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Chapter 18 Propagation at

Some knowledge of and antennas is essential to an understanding of transmission in microwave radio systems. This chapter provides certain basic concepts concerning propagation paths, path losses, and microwave antennas and their characteristics.

18. l PA TH CHARACTERISTICS

Propagation Paths The normal propagation paths between two radio antennas are illustrated in Fig. 18-1. The direct or free-space wave is shown in path 1, and the wave reflected from the ground is path 2. Path 3 indicates a which consists of the electric and magnetic fields associated with the currents induced in the ground. Its magni­ tude depends on the constants of the ground and the electromagnetic wave . The sum of these three paths, taking account of both magnitude and phase, is called the ground wave. There are induction fields and secondary effects of the ground which are also a part of this wave, but these effects are negligible beyond a few from the transmitting . Path 4, called the sky wave, depends on the presence of the ionized layers above the earth that reflect back some of the energy that otherwise would be lost in outer space. All of the paths shown in Fig. 18-1 exist in any radio propagation problem, but some are negligible in certain ranges. At frequencies less than about 1500 kHz, the surface wave provides the

433 434 Radio Propagation at Microwave Frequencies Chap. 18

Ionosphere 111111111111111111~1111111111 I I I I 0 ~ ~ Direct (free-space) wa'fe

Fm. 18-1. Transmission paths between two antennas.

primary coverage, and the sky wave helps to extend this coverage at night when the absorption of the is at a minimum. At frequencies above about 30 to 50 MHz, the free-space and ground­ reflected waves are frequently the only paths of importance. At these frequencies the surface wave can usually be neglected as long as the antenna heights are not too low, and the sky wave is only a source of occasional long distance interference rather than a reliable signal for communication purposes. At frequencies in the order of thousands of megahertz, where the microwave systems under discussion operate, the free-space wave is usually controlling on good optical paths, although in many cases attention must also be given to the reflected wave. Thus, in this chapter, the surface and sky are neglected, and attention is focused only on those phenomena that affect the direct and reflected waves. Free-space transmission is considered first, then deviations from free-space transmission, and finally antenna prop­ erties and types. Path Characteristics 435

Free-Space

Consider first a given amount of power, Pr, radiated from an iso~ tropic transmitting antenna, a radiating power equally in all directions. Imagine a sphere of radius d, centered upon the point source. If free-space transmission is assumed (i.e., straight line transmission through a vacuum or ideal , with no absorp­ tion or of energy by nearby objects), the radiated power density will be equal at all points on the surface of the sphere, and the total radiated power, Pr, will pass outward through the surface of the sphere. The radially directed power density at any point on the surface of the sphere, therefore, will be

(18-1) Power density = 4:~

If a receiving antenna with an effective* area, AR, is located on the surface of the sphere, the received power, PR, will equal the power density times the area of the antenna; that is,

PT A (18-2) PR= 47Td2 R

It can be shown [1] that a transmitting antenna which concen­ trates its radiation within a small solid angle or beam has an on-axis transmitting with respect to an isotropic radi­ ator of

(18-3)

This is equivalent to concentrating the radiation in a solid angle of

rad 2 (18-4)

and comparing this angle to 4'77"(radian) 2 which is a whole solid angle.

*In actual antennas, imperfect reflector illumination and re-radiated energy result in a power loss. The discrepancy between theoretical and actual gain leads to the concept of an effective area which is smaller than the physical area. 436 Radio Propagation at Microwave Frequencies Chap. 18 Grouping the results of the previous two paragraphs,

(18-5)

It is now convenient to rearrange the terms, primarily to get the transmitting and receiving antenna gains into identical forms. In this way, both transmitting and receiving antennas are specified as to their gain relative to isotropic radiators.

