ANTENNAS 279

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LJ'! I m.1FIGURE 9.24 Folded dipole.

If elements of unequal diameters are used, transformation ratios from 1.5 to 25are practicable, and if greater ratios are required, more arms can be used. Although thefolded dipole has the same radiation pattern as the ordinary dipole, it has many advan-tages: itSohigherinput impedance and its greater bandwidtp (as explained in Section9-8), as well as ease and cost of construction and impedance matching.

The Yagi-Uda antenna A Yagi-Uda antenna is an array consisting of a driven ele-ment and one or more parasitic elements. They are arranged collinearly and closetogether, as shown in Figure 9-25, together with the optical equivalent and the radia-tion pattern.

Since it is relatively unidirectional, as the radiation pattern shows, and has a

moderate-gain in the vicinity of 7 dB4the Yagi antenna is used as an HF transmittingantenna. It is also employed at higher frequencies, particularly as a VHF televisionreceiving antenna. The back lobe of Figure 9-25b may be reduced, and thus thefront-to-back ratio of the antenna improved, by bringing the radiators closer. However, thishas the adverse effect of lowering the input impedance of the array, so that the separa-tion shown, O.IA, is an optimum value.

ReflectorDirector

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Radiation pattern

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Drivenelement (u)

r7 Source nMirror II . V Lens

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FIGURE 9-25 Yagi antenna. (a) Antenna and pattern; (6) optical equivalent.

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280 ELECTRONIC COMMUNICAnON SYSTEMS

The precise effect of the parasitic element depends on its distance and tuning,i.e., on the magnitude and phase of the current induced in it. As already mentioned, aparasitic element resonant at a lower frequency than the driven element (i.e., longer)will act as a mild reflector, and a shorter parasitic will act as a mild" director" ofradiation. As a parasitic element is brought closer to the driven element, it will load thedriven element more and reduce its input impedance. This is perhaps the main reasonfor the almost invariable use of a folded dipole as the driven element of suc_han array.

The Yagi antenna admittedly does not have high gain, but it is verycomPact~relatively brOO1lbaiidroecauseof the folded dipole used and has quite a good umdir~-

tional radiation pattem.l's used in practice, it has one reflector and several directorswhich are either of equal length or de<;reasingslightly away from the driven element.Finally, it must be mentioned that the folded dipole, along with one or two otherantennas, is sometimes called a supergain antenna, because of its good gain andbeamwidth per unit area of array.

9-6.3 Nonresonant Antennas-The RhombicA major requirement for HF is the need for a multiband antenna capable of operatingsatisfactorily over most or all of the 3- to 30-MHz range, for either reception ortransmission. One of the obvious solutions is to employ an array of nonresonant anten-nas, whose characteristlcs will not change too drastically over this frequency range.

A very interesting and widely used antenna array, especially for point-to-po~communications, is shown in Figure 9-26. This is the rhombic antenna, which consistsof nonresonant elements arranged differently from any previous arrays. It is a planarrhombus which may be thought of as a piece of parallel-wire transmission line bowerlin the ~iddle. Th6kng'tl1s:or the (equal) radiators vary from 2to 8 ~,and the radiatia:.,,""" . --angle, f!>'Jvariesfromr4Q'iQ"'75?!;'being mostly determined by the leg length.

The four legs rreco1lsldered as nonresonant antennas. This is achieved h'::treating the two sets as a transmission line correctly terminated in its characteristicimpedance at the far end; thus only forward waves are present. Since the terminat:IDcabsorbs some power, the rhombic antenna must be terminated by a resistor which, fO£transmission, is capable of absorbing about one-third of th~ower fed to the antenna..The tefiiii!iati~gJresi§!a1lc~is often in the vicinitYof~800 q~d,:!he ii:ipiif~"iin.~varies1roIn 6jQ.,tQ.,700>-fl.The directivity of the rhombic vari~s,fJo.mabOiirZ01O9a'"increasing with leg length up to about 8 A. However, the,.power absorbed by ~

Radiation patternin plane of antenna

Individualpatterns R, ~

FIGURE 9-26 Rhombic antenna and radiation patterns.

