Title Microwave Propagation Characteristics

Author(s) Inami, Tadao

Citation琉球大学農家政工学部学術報告 = The science bulletin ofthe Division of Agriculture, Home Economics & Engineering,University of the Ryukyus(7): 1-117

Issue Date 1960-12

URL http://hdl.handle.net/20.500.12000/25018

Rights

Microwave Propagation Characteristics**

By

Tadao lNAMI*

PREFACE

Although the study of the propag::ttion of r adio waves at frequencies above

30 mc/ s began in relatively recent years, numerous such field-strength measure­

ments are now available and one is able to draw certain conclusions concerning

propagation characteristics of the waves in the said frequency range. In the

present paper, the author has analyzed, compared and criticized such data;

and has presented empirical formulas based on the present state of knowledge

where such are desirable.

Problems concerning propagation of radio waves at the said frequency

range within and beyond the r adio horizon are discussed, including phenomena

of reflection, multipath interference, refraction, diffraction, absorption, scatter­

ing, fading, time-variation of field-strength level, effects of refractive index

variations and of propagation path characteristics. However, the angle of

arrival of waves, echo delays, back-scatters, astral- and solar-radiations, velocity

of propagation, wave-front shifts, phase variations, selective fading, band-width

capabilities, distortion of waves, and reliable antenna-gain considerations are

not within the scope of the present work.

I. Introduction

1.1 Toward higher frequenci es. The recent trend in radio communications

has been toward the use of higher and higher frequencies. Among the principal

reasons for this trend are the following:

1. Lower frequency ranges are already too crowded to allow the introduction of new communication systems.

2. Improvement in communications generally occurs when higher frequencies are used, for noise is reduced.

* Agriculture, Home E conomics and Engineering Division, University of the Ryukyus. ** This paper is in part based on the doctoral dissertation presented by the author

to the faculty of the graduate school of the University of Texas.

2 T. · INAMJ

3. Higher frequencies . are suited for broadband communication systems (e.g., television, high-fidelity sound-transmission, etc.).

4. Shorter propagation range of waves with frequencies above 30 mc / s is ad­vantageous for certain purposes, as intra-city communications; and permits duplication of waves of the same or nearly the same frequency when the sources are sufficiently distant.

5. Higher directivity, achieved by shorter waves, is suited for point-to-point com­munications (e.g., television and radio-relay systems).

6. Certain properties of shorter waves are useful for some applications (e.g., radar, microwave heater, etc.).

7. More channels are available at higher frequencies. 8. Since the waves at frequencies above 30 mc/ s are usually free of ionospheric

echoes, distortions due to selective fading on that account are absent.

1.2 Present state of knowledge on the subject. For the above-stated reasons,

radio waves of frequencies above 30 mc/ s have been applied widely in recent

times. Not only as a result of necessity and demand but also because of intel­

lectual curiosity, the propagation characteristics of such waves have been in­

vestigated rather intensively, and a great amount of data on the characteristics

is now available despite the relative newness of the study. Some of the more

important studies are referred to in the following chapters of this paper.

It is not easy to draw clear-cut conclusions nor to visualize the subject

clearly since the information pertaining to higher frequencies is scattered

throughout the literature. Moreover, the existing data are based on widely

differing conditions and are sometimes apparently conflicting. For these reasons,

it is necessary to analyze and compare these data and evaluate them in the light

of the corresponding experimental conditions.

1.3 Object and scope of this paper. The object of this investigation is to

examine the mass of experimental data available and to analyze, compare,

evaluate, and criticize the results of the various experiments in VHF, UHF,

SHF, and EHF propagation. Unfortunately much of the work on SHF and

EHF propagation is "classified;" due to its military importance, and is not

available to the general public. Hence, the main emphasis of this paper is

focused on the propagation characteristics of VHF and UHF waves.

Various discrepancies in the experimental results are explained, and graphs

are presented to show general conclusions where desirable. A statistical approach

is adopted where it is considered to be justified. Original experimental formulas are presented when possible.