2 47TAT) (47TA.R)( A ) PR = PT ( )\2- ~! 41rd (18-6) Trans Rec ant ant gain gain

Stated in , the ratio of PT to PR equals

4 1 4 4 10 log PT - -10 log 7TA ~ --10 IO!' 1r AR +20 log 1rd (18-7) PR - A.2 ' >..2 A

The manipulation of antenna gain terms in the previous paragraph results in a distance and frequency-dependent term which is called the free-space path loss between isotropic radiators.

Free-space path loss in decibels = 20 log 4:d (18-8)

This term is plotted in Fig. 18-2 for representative path lengths and frequencies.

Section Loss Section loss is defined as the loss in decibels between a radio trans­ mitter output and the following input.. It includes the loss as determined by Eq. (18-7), plus all the and network losses at both ends of the hop. Addition of these factors to Eq. (18-7) defines the section loss in dB as :

. 47Td 41rAT Section loss - 20 log -- -10 41rAu - A log ---A.2 --10 log ---A.2

+ waveguide losses+ network losses (18-9) Path Characteristics .437

150

145

iii' 140 ~ 1! -£ a." 135 e fl-" ;, ,t 130

125

Frequency (GHz)

Fm. 18-2. Free-space path loss versus frequency and path length.

The following example illustrates these relations.

Example 18.1

Problem Determine the receiver input power for a 4-GHz radio hop given the following conditions : output power = 37.0 dBm (5 watts) Gain of each antenna = 39.6 dB Loss of networks in receiving waveguide = 1.9 dB Loss of networks in transmitting waveguide = 1.9 dB Transmitting waveguide loss = 2.1 dB Receiving waveguide loss = 2'.l dB Frequency = 4.0 GHz Path length = 28.5 miles 438 Radio Propagation at Microwave Frequencies Chap. 18 Solution From Fig. 18.2, the free-space path loss at 4 GHz :for a path length of 28.5 miles is 137.5 dB. Thus, using Jiiq. (18-9), the section loss is

Section loss= 137.5 - 39.6 -89.6 + 2(2.1 + 1.9) = 66.3 dB The input power to the radio receiver is equal to the transmitter output power minus the section loss. Thus,

Receiver input power= 37.0 - 66.3

= --29.3 dBm

Antenna Heights and Path Clearc:mce Up to this point, only free-space transmission has been considered. The presence of the earth and the nonuniformity of the atmosphere may markedly affect the actual operating conditions. For a large percentage of the time, the path loss of a typical microwave link can be made to approximate closely the calculated free-space loss. This can be done by engineering the path between antennas to provide an optical line-of-sight transmission path which has adequate clearance with respect to surrounding objects. This clearance is necessary not only to keep the path loss under normal atmospheric conditions from deviating from the free--space value, but also to reduce severe problems during abnormal conditions. The importance of adequate clearance can be seen by considering Fig. 18-3, which shows the profile of the path between two antenna sites. For the antenna heights shown, the distance H represents the clearance of the line-of-sight path, AB, and the intervening ter­ rain. Path ACB represents a secondary transmilssion path via reflection from a projection. With no phase reversal at the point of reflection, the signal from the two paths would partially cancel whenever AB and ACB differed by an odd multiple of a half wave­ length. When the grazing angle of the secondary wave is small, which is typically the case, a phase reversal will normally occur at the point of reflection. Therefore, whenever AB and ACB differ by an odd multiple of a half , the energies of the received signals add, rather than cancel. Conversely, if the two paths differ by a whole number of wavelengths, the signals from thEi two paths will tend to cancel. Path Characteristics 439

1200

,_,.---- _. ------First Fresnel ------.....-... B 1000 ,,,..,...... -- zones A= 3 meters,:;-,, ~ 800 ,," ... Line-ohf-sdight A = 3 centimeters ' ' ; , ~- & ~ ~ ~., , " ~ - --- -~ -- __- _:.,,,,.,-7- -:~ ,, 600 I _ ------.,-•"" I ::, , ____ - --r- - -- H .,,,, I ~ ---=-==-=-----=-=====-,. .,---' ~/ ~~ d, ------,.___c,,/ 400 ,,A ,,,..,.,,,. ', ...._ ,, 200 ----

0 0 2 4 6 8 12 14 16 18 20 22

Distance between antennas (miles)

Fm. 18-3. Typical profile plot showing first Fresnel zones for 100 MHz and 10 GHz.

