for this

antenna's radiation. The maximum possible gain of the antenna can be

expressed in terms of the physical area of the aperture:

The actual gain is in terms of theeffective aperture,which is related to the

physical area by the efficiency term ( ). This efficiency term will often be on

the order of 0.6-0.7 for a well designed dish antenna:

Understanding this efficiency will also aid in understanding the trade-offs

involved in the design of a parabolic reflector. The efficiency can be written as

the product of a series of terms:

We'll walk through each of these terms.

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses,

as discussed on theefficiencypage. Sincehorn antennasare often used as

feeds, and these have very little loss, and because the parabolic reflector istypically metallic with a very high conductivity, this efficiency is typically

close to 1 and can be neglected.

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antenna's aperture. In general, an antenna will have the maximum

gain if the E-field is uniform in amplitude and phase across the aperture (the

far-field is roughly the Fourier Transform of the aperture fields). However, the

aperture fields will tend to diminish away from the main axis of the reflector,

which leads to lower gain, and this loss is captured within this parameter.

This efficiency can be improved by increasing theF/Dratio, which also lowers

the cross-polarization of the radiated fields. However, as with all things in

engineering, there is a tradeoff: increasing theF/Dratio reduces the spillover

efficiency, discussed next.

Spillover Efficiency

The spillover efficiency is simple to understand. This measures the amount

of radiation from the feed antenna that is reflected by the reflector. Due to the

finite size of the reflector, some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than , thus not being

reflected. This efficiency can be improved by moving the feed closer to the

reflector, or by increasing the size of the reflector.

Other Efficiencies

There are many other efficiencies that I've lumped into the parameter . This

is a major of all other "real-world effects" that degrades the antenna's gain and

consists of effects such as:

Surface Error- small deviations in the shape of the reflector degrades

performance, especially for high frequencies that have a small wavelength and

become scattered by small surface anomalies

Cross Polarization- The loss of gain due tocross-polarized(non-desirable)

radiation

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Aperture Blockage- The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector.

Non-Ideal Feed Phase Center- The parabolic dish has desirable properties

relative to a single focal point. Since the feed antenna will not be a point

source, there will be some loss due to a non-perfect phase center for a horn

antenna.

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms ofF

andD) and the feed antenna's radiation pattern. Instead of introducing complex

formulas for some of these terms, we'll make use of some results by S. Silver

back in 1949. He calculated the aperture efficiency for a class of radiation

patterns given as:

TYpically, the feed antenna (horn) will not have a pattern exactly like the

above, but can be approximated well using the function above for some value

of n. Using the above pattern, the aperture efficiency of a parabolic reflector

can be calculated. This is displayed in Figure 1 for varying values of and the

F/Dratio.

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Figure 1. Aperture Efficiency of a Parabolic Reflector as a function ofF/Dorthe angle , for varying feed antenna radiation patterns.

Figure 1 gives a good idea on design of optimal parabolic reflectors. First,Dis

made as large as possible so that the physical aperture is maximized. Then the

F/Dratio that maximizes the aperture efficiency can be found from the above

graph. Note that the equation that relates the ratio ofF/Dto the angle can be

foundhere.

In the next section, we'll look at the radiation pattern of a parabolic antenna.

In this section, the 3d radiation patterns are presented to give an idea of what

they look like. This example will be for a parabolic dish reflector with the

diameter of the dishDequal to 11 wavelengths. TheF/Dratio will be 0.5. A

circular horn antenna will be used as the feed.

The maximum gain from the physical aperture is ; the

actual gain is 29.3 dB = 851, so we can conclude that the overall efficiency is

77%. The 3D patterns are shown in the following figures.

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As can be seen, the pattern is highly directional. TheHPBWis approximately 5

degrees, and thefront-to-back ratiois approximately 33 dB.