II. Propagation of VHF, UFH, SHF and EHF

Within Radio Horizon

2.1 Theory of propagation of VHF, UHF, SHF and EHF. The problem of

Microwave Propagation Characteristics 3

diffraction of radio waves around the earth was first solved mathematically by Sommerfeld1 in 1896 on the basis of the following asssumptions:

1. The earth may be considered to be a sphere. 2. The earth is surrounded by a uniform homogeneous atmosphere filling up all

space with the same refractive index as that near the surface of the earth. 3. The earth's surface is homogeneous. 4. The earth has infinite conductivity.

The solution was later generalized to account for the finite conductivity2 and

put in a form suitable for computations.3- 6 The notion of fictitious "effective

earth radius" was introduced to account for linear decrease of refractive index

with height. According to the "smooth earth" theory, the field-strength at a

distance d meters from transmitter is given by7

where

v'PG E=7- d

P: Radiated power, watts.

volts per meter

G: Gain of antenna with respect to a halfwave dipole.

d: Distance from transmitter, meters.

p : Reflection coefficient of the ground when the earth is considered a plane.

D: Divergence factor.

¢ : Phase difference between direct and reflected waves when the earth is considered a plane.

k : Correction factor of the phase difference to allow for the sphericity

of the earth.

The equation applies for regions where the ray theory approximation is

valid. D and k may be obtained from graphs given by Domb and Pryce,s and

p from the work of McPetrie.o

If the earth may be regarded as plane, i.e., D=l and k=l, and pis assumed

to be 1 L.rr, the above equation reduces to

provided that

sin¢~¢

which is true when

where d ~ h1 + h2

h1 : Effective height of transmitting antenna above ground.

h2 : Effective height of receiving antenna above ground.

4 T. INAMI

Curves for this equation covering the frequency band 30-150 mc/s were

published in 1938,10 in which the atmosphere was assumed homogeneous with

refractive index equal to unity. For a standard refraction, the treatments of

Eckersley and Millington,l,l Domb and Pryce,8 Burrows and Gray,l~ or Norton13

may be valuable.

Although the manner in which variations in the atmospheric refractive index

affect field-strengths at frequencies within and above the VHF band is now

reasonably well understood, the transmission characteristics for a given fre­

quency over a given path cannot be predicted in detail on a long-term basis.14

On the other hand, there is considerable data on the long-range propagation-up

to two hundred miles or so-of VHF waves for several geographical regions, and

it is possible to estimate the variations of field-strength to be expected in typical

cases on a statistical basis. Such estimates can be made with a reasonable

degree of accuracy in the lower VHF band, but sufficient experimental data are

not yet available to allow similarly accurate estimates for frequencies higher

than about 200 mc/s.

2.2 Field-strength level versus distance. In general, the field-strength level

for constant terminal heights and for propagation well within the standard radio

horizon decreases as the square of the distance from the transmitter and agrees

quantitatively with the theoretical prediction at VHF and UHF provided:

1. The ground (reflecting surface) is sufficiently smooth according to

Rayleigh's criterion.t:;

2. Terminal heights are very small compared with the distance between

them.

Figures 1 and 2 are results of field-strength measurements by Trevor and

Carter16 at 61 and 41.4 mc/s over level ground (airport-runway) with horizontal

and vertical polarization. Free space values are also shown. Wires 2.11 and 3.81

meters long were used as receiving antennas for vertical and horizontal polariza­

tions, respectively. Unfortunately the value of radiated power and the type of

transmitting antenna employed are not reported in the paper, thus making it

impossible to deduce possible interference pattern.

It should be noted that in Figs. 1 and 2, horizontally polarized waves are

attenuated more rapidly with distance than the vertically polarized waves (see

Section 2-9) .