The amount of clearance is generally described in terms of F'resnel * zones. All points from which a wave could be reflected with an addi­ tional path length of one-half wavelength form an ellipse which defines the first . Similarly, the boundary of the nth Fresnel zone consists of all points from which the delay is n/2 wave­ lengths. For any distance, d1, from antenna A, the distance H n from the line-of-sight path to the boundary of the nth Fresnel zone is approximated by the parabola:

_ • /n>..d1(d-d1) (18-10) H n-v d where >..,the wavelength, and d and d1, the path lengths, are meas­ ured in identical units. The boundaries of the first Fresnel zones for>..= 3 meters (100 MHz) and>..= 3 centimeters (10 GHz) in the vertical plane through AB are shown in Fig. 18-3. In any plane normal to AB, the Fresnel zones are concentric circles. Measurements have shown that to achieve a normal transmission loss approximately equal to the free-space loss, the transmission path should pass over all obstacles with a clearance of at least 0.6 times the first Fresnel zone distance, and preferably by an amount equal to the first Fresnel zone distance. However, because of *Fresnel (Fra-nell'). 440 Radio Propagation at Microwave Frequencit~s Chap. 18 effects, greater clearance is usually provided in order to reduce deep fading under adverse atmospheric conditions. The effective path clearance varies with time because radio waves seldom follow truly straight lines. , resulting from variations in the dielectric with height, causes the radio signal to bend slightly from its ideal straight line path. This effect can be visualized by assuming that the does travel exactly in a straight line but over an earth with a fictitious radius which is either greater or less than thie true earth radius. On the average, the radio wave is bent downward as if the earth radius were 4/3 of its actual value. For this reason, it is frequently con­ venient to plot the elevations of a path on special profile paper on which the earth's radius is assumed to be 4/3 of its actual value. The radio path is then plotted as a straight line and the earth's curvature appears to flatten. The effective earth radius factor K (ratio of effective earth radius to true earth radius) is a function of atmospheric conditions and may be as low as 1/2 for a small percentage of the time. This corresponds to a so-called [2] condition and may result in a consider­ able increase in path loss over a wide range of frequencies unless adequate path clearance is provided. On the other hand, when the effective earth radius factor is infinite, it is as if the earth were com­ pletely flat, and long-range inter­ ference from same--channel stations may iresult because the shielding by the earth curvature has tempo­ rarily been removed. The deviations :in the curvature of the, radio waves and the corre­ (a) Effective earth profiles versus K sponding values for the effective earth radius factor are contrasted in Fig. 18-4 for several values of K. -2 ,....------;;-----...... ___ 3-r--, An infinite effective radius does not imply a limit; negative values ~-:::.--;:: _____ 1____ ...... ~~ --- of K can be pictured as a "de­ pressed" earth, but more impor­ tantly, negative values represent (b) Actual radio paths versus K conditions for which the atmos- phere acts like a duct or waveguide FIG. 18-4. Effect of K on radio paths. for propagation over relatively long distances. Path Characteristics 441

In determining suitable tower heights, a profile plot of the terrain between the proposed antenna sites is obtained, and the worst obstacle in thP. path, such as the ridge shown in Fig. 18-3, is located. This obstacle is then used as a leverage point from which the most suitable antenna height at each location can be chosen to provide the proper clearance. Path testing using portable antennas is frequently done to verify the appropriateness of paths and determine optimum antenna heights.