LENS ANTENNA.Another antenna that can change spherical waves into flat plane waves is thelens antenna. This antenna uses a microwave lens, which is similar to an optical lens to straighten the

spherical wavefronts. Since this type of antenna uses a lens to straighten the wavefronts, its design is

based on the laws of refraction, rather than reflection. Two types of lenses have been developedto provide a plane-wavefront narrow beam for tracking radars, while avoiding the problems

associated with the feedhorn shadow. These are the conducting(acceleration) type and

the dielectric (delay) type. The lens of an antenna is substantially transparent to microwave energy thatpasses through it. It will, however, cause the waves of energy to be either converged or

diverged as they exit the lens. Consider the action of the two types of lenses. The conducting type of lens

is illustrated in figure 1-10, view A. This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength. To the wave

these strips look like parallel waveguides. The velocity of phase propagation of a wave is greater in a

waveguide than in air. Thus, since the lens is concave, the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion.

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Helical AntennaAntennas List Antenna Theory Home

Helix antennas have a very distinctive shape, as can be seen in the following

picture.

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Photo courtesy of Dr. Lee Boyce.

The most popular helical antenna (often called a 'helix') is a travelling wave

antenna in the shape of a corkscrew that produces radiation along the axis of thehelix. These helixes are referred to as axial-mode helical antennas. The benefits of

this antenna is it has a wide bandwidth, is easily constructed, has a real input

impedance, and can producecircularly polarizedfields. The basic geometry is

shown in Figure 1.

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Figure 1. Geometry of Helical Antenna.

The parameters are defined below.

D- Diameter of a turn on the helix.

C- Circumference of a turn on the helix (C=pi*D).

S- Vertical separation between turns.

- pitch angle, which controls how far the antenna grows in the z-direction per

turn, and is given by

N- Number of turns on the helix.

H- Total height of helix,H=NS.

The antenna in Figure 1 is a left handed helix, because if you curl your fingers on

your left hand around the helix your thumb would point up (also, the waves

emitted from the antenna are Left Hand Circularly Polarized). If the helix was

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wound the other way, it would be a right handed helical antenna.

The pattern will be maximum in the +z direction (along the helical axis in Figure

1). The design of helical antennas is primarily based on empirical results, and the

fundamental equations will be presented here.

Helices of at least 3 turns will have close to circular polarization in the +z

direction when the circumference Cis close to a wavelength:

Once the circumference Cis chosen, the inequalites above roughly determine the

operating bandwidth of the helix. For instance, if C=19.68 inches (0.5 meters),

then the highest frequency of operation will be given by the smallest wavelengththat fits into the above equation, or =0.75C=0.375 meters, which corresponds

to a frequency of 800 MHz. The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation, or =1.333C=0.667

meters, which corresponds to a frequency of 450 MHz. Hence, thefractional BW

is 56%, which is true of axial helices in general.

The helix is a travelling waveantenna, which means the current travels along the

antenna and the phase varies continuously. In addition, the input impedance is

primarly real and can be approximated in Ohms by:

The helix functions well for pitch angles ( ) between 12 and 14 degrees.

Typically, the pitch angle is taken as 13 degrees.

The normalized radiation pattern for the E-field components are given by:

For circular polarization, the orthogonal components of the E-field must be 90

degrees out of phase. This occurs in directions near the axis (z-axis in Figure 1) of

the helix. Theaxial ratiofor helix antennas decreases as the number of loopsNis

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added, and can be approximated by:

The gain of the helix can be approximated by:

In the above, cis the speed of light. Note that for a given helix geometry

(specified in terms of C, S, N), the gain increases with frequency. For anN=10

turn helix, that has a 0.5 meter circumference as above, and an pitch angle of 13

degrees (giving S=0.13 meters), the gain is 8.3 (9.2 dB).

For the same example helix, the pattern is shown in Figure 2.

Figure 2. Normalized radiation pattern for helical antenna (dB).

The Half-Power Beamwidth for helical antennas can be approximated (in degrees)

by:

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Yagi-Uda AntennaAntennas List Antenna Theory .com

The Yagi-Udaantenna or Yagi is one of the most brilliant antenna designs. It is

simple to construct and has a highgain,typically greater than 10 dB. These

antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz),

although theirbandwidthis typically small, on the order of a few percent of the

center frequency. You are probably familiar with this antenna, as they sit on top

of roofs everywhere. An example of a Yagi-Uda antenna is shown below.

The Yagi antenna was invented in Japan, with results first published in 1926. The

work was originally done by Shintaro Uda, but published in Japanese. The work

was presented for the first time in English by Yagi (who was either Uda's

professor or colleague, my sources are conflicting), who went to America and

gave the first English talks on the antenna, which led to its widespread use.