Curves, apparently similar to Figs. 1 and 2, are also reported by the

authors (Figs. 21 and 26 in Ref. 16). Evaluation of these curves is impossible

because on information is given on the following: 1. The path profile. 2. The

heights of the antennas above sea level. 3. The kind of antennas used in the

experiments. It should be noted that horizons indicated in Fig. 26, Ref. 16, are

Microwave Propagation Characteristics 5

........ Frequency of Radiation: 41.4 mc/s ........ s:: Transmitter Ht. Above Ground: 2.5 m 0 s:: ..-{

0 +' Free Space Value } ..-{ a!"

i.l N ..-{ 0 Experimental Value

N H ..-{ a!

ti 105 'd 104 Horizontal Polarization rl P< (h2 = 1.6 m above ground) 0 P< 'Gl

'Gl ~ --:. Free Space Value ~ () 0 ..-{ N 0 : Experimental Value +' ..-{

H H

~ 0 .<:1 Vertical Polarization

1-< !-i " (h2 = 3.15 m above ground) 0 0 ...... ...... <II 104 ~ 103

·~ a! () () til til ......-;. H Q) Cll +' +' ~ ~ H H Cll Cll P< P<

+' +' rl 103 'd 102 0

~ ~ H 1-1 () ()

..-{ 11 a ~ s::

•rl

.<:1 to +' bO s:: s:: Cll <II 1-1 1-i +'

102 +'

<I) ~ 10 I rei rei rl rl ij) Cll

•rl -rl rr. rr.

0 o. 1.2 1.6 Distance from Transmitter "in Kilometers

Fig. 1. Field-Strength vs. Distance at 41.4 mc/s Over Level Ground. Reproduced with Permission of the Institute of Radio Engineers.

not the radio horizons customarily used, but probably either geometrical or optical

horizons. The ambiguity is not resolved because of the lack of the information

just cited.

Similar field-strength versus distance curves at 37.5 and 43 mc/ s are reported

by Beverage, et alP These curves also lack the information given in the para­

graph above. In addition, the work fails to provide any data on: 1. The height

of the antennas above ground. 2. The polarization of the radiation. 3. Whether

6 T. lNAMI

measurements were taken over-sea, over-land, or over composite-path.

When one of the terminals is relatively high above ground, field-strength

versus distance curve shows interference between direct and reflected waves,

provided: 1. The ground (reflecting surface) is smooth enough to result in

specular reflection at the frequency used. 2. The receiver is in the interference

region of the transmitter.

This type of field-strength-distance variation is quite common in VHF and

UHF ground-to-air, air-to-air, or air-to-ground propagation, particularly over

0 0.2 0.4

Frequency of Radiation: 61 mc/s Transmitter Ht. Above Ground: 2.9 m

0

X

Free Space Value } Experimental Value

Horizontal Polarization (h2 = 1.6 m Above Ground)

Free Space Value } Experimental Value Vertical Polarization (h2 = 3.15 m Above Ground)

0.6 0.8 1.0 Distance from Transmitter in Kilometers

Fig. 2. Field-Strength vs. Distance at 61 mc/s Over Level Ground. Reproduced with Permission of the Institute of Radio Engineers.

Microwave Propagation Characteristics 7

water.

Experimental results agree quantitatively with conventional theory provided

the following conditions are fulfilled in addition to the conditions mentioned

above: 1. The reflection coefficient of the reflecting surface at the frequency

and grazing angle involved is known. 2. The refractive index profile over the

propagation path is known and is uniform. 3. The time-variation of refractive

t!l

~ Q)

+'

liJ ~ Q) 't.l 41 1-1 til Ul 0 1-1 () al

t!l +' ..... ~ 0 1-(J .,.. IS 1'1

.,..f

~ bO

.,..f t!l

"d Q)

> .,..f Q) () Q)

p:;

Frequency of Radiation: 328.2 mc/s Transmitter Height: . lO,OOO ft. Receiver Height: 75 ft.

(a) Vertical Polarization

. ~

1

(b) Horizontal Polarization

1

(c) Circular Polarization

Distanoe from Transmitter in Miles

Fig. 3. Variation of Field-Strength with the Distance from the Transmitter for Three Polarizations.

Reproduced with Permission of the Institute of Radio Engineers.

8 T. INAMI

index during the experimental run is negligible. 4. The antenna radiation

patterns are known.

Figure 3 shows an example of such an interference pattern at 328.2 mc/s

due to Kirby, Herbstreit and Norton.18 In this experiment, propagation was

over water and dipoles were used for both transmitting and receiving antennas.

Transmitter power was 6 watts and antenna gains were 2.15 decibels above the

isotropic antenna system. Communication system loss of 6 decibels and values

of dielectric constant of 81 and of permittivity of 4.64 mho per meter were

assumed in calculating theoretical values which are shown as chained curves

in Fig. 3.