Fading Substandard atmospheric refraction (K < 1) may transform a line-of-sight path into an obstructed one, because the effective path clearance becomes zero or negative. This situation can happen under conditions of heavy ground or extremely cold air over warm earth. The result is a substantial increase in path loss over a wide frequency band. The magnitude and frequency of occurrence of this type of slow, flat fading can be reduced only by the use of greater antenna heights. The more common form of microwave fading on paths with ade­ quate clearance is a relatively fast, frequency selective type of fading caused by interference between two or more rays in the atmosphere. The separate paths between transmitter and receiver are caused by the irregularities (second and higher order derivatives) in the vari­ ations in dielectric permittivity with height. The refraction effect mentioned earlier depends on the average slope (first derivative) of the same variation in dielectric permittivity. The transmission mar­ gins that must be provided against both types of fading are important in determining the overall system parameters. An interference type fade can have any depth, but fortunately the deeper the fade the less frequently it occurs and the shorter its duration when it does occur. Figure 18-5 shows the median duration of fades of various depths on a 4-GHz system with typical re­ peater spacings of about 30 to 35 miles. It will be noted that the median duration of a 20-dB fade is about 30 seconds, and the median duration of a 40-dB fade is about 3 seconds. At any given depth of fade, the duration of 1 per cent of the fades may be as much as ten times or as little as 1/10 of the median duration. Multipath fading occurs primarily at night on typical 4-GHz line­ of-sight paths. During the day or whenever the lower atmosphere is thoroughly mixed by rising convection currents and winds, the signals 442 Radio Propagation at Microwave Frequenci•~s Chap. 18

2 ___ ....______..._ __ ...... ______

0 10 20 30 40 50

Depth of fade - dB below normal

FIG. 18-5. Median duration of fast fading. on line-of-sight paths are normally steady and at or near the pre­ dicted free-space values. On clear nights with little or no wind, how­ ever, sizable irregularities or layers can collect at random elevations, and these irregularities in refraction result in multipath transmission on path lengths of the order of a million wavelengths or longer. Multipath fading tends to build up durJlng the night with a peak in the early morning hours and then to disappear as the layers are broken up by the convection caused by the heat of the early morning sun. Both the number of fades and the percentage of time below a given level tend to increase as either the repeater spacing or the frequency increases. Multiple paths are usually overhead, although ground reflections can be a factor in some cases. The effects of multipath fading can be minimized by the use of either frequency or space diversity.

Absorption Rainfall and water vapor also produce pronounced effects at the higher microwave frequencies. It is well known that certain absorption bands occur in the spectrum of visible light, and the theory of these absorption bands indicates that they should be found throughout the . The first absorption Path Characteristics 443 band due to water vapor peaks at about 22 GHz, and the first absorp­ tion band due to the oxygen in the atmosphere peaks at about 60 GHz [3]. The effect of rain on microwave radio propagation in the region of 4 to 6 GHz is small relative to the losses introduced by other causes of fading. At higher frequencies, however, rain attenuate.s radio transmission to a much greater degree. The radio energy is absorbed and scattered by the rain drops, and this effect becomes more pro­ nounced as the wavelength approaches the size of the raindrops. Figure 18-6 indicates the estimated atmospheric absorption for vari-

50 ..--- - ~ / 20 ~ 10 r" / ,::l'9w, 5 -- ,o"' / 0 - - ~ ~ V 2 r" ,;/> .--~ / o,❖ •r - ~0~~ I V 0.5 / 1<1-"_,,,, ~"'"'~ i,.,--- - ~ /' E 0.2 V o'e ~o9 ..~ ~- 2 :ii ~ ,· '~ ;; "'"'~ j Q. 0.1 / / , ~~ ~ ~- .,,"' , I / ~if'~'l" } 0.05 / I V /~ ,/ ~~ ~ / _./ ' 0.02 I / --i---- '/_ /_ ...... ~'- Oxygen in atmosphere 0.01 -- -- -·~, ' {760mmHg) - 0.005 / / j I v Water vapor at 15 g/m 3 88% rh at 68°F ,/,. 50% rh at 86°F 0.002 V ~· /' 0.001 I 2.5 3.0 3.7 5 5,0 6.0 7.5 10 12 15 20 24 30 40 Frequency {GHz)

FIG. 18-6. Estimated atmospheric absorption. 444 Radio Propagation at Microwave Frequenci1~s Chap. 18 ous conditions of rainfall. From this figure it is evident that rain attenuation must be considered in any system operating at frequencies of 10 GHz or above and perhaps at lower frequency in areas where heavy rains occur frequently. It is also evident that rain attenuation over any individual microwave band is almost independent of fre­ quency, and therefore no protection is offered by the use of inband frequency diversity.