Hence, even though the antenna is often called a Yagi antenna, Uda probably

invented it. A picture of Professor Yagi with a Yagi-Uda antenna is shown below.

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In the next section, we'll explain the principles of the Yagi-Uda antenna.

The basic geometry of a Yagi-Uda antenna is shown in Figure 1.

Figure 1. Geometry of Yagi-Uda antenna.

The antenna consists of a single 'feed' or 'driven' element, typically adipoleor a

folded dipoleantenna. This is the only member of the above structure that is

actually excited (a source voltage or current applied). The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular

direction. The length of the feed element is given in Figure 1 asF. The feed

antenna is almost always the second from the end, as shown in Figure 1. This

feed antenna is often altered in size to make itresonantin the presence of the

parasitic elements (typically, 0.45-0.48 wavelengths long for a dipole antenna).

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The element to the left of the feed element in Figure 1 is the reflector. The

length of this element is given asRand the distance between the feed and the

reflector is SR. The reflector element is typically slightly longer than the feed

element. There is typically only one reflector; adding more reflectors improves

performance very slightly. This element is important in determining thefront-

to-back ratioof the antenna.

Having the reflector slightly longer than resonant serves two purposes. The first

is that the larger the element is, the better of a physical reflector it becomes.

Secondly, if the reflector is longer than its resonant length, the impedance of

the reflector will be inductive. Hence, the current on the reflector lags the

voltage induced on the reflector. The director elements (those to the right of the

feed in Figure 1) will be shorter than resonant, making them capacitive, so that

the current leads the voltage. This will cause a phase distribution to occur

across the elements, simulating the phase progression of a plane wave across

the array of elements. This leads to the array being designated as a travelling

wave antenna. By choosing the lengths in this manner, the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in

Figure 1.

The rest of the elements (those to the right of the feed antenna as shown in

Figure 1) are known as director elements. There can be any number of directors

N, which is typically anywhere fromN=1 toN=20 directors. Each element is of

lengthDi, and separated from the adjacent director by a length SDi. As alluded

to in the previous paragraph, the lengths of the directors are typically less than

the resonant length, which encourages wave propagation in the direction of the

directors.

The above description is the basic idea of what is going on. Yagi antenna

design is done most often via measurements, and sometimes computer

simulations. For instance, lets look at a two-element Yagi antenna (1 reflector,

1 feed element, 0 directors). The feed element is a half-wavelength dipole,

shortened to be resonant (gain = 2.15 dB). The gain as a function of the

separation is shown in Figure 2.

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Figure 2. Gain versus separation for 2-element Yagi antenna.

The above graph shows that the gain is increases by about 2.5 dB if the

separation SDis between 0.15 and 0.3 wavelengths. Similarly, the gain can be

plotted as a function of director spacings, or as a function of the number ofdirectors used. Typically, the first director will add approximately 3 dB of

overall gain (if designed well), the second will add about 2 dB, the third about

1.5 dB. Adding an additional director always increases the gain; however, the

gain in directivity decreases as the number of elements gets larger. For

instance, if there are 8 directors, and another director is added, the increases in

gain will be less than 0.5 dB.

In the next section, I'll go further into the design of Yagi-Uda antennas.

The design of a Yagi-Uda antenna is actually quite simple. Because Yagi antennas havebeen extensively analyzed and experimentally tested, the process basically follows this

outline:

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically), and tweak it till the performance is acceptable

As an example, consider the table published in "Yagi Antenna Design" by P Viezbicke

from the National Bureau of Standards, 1968, given in Table I. Note that the "boom" is

the long element that the directors, reflectors and feed elements are physically attached to,

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and dictates the lenght of the antenna.