The discrepancy of the experimental result with the theoretical expectation

is probably due to the following facts: 1. The reflecting surface fluctuated in

space and time. 2. The reflecting surface is not smooth enough according to

Rayleigh's criterion. 3. The reflection coefficient assumed is not accurate. 4. The

power output of the transmitter is not accurately estimated.

Similar interference curves at 44 mc/ s are reported by Beverage, Peterson

and HansellP and at 139.14 mc/ s, 243 mc/ s and 328.2 mc/ s by Reed and Russell.10

A similar result at EHF, reported by Lamont and Watson,2o is rather unexpected

in that the reflecting surface (ocean surface in this case) is too rough at such

a high frequency to present specular reflection according to Rayleigh's criterion.

2.3 Vertical distribution of field-strength. When the ground-reflecting sur­

face-is smooth enough to result in a specular reflection, the vertical distribution

of field-strength exhibits a familiar interference pattern for propagation well

within the radio horizon. Figure 4 shows a typical pattern observed in field­

strength versus height curve as reported by Stration, LaGrone, Tolbert and

Williams.21 The field-strength versus height curves for wavelengths of 26.5

centimeters (vertically polarized), 9.0 centimeters (vertically polarized), and

3.2 centimeters (horizontally polarized) are shown. Angles between half-power

points and antenna types corresponding to each of these curves are, respectively:

21.0 degrees and 40 inch parabolic reflector; 15.2 degrees and 18 inch parabolic

reflector; 15.8 degrees and 4 inch horn of square aperture; and 20.0 degrees

and 1 inch circular horn. . Identical antennas were used at the two ends for each

measurement. These waves were propagated over a 1000-foot propagation path

of relatively fiat ground.

It may be observed in Fig. 4 that, while the three lower frequency waves

present clear interference patterns, the 0.86 cntimeter wave gives, in places,

a diffused reflection. This is probably due to the fact that, at this frequency, the

gt·ound is too rough according to Rayleigh's criterion.

Similar interference patterns were reported by Epstein and Peterson. 22

Microwave Propagation Characteristics

Rece iver Antenna Height Above Ground

~ ~~~~4~o~~~3~5~~~31o~~~2~5~~~·~2ro~~e!~~~1~o~~ 20

Ul r-i Q)

.a 4o 5 •n

" 20 ~· 'tJ

0:: •n

..c:: ;.> b() 10 0:: UJ

" ;.> Ul I

"" r-i

"' ·n 'H

"' ~ ·n ;.> a:! 10

..-!

~· o::;

40 35 30 25 20 15 10 5 Wavelength 0.86 Cent i met e r Vertically Polari zed

14

0

Fig. 4. Variation of Field-Strength with Height of Receiving Antenna-Interference Pattern Due to Specular Reflection.

9

In the experiments conducted by them, a horizontally polarized wave at the

frequency of 850 mc/ s was propagated over a 3.5 mile swamp path covered by

six-foot grass. Similar results have been reported at 68.3 mc/ s by Yagi ;23 at

34 mc/ s and 61 mc/ s by Trevor and Carter; 10 at 44 mc/ s by Jones; 24 at 170 mc/ s,

520 mc/ s, 1000 mc/ s, 3300 mc/ s, 9375 mcjs and 24,000/ s by Day and Trolese ;25

and at 44 mc/ s by Beverage and othersP

2.4 Effect of terrain irregularity. Heretofore the surface of the earth has

been treated as if it is smooth. The ground-surface is, however, generally far

from smooth as defined by Ralyeigh's criterion; and as the frequency increases

the surface roughness becomes greater in effect. Thus, several problems at

10 T. lNAMI

once arise and are listed as follows :

1. Within the radio horizon, the field at the recervmg antenna is ideally given by the vector addition of two component fields, one due to a wave travelling directly from the transmitter to the receiver, and the other to a wave reflected at the ground-surface (neglecting scattered and elevated layer-reflected com­ponents). There are ground configurations that can give rise to more than one reflected wave. Furthermore, it must be remembered that, as the fre­quency is raised, it becomes increasingly possible for such multipath effects to occur, since relatively small areas of the ground surface are required to give effective reflection. With irregular terrain, these areas may be expected to occur more frequently with a disposition suitable for producing a field due to a reflected wave at the receiving point.