18.2 MICROWAVEANTENNAS

Antenna Characteristics Many antenna characteristics are important in microwave systems. The first of these, antenna gain, has already been defined. An antenna has gain because it concentrates the radiated power in a narrow beam rather than sending it uniformly in all directions. Since it reduces section loss, high antenna gain is obviously desirable. Closely associated with antenna gain is beam width. Since an antenna achieves gain by concentrating power in a narrow beam, the width of the beam will decrease as the antenna gain is increased. Antennas used in microwave systems ordinarily have half-power beam widths of the order of one degree (see Fig. 18-7). A narrow beam minimizes interference from outside sources and adjacent antennas. A very narrow beam, however, imposes severe mechanical stability requirements and leads to problems in antenna lineup and fading. All of the energy from an antenna does not lie in the direction of the main beam; some of it is concentrated in minor beams called sidelobes, which are potential sources of interference into or from other microwave paths. Figure 18-8 illustrates the relationship be­ tween the main beam and sidelobes for a horn-reflector antenna, which is discussed later. Several antenna characteristics are :important in evaluating the coupling of interference between adjacent antennas or radio paths. The front-to-back ratio of an antenna may be defined as the ratio of its maximum gain in the forward or intended direction to its maximum gain in the region of its backward direction. The front­ to-back ratio of an antenna in an actual installation may be 20 to 30 dB less than its isolated or free-space value because of foreground reflections from objects in or near the main transmission lobe or beam. The front-to-back ratio of the antenna is critical in repeater Microwave Antennas 445

50 3 co :s ,;- ·;;C I!!" "' 0"' C :s" C 40 ~ t C l 0 "i: -;; E :, 0 t; < "'"

30 ~T 0.3 Beamwidri,

Antenna area A/.\ 2 (square wavelengths) A A' Antenna 4GHz Note: 6GHz 11 GHz Abscissa is actual antenna area, and "actual 8-foot paraboloid 8(10)2 2(10)3 6(10)3 antenna gain" is taken to be 3 dB below 4-loot paraboloid 5(10)2 5(10)" 1.5(10)3 theoreticaJ. 8-foot square 1(10)3 2.5(10)" 8(10)3

Fm. 18-7. Approximate antenna gain and beam width. systems, especially when the same signal frequencies are to be used in both directions from one station. Additional characteristics in­ volving two or more antennas at the same station are side-to-side coupling and back-to-back coupling. These factors express in dB the coupling losses between antennas carrying transmitter output sig­ nals and antennas carrying receiver input ,signals. Typical trans­ mitter outputs are some 60 dB higher in level than receiver input levels, and accordingly the coupling losses must be high to avoid unwanted interferences, particularly when the desired signal is fading.

Use of Polarization To improve adjacent channel discrimination and to facilitate the design of channel combining and dropping networks, it is common 446 Radio Propagation at Microwave FrequenciE~S Chap. 18

Angle (degrees}

40

310 50

300 60

290 70

280 80

260 100

110

120

230 220 210 200 190 180 17C, 160 150 140 130

FIG. 18-8. Horizontal of horn-reflector antenna with vertically polar­ ized signal at 3740 MHz. practice in microwave relay systems to interleave alternate radio channel frequencies on horizontal and vertical polarizations of the transmitted signal. Polarization refers to the alignment of the electric field in the radiated wave. Another orthogonal system with left- and right-hand circular polarization could be used, but the practical problems of maintaining Microwave Antennas 447 polarization discrimination over relatively wide bandwidths and in the presence of reflections do not make it attractive. When energy is radiated in one polarization, a small portion may be converted to the other polarization by imperfections in the antenna system and path. The ratio of the power received in the desired polarization to the power received in the opposite polarization is called the cross-polarization discrimination. Cross-polarization dis­ criminations of 25 to 30 dB for an entire hop are routinely obtained with ordinary antenna systems.