Table I. Optimal Lengths for Yagi-Uda Elements, for Distinct Boom Lengths

d=0.0085

SR=0.2

Boom Length of Yagi-Uda Array (in )

0.4 0.8 1.2 2.2 3.2 4.2

R 0.482 0.482 0.482 0.482 0.482 0.475

D1 0.442 0.428 0.428 0.432 0.428 0.424

D2 0.424 0.420 0.415 0.420 0.424

D3 0.428 0.420 0.407 0.407 0.420

D4 0.428 0.398 0.398 0.407D5 0.390 0.394 0.403

D6 0.390 0.390 0.398

D7 0.390 0.386 0.394

D8 0.390 0.386 0.390

D9 0.398 0.386 0.390

D10 0.407 0.386 0.390

D11 0.386 0.390

D12 0.386 0.390

D13 0.386 0.390

D14 0.386

D15 0.386

Spacing

between

directors,

(SD/ )

0.20 0.20 0.25 0.20 0.20 0.308

Gain (dB) 9.25 11.35 12.35 14.40 15.55 16.35

There's no real rocket science going on in the above table. I believe the authors of

the above document did experimental measurements until they found an

optimized set of spacings and published it. The spacing between the directors is

uniform and given in the second-to-last row of the table. The diameter of the

elements is given by d=0.0085 . The above table gives a good starting point to

estimate the required length of the antenna (the boom length), and a set of lengths

and spacings that achieves the specified gain. In general, all the spacings, lengths,

diamters (including the boom diameter) are design variables and can be

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continuously optimized to alter performance. There are thousands of tables that

further give results, such as how the diamter of the boom affects the results, and

the optimal diamters of the elements.

As an example of Yagi-antenna radiation patterns, a 6-element Yagi antenna (with

axis along the +x-axis) is simulated in FEKO (1 reflector, 1 driven half-

wavelength dipole, 4 directors). The resulting antenna has a 12.1 dBi gain, and the

plots are given in Figures 1-3.

Figure 1. E-plane gain of Yagi antenna.

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Figure 2. H-Plane gain of Yagi antenna.

Figure 3. 3-D Radiation Pattern of Yagi antenna.

The above plots are just an example to give an idea of what the radiation pattern

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of the Yagi-Uda antenna resembles. The gain can be increased (and the pattern

made more directional) by adding more directors or optimizing spacing (or rarely,

adding another refelctor). Thefront-to-back ratiois approximately 19 dB for this

antenna, and this can also be optimized if desired.

A LONG-WIRE ANTENNAis an antenna that is a wavelength or more long at the operating frequency.These antennas have directive patterns that are sharp in both the horizontal and vertical planes.

BEVERAGE ANTENNASconsist of a single wire that is two or more wavelengths long.

A V ANTENNAis a bi-directional antenna consisting of two horizontal, long wires arranged to form a V.

The RHOMBIC ANTENNAuses four conductors joined to form a rhombus shape. This antenna has a

wide frequency range, is easy to construct and maintain, and is noncritical as far as operation and

adjustment are concerned.

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The TURNSTILE ANTENNAconsists of two horizontal, half-wire antennas mounted at right angles to

each other.

LOG-PERIODIC ANTENNALOG-PERIODIC ANTENNA

Intelecommunication,a log-periodic antenna(LP,

also known as a log-periodicarray) is abroadband,multielement,

unidirectional,narrow-beamantennathat hasimpedanceand

radiationcharacteristics that are regularly repetitive as a

logarithmic function of the excitationfrequency.The individual

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components are oftendipoles,as in a log-periodic dipole array

(LPDA).

Log periodic antennas are arrays that are designed to be

self-similarand thus arefractal antennaarrays. It is normal to

drive alternating elements with a circa180o ( radian) phase shiftfrom the last element. This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

line.The length and spacing of the elements of a log- increase

logarithmically from one end to the other.The result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

i.e. the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence thename.

Log.-Periodic Antenna, 2502400 MHz

Mutual impedance& self-impedanceThe method helps us to compute voltages, currents and

impedances in antenna systems. The method understands the

voltage, which is observed at the input port of every single

antenna element, being induced by the radiation of allthe

antenna elements (including the own element). The voltage

can be composed from contributions of single elements. Each

contribution is proportional to the current of the respective

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element. E.g., voltage U1 at the input of the first antenna

element equals to the summation

whereI1,I2,I3 are currents at the input ports of singleelements,Z11,Z12,Z13 are impedances.Z11 is self-impedance,Z1n are mutual impedances between the first

element and the other elements in the antenna system. These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antennaconsists of an arrangement of twoconicalconductors,which is

driven bypotential,charge,or an alternatingmagnetic field(and the associatedalternating electric current)at thevertex.The conductors have a commonaxisand vertex.The two cones face in opposite directions. Biconical antennas are broadband dipole

antennas, typically exhibiting a bandwidth of 3octavesor more.