2. While it is possible to calculate with reasonable accuracy the effect on field­strength of one, or perhaps a few, well-defined diffracting obstacles-hills, singly or in ridges--or an otherwise smooth transmission path, there is no satisfactory theory to deal with the problem when a large number of irregular obstacles are present, i.e., there exists no rigorous theory that can deal suc­cessfully with all of the departures from the ideal spherical earth case caused by surface irregularities of a completely general character.

3. The roughness of the ground-surface along the propagation path reduces the magnitude of the reflection-coefficient; i.e., the ground-reflected component of the recei~ed signal is smaller for propagation over rough terrain than that over smooth terrain; so that the deep field-strength minima at certain points within the horizon expected under smooth-earth conditions are less likely to occur.

In general, when propagation is over irregular terrain, experimental field­

strength deviates considerably from the expectation of conventional theory,

particularly at VHF and above. Figures 5 and 6 give typical examples of mass­

plot of field-strength level at various distances from the transmitter, together

with free space curves (J ones24 ). The data for Fig. 5 are at 44 mc/s 0 = 6.8 m)

with a transmitter output of approximately 2 kilowatts. The data for Fig. 6

are at 61 mc/s (A =4.9 m) with a transmitter output of approximately 1 kilowatt.

In both experiments, half-wave vertical elements were used as transmitting

and receiving antennas, with a transmitting antenna height of 1300 feet (396

meters) above ground and the receiving antenna at ground level. The receiving

points at less than 30 miles are chosen at random, but the points at more than

30 miles are mostly on hill tops. Each point on the graphs represents an average

of about five maximum and minimum indications near a given location.

Similar examples may be found elsewhere (Ref. 26 and the literature quoted

in the next section).

2.5 Ground-irregularity correction factor. A mass-plot of the deviation of

actual received field-strength from the theoretical value, taken from various

sources, is found in Fig. 7.

Points (a) in Fig. 7 are results of experiments at 593.6 mc/s and 102.6

Microwave Propagation Characteristics 11

-----· 10.0

44 mc/s Frequency:

• Wavelength: 68 m •

" • • • •

•

• • • • • >.! • • •• • Q) • • +' Q) 1.0 • s • >.! Q) • P;

UJ • +' • rl 0 :> •rl rl rl ·rl s • .:: •rl • .<:: +' bD .:: (])

>.! +' CJl 0.1 I

-cJ rl (]) ·rl Free-space field li<

•

1 2 4 20 4o 6o 8o 100 Distance in Miles

Fig. 5. Field-strength vs. Distance for Propagation Over Rough Terrain. Reproduced with Permission of the Institute of Radio Engineers.

mc/s (Saxton and Harden7 ). Horizontally polarized waves with a transmitter

at 79 meters above local ground (or 40 meters above mean sea-level) were used

for 102.6 mc/s signal, and horizontally polarized waves with a transmitter at

184 meters above local ground (or 365 meters above mean sea level) were used

for 593.6 mc/s signal. Radiated power and gain of the transmitting antenna

12

1-i Q)

+> Q)

a 1-i Q) p.

<ll +> rl 0 > ·rl rl rl •rl a s::: ·rl

..c: +> QO s::: Q)

1-i +> <ll I

'{j rl Q) ·rl P:..

•

0.1

T. INAMI

•

Frequency: 61 mp/s' Wave1~ngth: 4.9 m

• •

•

• • •

•

•

Free-space field

•

Distance in Miles

Fig. 6. Field-strength vs. Distance for Propagation Over Rough Terrain. Reproduced with Permission of the Institute of Radio Engineers.

o, _

_ -

-'V

-E

-10

-20

30

35.6

-20

lo

g

f ]

For

60

~

f ~

1000

50 f

0

100

db

' ' ' '

' ' ' '

500

10

00

30

00

Rad

io F

req

uen

cy i

n M

egac

ycl

es p

er

Sec

on

d ' '

'

Fi~

. 7

. D

epen

denc

e o

f T

err

ain

Facto

r on

Fre

qu

ency

of

Rad

iati

on. '

f-3

ro >-;

>-< m

.....