ANTENNAS 281

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termination must be taken into account, so that the power gain of this antenna rangesfrom about 15 to 60°. The radiation pattern is unidirectional as shown (Figure 9-26).

Because the rhombic is nonresonant, it does not have to be an integral numberof half-wavelengths long. It is thus a broadband antenna, with a frequency range atleast 4: 1 for both input impedance and radiation pattern. The rhombic ISideally suitedto HF transmission and reception and is a very popular antenna in commercial point-to-point communications.

9..7 UHF AND MICROWAVE ANTENNAS

Transmitting and receiving an!ennas designed for use in the UHF (0.3-3 GHz) andmicrowave (1-100 GHz) regions tend to be directive-some highly so. This conditionresults from a combination of factors, of which the first is undoubtedly feasibility. Thedimensions of an antenna must generally be several wavelengths in order for it to havehigh gain. At the frequencies under discussion, antennas need not be physically largeto have multiple-wavelength dimensions, and consequently several arrangements andconcepts are possible which might have been out of the question at 'lower frequencies.A number of UHF and microwave applications, such as radar, are in the direction-finding and measuring field, so that the need for directional antennas is widespread.Several applications, such as microwave communications links, are essentially point-to-point servicel, often in areas in which interference between various services must beavoided. The use of directional antennas greatly helps in this regard. As frequenciesare raised, the performance of active devices deteriorates. That is to say, the maximumachievable power from output devices falls off, whereas the noise of receiving devicesincreases. It can be seen that having high-gain (and therefore directional) antennashelps greatly to overcome these problems.

The VHF region, spanning the 30-300 MHz frequency range, is an "overlap"region. Some of the HF techniques so far discussed can be extended into the VHFregion, and some of the UHF and microwave antennas about to be discussed can alsobe used at VHF. It should be noted that the majority of antennas discussed in Section9-8 are VHF antennas. One of the most commonly seen VHF antennas used around theworld is the Yagi-Uda, most often used as a TV receiving antenna.

9-7.1 Antennas with Parabolic Reflectors ,

The parabola is a plane curve, defined as the locus of a point which moves so that itsdistance from another point (called the focus) plus its distance from a straight line(directrix) is constant. These geometric properties yield an excellent microwave orlight reflector, as will be seen.

Geometry of the parabola Figure 9-27 shows a parabola CAD whose focus is'at Fand whose axis is AB. It follows from the definition of the parabola that

FP + PP' = FQ + QQ' = FR + RR' = k (9-8)

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FIGURE 9-27 Geometry of the parabola.

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where k = a constant, which may be changed if a different shape of parabola isrequired

AF = focal lenflh of the parabola

Note that the ratio of the focal length to the mouth diameter (AF/CD) is calledthe aperture of the parabola, just as in camera lenses. -

Consider a source of radiation placed at the focus. All waves coming from thesource and reflected by the parabola will have traveled the same distance by the timethey reach the directrix, no matter from what point on the parabola they are reflected.All such waves will be in phase. As a result, radiation is very strong and concentratedalong the AB axis, but cancellation will till<eplace in any other direction, because ofpath-length differences. The parabola is seen to have properties that lead to the produc-ition of concentrated beams of radiation. - /

A practical reflector employing the properties of the parabola will be a three-dimensional bowl-shaped surface, obtained by revolving the parabola about the axisAB. ~.re~ting geometric surface is the paraboloid, often called a'pambtflic reflec-ftos or microwave aishf When it is used for reception, exactly the same-behavior is-manifested, so"that this is also a high-gain receiving directional antenna reflectoL Suchbehavior is, of course, predicted by the principle of reciprocity, which states that theproperties of an antenna are independent of whether it is used for transmission orreception. The reflector is directional for reception because only the rays arriving fromthe BA direction, i.e., normal to the directrix, are brought together at the focus. On theother hand, rays from any other direction are canceled at that point, again owing topath-length differences. The reflector provides a high gain because, like the mirror ofa reflecting telescope, it collects radiation f!,oma large area and concentrates it all atthe focal point.