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can

be printed directly onto a circuit board. They are becoming very widespread

within the mobile phone market. They are low cost, have a low profile and areeasily fabricated.

Consider the microstrip antenna shown in Figure 1, fed by a microstrip

transmission line. The patch, microstrip and ground plane are made of high

conductivity metal. The patch is of lengthL, width W, and sitting on top of a

substrate (some dielectric circuit board) of thickness hwithpermittivity .

The thickness of the ground plane or of the microstrip is not critically

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important. Typically the height his much smaller than the wavelength of

operation.

(a) Top View

(b) Side View

Figure 1. Geometry of Microstrip (Patch) Antenna.

The frequency of operation of the patch antenna of Figure 1 is determined by

the lengthL. The center frequency will be approximately given by:

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The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium.

The width Wof the antenna controls the input impedance. For a square patch

fed in the manner above, the input impedance will be on the order of 300

Ohms. By increasing the width, the impedance can be reduced. However, todecrease the input impedance to 50 Ohms often requires a very wide patch. The

width further controls the radiation pattern. The normalized pattern is

approximately given by:

In the above, kis the free-spacewavenumber,given by . The magnitudeof the fields, given by:

The fields are plotted in Figure 2 for W=L=0.5 .

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Figure 2. Normalized Radiation Pattern for Microstrip (Patch) Antenna.

The directivity of patch antennas is approximately 5-7 dB. The fields are

linearly polarized. Next we'll consider more aspects involved in Patch

(Microstrip) antennas.

Spiral antenna

Inmicrowavesystems, a spiral antennais a type of RFantenna.It is shaped as a two-

armspiral,or more arms may be used.[1]

Spiral antennas operate over a widefrequency

rangeand have circularpolarization.Spiral antennas were first described in 1956.

Applications

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A spiral antenna transmits EM waves having a circular polarization. It will receive

linearly polarized EM waves in any orientation, but will attenuate signals received with

the opposite circular polarization. A spiral antenna will reject circularly polarized wavesof one type, while receiving perfectly well waves having the other polarization.

One application of spiral antennas is wideband communications. Another application ofspiral antennas is monitoring of the frequency spectrum. One antenna can receive over a

wide bandwidth, for example a ratio 5:1 between the maximum and minimum frequency.

Usually a pair of spiral antennas are used in this application, having identical parametersexcept the polarization, which is opposite (one is right-hand, the other left-hand oriented).

Spiral antennas are useful for microwave direction-finding.[2]

Elements

The antenna includes two conductive spirals or arms, extending from the center outwards.

The antenna may be a flat disc, with conductors resembling a pair of loosely-nested clock

springs, or the spirals may extend in a three-dimensional shape like a screw thread. Thedirection of rotation of the spiral defines the direction of antenna polarization. Additional

spirals may be included as well, to form a multi-spiral structure. Usually the spiral is

cavity-backed, that is there is a cavity of air or non-conductive material or vacuum,surrounded by conductive walls; the cavity changes the antenna pattern to a

unidirectional shape. The output of the antenna

Measuring Radiation Pattern

and an Antenna's Gain

Antennas (Home)Antenna Measurements

HomePrevious: Measurements

Ranges

Now that we have ourmeasurement equipmentand anantenna range,we can

perform some measurements. We will use the source antenna to illuminate the

antenna under test with a plane wave from a specific direction. Thepolarization

andgain(for the fields radiated toward the test antenna) of the source antenna

should be known.

Due to reciprocity, the radiation pattern from the test antenna is the same for boththe receive and transmit modes. Consequently, we can measure the radiation

pattern in the receive mode for the test antenna.

The test antenna is rotated using the test antenna's positioning system. The

received power is recorded at each position. In this manner, the magnitude of the

radiation patternof the test antenna can be determined. We will discussphase

measurementsandpolarization measurementslater.

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The coordinate system of choice for the radiation pattern isspherical coordinates.

Measurement Example

An example should make the process reasonably clear. Suppose the radiation

pattern of amicrostrip antennais to be obtained. As is usual, lets let the direction

the patch faces ('normal' to the surface of the patch) be towards the z-axis.

Suppose the source antenna illuminates the test antenna from +y-direction, as

shown in Figure 1.