Typical Microwave Antennas Parabolic Antenna. The parabolic (or dish) antenna consists of a paraboloid reflector illuminated with microwave energy by a feed system located at the focus. Depending on the design, one to four waveguide runs in one or two radio bands may be fed to the antenna simultaneously. These antennas in the 5- to 10-foot diameter range are widely used in short-haul systems and occasionally on lightly loaded long-haul routes where economic considerations control the choice of antenna systems. Horn-Reflector Antenna. In the horn-reflector antenna, Fig. 18-9, a vertically mounted horn tapering outward from the focal point is used to illuminate a section of a parabolic surface which then reflects the energy outward. Because of the design and size of the horn, the impedance match of this antenna to its waveguide feed is very good, the return loss being between 40 and 50 dB. It is a broadband antenna and can be used with both vertical and horizontal polariza­ tion in the 4-, 6-, and 11-GHz bands. Its nominal characteristics are tabulated in Fig. 18-10, and Fig. 18-8 shows its horizontal directivity. The horn-reflector antenna has small sidelobes and radiates very little power to the rear, resulting in a nominal 70-dB front-to-back ratio. Measurements made at 6 GHz on a large number of antenna installa­ tions have shown that in horn-reflector antenna systems, side-to-side coupling and back-to-back coupling, as well as cross-polarization dis­ crimination, follow approximately normal distributions. The mean and standard deviations of these distributions are listed in Fig. 18-11. The side-to-side and back-to-back coupling of the antenna system will vary considerably from location to location as a result of fore­ ground reflections and leakage of energy at the joints of the wave­ guide run feeding the antennas. 448 Radio Propagation at Microwave Frequencies Chap. 18

FIG. 18-9. Horn-reflector antenna.

Frequency 4 GHz 6 GHz 11 GHz

Polarization Vert Hor Vert Hor Vert Hor

Midband gain (dB) 39.6 39.4 4:3:.2 43.0 48.0 47.4 Front-to-back ratio (dB) 71 77 71 71 78 71 Beam width (azimuth) 2.5 1.6 1..5 1.25 1.0 0.8 (degrees) Beam width (elevation) 2.0 2.13 1.:25 1.38 0.75 0.88 (degrees) Sidelobes ( dB below 49 54 49 57 54 61 main beam) Side-to-side coupling (dB) 81 89 ll!O 122 94 112 Back-to-back coupling 140 122 uo 127 139 140 (dB)

FIG. 18-10. Horn-reflector antenna characteristics for a particular pair of an­ tennas without any waveguide system attached. Microwave Antennas 449

Mean Standard deviation

Side-to-side coupling ( same polarization) 102 8.1 Side-to-side coupling ( opposite polarization) 109 9.0 Back-to-back coupling ( same polarization) 125 10.3 Back-to-back coupling ( opposite polarization) 127 10.3 Cross-polarization discrimination 28 5.0

FIG. 18-11. Horn-reflector antenna and its waveguide system characteristics in dB at 6 GHz.

REFERENCES

1. Kraus, J. D. Antennas (New York: McGraw-Hill Book Company, Inc., 1950). 2. Schelleng, J. C., C. R. Burrows, and E. B. Ferrell. "Ultra Short-Wave Propagation," Proc. IRE, vol. 21, no. 3 (March 1933), pp. 427-463. 3. Medhurst, R. G. "Rainfall Attenuation of Centimeter Waves: Comparison of Theory and Experiment," Trans. IEEE, AP-13, no. 4 (1965), pp. 550-564.