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Properties of paraboloid reflectors The directional pattern of an antenna using aparaboloid reflector has a very sharp main lobe, surrounded by a number of minor

ANTEN~AS 283

k)bes which are much smaller. The three-dimensional shape of the main lobe is likethat of a fat cigar (Figure 9-27), in the direction AB. If theprimary, orfeed, antenna isnondirectional, then the paraboloid will produce a beam of radiation whose width isgiven by the formulas.

70AcP=-

D

cPo= 2cP

(9-9)

(9-9')

where A = wavelength, m

cP = beamwidthbetweenhalf-powerpoints, degrees

cPo='"beamwidth.between nulls, degrees

D = mouth diameter, m .

Both equations are simplified versions of more complex ones, but they applyaccurately to large apertures, that is, large ratios of mouth diameter to wavelength.They are thus accurate for small beamwidths. Although Equation (9-9') is fairly uni-versal, Equation (J-9) contains a restriction. It applies in the specific, but common,case of illumination which falls away uniformly from the center to the edges of theparaboloid r~flector. This decrease away from the center is such that power density atthe edges of the reflector is 10 dB down on the power density at its center. There aretwo reasons for such a decrease in illumination: (I) No primary antenna can be trulyisotropic, so that some reduction in power density at the edges must be accepted. (2)Such a uniform decrease in illumination has the beneficial effect of reducing thestrength of minor lobes. Note that the whole area of the reflector is illuminated, despitethe decrease toward the edges. If only half the area of the reflector were illuminated,the reflector might as well have been only half the size in the first place.

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The gain of an antenna using a paraboloid reflecto.risinfluenced by the apertureratio (D/A) and the uniformity (or otherwise) of the illumination. If the antentlai~lossless, and its illumination falls away to the edges as previously discussed, then thepower gain, as a good approximation, is given by

Ap= 6(~r (9-10)

284 ELECTRONIC COMMUNICAnON SYSTEMS

where Ap = directivity (with respect to isotropic antenna)

Gp = powergain if antennais lossless -'D = mouth diameter of reflector, m

It will be seen later in this sectIon how this relationship is derived from a morefundamental one. It is worth pointing out that the power gain of an antenna with auniformly illuminated paraboloid, with respect to a half-wave dipole, is given by aformula approximately the same as Equation (9-10).

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EXAMPLE 9-5.Calculate tile gain"onthe antenna o~Ex!1DPte 9-4.~ " ..

SOLUTION

Ap = 6(~r = 6~2ir = 9600

Example 9-5 shows that the effective radiated power (ERP) of such an antennawould be 9600 W if the actual power fed to the primary antenna were 1 W. The ERP isthe product of power fed to the antenna and its power gain. It is seen that very largegains and narrow b~mwidths are obtainable with paraboloid reflectors-excessivesize is the reason why they are not used at lower frequencies, such as the VHF regionoccupied by television broadcasting. In order to be fully effective and useful, a parabo-loid must have a mouth diameter of at least 10 A. At the lower end of the television

band, at 63 MHz, this diameter would need to be at least 48 m. These figures illustratethe relative ease of obtaining high directive gains from practical microwave antennas.

Feed mechanisms The primary antenna is placed at the focus of the paraboloid forbest results in transmission or reception. The direct radiation from the feed, which isnot reflected by the paraboloid, tends to spread out in all directions and hence partiallyspoils the directivity. Several methods are used to prevent this, one of them being theprovision of a small spherical reflector, as shown in Figure 9-28, to redirect all such

Primary antenna

at the focus

FIGURE 9-28 Center-fed paraboloid reflector with spherical shell.

ANTENNAS 285

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FIGURE 9-29 Paraboloid reflector with horn feed. (Courtesyof theAndrewAntennasof Aus-tralia.)

radiation back to the paraboloid. Another method is to use a small dipole array at the-focus, such as a Yagi-Uda or an end-fire array, pointing at the paraboloid reflector.