Figure 1. A patch antenna oriented towards the z-axis with a Source illumination

from the +y-direction.

In Figure 1, the received power for this case represents the power from the angle:

. We record this power, change the position and record again.

Recall that we only rotate the test antenna, hence it is at the same distance from

the source antenna. The source power again comes from the same direction.

Suppose we want to measure the radiation pattern normal to the patch's surface(straight above the patch). Then the measurement would look as shown in Figure

2.

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Figure 2. A patch antenna rotated to measure the radiation power at normal

incidence.

In Figure 2, the positioning system rotating the antenna such that it faces the

source of illumination. In this case, the received power comes from direction

. So by rotating the antenna, we can obtain "cuts" of the radiationpattern - for instance theE-planecut or theH-planecut. A "great circle" cut is

when =0 and is allowed to vary from 0 to 360 degrees. Another common

radiation pattern cut (a cut is a 2d 'slice' of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees. By measuring the radiation pattern

along certain slices or cuts, the 3d radiation pattern can be determined.

It must be stressed that the resulting radiation pattern is correct for a given

polarization of the source antenna. For instance, if the source is horizontally

polarized (seepolarization of plane waves), and the test antenna is vertically

polarized, the resulting radiation pattern will be zero everywhere. Hence, theradiation patterns are sometimes classified as H-pol (horizontal polarization) or

V-pol (vertical polarization). See alsocross-polarization.

In addition, the radiation pattern is a function of frequency. As a result, the

measured radiation pattern is only valid at the frequency the source antenna is

transmitting at. To obtain broadband measurements, the frequency transmitted

must be varied to obtain this information.

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Measuring Gain

Antennas (Home) Antenna Measurements

Back: Measurement of

Antenna Radiation

Patterns

On the previous page onmeasuring radiation patterns,we saw how the radiation

pattern of an antenna can be measured. This is actually the "relative" radiation

pattern, in that we don't know what the peak value of thegainactually is (we're

ust measuring the received power, so in a sense can figure out how directive an

antenna is and the shape of the radiation pattern). In this page, we will focus on

measuring the peak gain of an antenna - this information tells us how much power

we can hope to receive from a given plane wave.

We can measure the peak gain using theFriis Transmission Equationand a "gainstandard" antenna. A gain standard antenna is a test antenna with an accurately

known gain and polarization (typically linear). The most popular types of gain

standard antennas are thethin half-wave dipole antenna(peak gain of 2.15 dB)

and thepyramidal horn antenna(where the peak gain can be accurately calculated

and is typically in the range of 15-25 dB). Consider the test setup shown in Figure

1. In this scenario, a gain standard antenna is used in the place of the test antenna,

with the source antenna transmitting a fixed amount of power (PT). The gains of

both of these antennas are accurately known.

Figure 1. Record the received power from a gain standard antenna.

From the Friis transmission equation, we know that the power received (PR) is

given by:

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If we replace the gain standard antenna with our test antenna (as shown in Figure

2), then the only thing that changes in the above equation is GR- the gain of thereceive antenna. The separation between the source and test antennas is fixed, and

the frequency will be held constant as well.

Figure 2. Record the received power with the test antenna (same source antenna).

Let the received power from the test antenna bePR2. If the gain of the test

antenna is higher than the gain of the "gain standard" antenna, then the receivedpower will increase. Using our measurements, we can easily calculate the gain of

the test antenna. Let Ggbe the gain of the "gain standard" antenna,PRbe the

power received with the gain antenna under test, andPR2be the power received

with the test antenna. Then the gain of the test antenna (GT) is (in linear units):

The above equation uses linear units (non-dB). If the gain is to be specified indecibels,(power received still in Watts), then the equation becomes:

And that is all that needs done to determine the gain for an antenna in a particular

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direction.

Efficiency and Directivity

Recall that thedirectivitycan be calculated from the measured radiation pattern

without regard to what the gain is. Typically this can be performed byapproximated the integral as a finite sum, which is pretty simple.

Recall that theefficiencyof an antenna is simply the ratio of the peak gain to the

peak directivity:

Hence, once we have measured the radiation pattern and the gain, the efficiencyfollows directly from these.

In the next section, we'll look at measuring the phase of an antenn