Figure 9-29 shows yet another way of dealing with the problem. A horn an-tenna (to be discussed in Section 9-7.2) pointing at the main reflector. It has a mildlydirectional pattern, in the direction in which its mouth points. Direct radiation from thefeed antenna is once again avoided. It should be mentioned at this point that, althoughthe feed antenna and its reflector obstruct a certain amount of reflection from the

paraboloid when they are placed at its focus, this obstruction is slight indeed. Forexample, if a 30-cm-diameter reflector is placed at the center of a 3-m dish, simplearithmetic shows that the area obstructed is only I percent of the total. Similar reason-ing is applied to the horn primary, which obscures an equally small proportion of thetotal area. Note that in conjunction with Figure 9-29, that the actual horn is not shownhere, but the bolt-holes in the waveguide flange indicate where it would be fitted.

Another feed method, the Cassegrainfeed, is named after an early-eighteenth-century astronomer and is adopted directly from astronomical reflecting telescopes; itis illustrated in Figures 9-30 and 9-31. It uses a hyperboloid secondary reflector. Oneof its foci coincides with the focus of the paraboloid, resulting in the action shown (for

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286 ELECTRONIC COMMUNICAnON SYSTEMS

Waveguide

Paraboloid primaryreflector

Feed antenna (horn) --- Obstructed ray

FIGURE 9-30 Geometry of the Cassegrain feed.

transmission) in Figure 9-30. ThJrays emitted from the feed horn antenna are reflectedfrom the paraboloid mirror. The effect on the main paraboloid reflector being the sameas that of a feed antenna at the focus. The main reflector then collinates (rendersparallel) the rays in the usual manner.

The Cassegrain feed is used when it is desired to place the primary antenna ina convenient position and to shorten the length of the transmission line or waveguideconnecting the receiver (or transmitter) to the primary. This requirement often appliesto low-noise receivers, in which the losses in the line or waveguide may not be toler-ated, especially over lengths which may exceed 30 m in large antennas. Another solu-tion to the problem is to place the active part of the transmitter or receiver at the focus.With transmitters this can almost never be done because of their size, and it may alsobe difficult to place the RF amplifier of the receiver there. This is either because of itssize or because of the need for cooling apparatus for very low-noise applications (inwhich case the RF amplifier may be small enough, but the ancillary equipment is not).Such placement of the RF amplifier causes servicing and replacement difficulties, andthe Cassegrain feed is often the best solution.

As shown in Figure 9-30, an obvious difficulty results from the use of a second-ary reflector, namely, the obstruction of some of the radiation from the main,reflector.This is a problem, especially with small reflectors, because the dimensions of thehyperboloid are determined by its distance from the horn primary feed and the mouthdiameter of the horn itself, which is governed by the frequency used. One of the waysof overcoming this obstruction is by means of a large primary reflector (which is notalways economical or desirable), together with a horn placed as close to thesubreflector as possible. This is shown in Figure 9-31 and has the effect of reducing therequired diameter of the secondary reflector. Vertically polarized waves are emitted bythe feed, are reflected back to the main mirror by a hyperboloid consisting of vertical

ANTENNAS 287

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FIGURE 9-31 27.5-m paraboloid reflector with Cassegrain feed. (Courtesyof OverseasTele-communications Commission, Australia.)

bars and have their polarization twisted by 90° by a mechanism at the surface of theparaboloid. The reflected waves are now horizontally polarized and pass freely throughthe vertical bars of the secondary mirror.

Other parabolic reflectors The full paraboloid is not the only practical reflector thatutilizes the properties of the parabola. Several others exist, and three of the mostcommon are illustrated in Figure 9-32. Each of them has an advantage over the fullparaboloid in that it is much smaller, but in each instance the price paid is that the beamis not as directional in one of the planes as that of the paraboloid. With the pillboxreflector, the beam is very narrow horizontally, but not nearly so directional vertically.

, First appearances might indicate that this is a very serious disadvantage, but there are anumber of applications where it does not matter in the least. In ship-to-ship radar, forinstance, azimuth directivity must be excellent, but elevation selectivity is immaterial-another ship is bound to be on the surface of the ocean!