;:I ....,

a::

Ill

()

;;·

c+

.... 0

0 >-

; ::;1

!»

!t

<

1\)

(!

)

CD

'1:

1 .... t-<

0 '0

0

!»

CQ

OQ

I)> <+

8

>-rj

c;·

~

'"" 1:$

(]

) (]

) 0

0 f-

' >

-;H

P.,

::r

!»

(])

>-;

I

..., ,+

'i

m

!»

'""

(ll

c+

<>

<+

UJ(

) 0'

1 >-;

(!

)

c+P

J ~~

:::t

>-;

f-'

"' (]

) ll

l0'1

<+

;:I

<

>-;

c+

;;·

0'1

PJ

!:J"

Ill

c+

f-'

8 !:

J"~

(]) ::u

(])

>-;

(])

>-;

()

0

Ill

(])

...., '"

" '""

;:I

<

'"':!

(])

'"" p.

, (]

) f-'

0 p.

, <

(]

) >-;

.... <:.:>

14 T. INAMI

were 70 watts and 7 decibels for the former and 150 watts and 12 decibels for

the latter.

Points (b) in Fig. 7 are based on experiments by Brown, Epstein and

Peterson27 at 67.27 mc/ s, 288 mc/ s, 510 mc/ s and 910 mc/ s, for distances out

to 64 kilometers with the transmitting and receiving antenna heights of 381

and 9 meters, respectively.

Point (c) is based on experiments at 505.25 mc/ s by Brown2s with trans­

mitter!'! and receiver heights of 109 and 9 meters, respectively, and at ranges up

to 16 kilometers.

Point (d) is the average of results reported by Fisher,29 at 60 locations in

a 1 to 23 mile range at 505.25 mc/ s, with nearly the same terminal heights as

those in Brown's experiments.

Points (e) in Fig. 7 are based on experiments at 530.25 and 850 mc/ s by

Epstein and Peterson,ao with a transmitting antenna height of 100 meters and

76 meters for lower and higher frequency, respectively, and a receiving antenna

height of 3 meters and at ranges up to 32 kilometers.

Point (f) is the average of results, as reported by Kirke, Rowden and

Ross,31 at numerous locations over various radii at 90.8 mc/ s with vertically

polarized waves and effective radiated power at 0.85 kilowatt. Dipoles were

used at both ends of the propagation path with a transmitting antenna height

of 220 feet. Receiver antenna heights are not reported.

Points (g) are based on FCC data32 up to 804 miles on 63 radials at UHF

and on 1400 measurements at VHF.

The experimental values of deviation in Fig. 7 indicate that the following

relation holds:

Terrain irregularity correction factor

E' = 20 log Ff · = 20 log f 0-20 log f db

for fo::::; f::::; 1000 and d < 50km

where:

E': Median of field-strength over irregular terrain taken at a given radius

from the transmitter. About 50% of the locations should give at least

this value of field-strength for any given distance from the transmitter.

E : Theoretical value of the field-strength at the given distance from the

transmitter.

f : Frequency of radiation in mc/ s.

/ 0 : Frequency at which E' equals E.

Saxton14 gives the value of fo as 70 mc/ s while Egli33 proposes / 0 =40 mc/ s.

After examining more experimental data than either of the investigators, the

Microwave Propagation Characteristics 15

author finds / 0 =60 mc/ s. The curve based on this value of / 0 is plotted in Fig. 7.

The expected field-strength realized for 50% of the locations for propagation

over irregular terrain can be calculated from the theoretical value wherein the

effective height of the antennas is taken to be the actual height above local

ground, together with the terrain irregularity factor given by the equation,

except when either transmitting or receiving antenna is located at a position

very high or very low with respect to the surrounding terrain.

In very mountainous country or in densely built up areas, lower field-strength

will be expected than the equation indicates because the equation is based on the

statistical average of various degrees of roughness normally encountered; whereas

in flat countries the correction factor is likely to be smaller, and may even be

negligible at times. In propagation over the ocean, transmission characteristics

should approach those predicted for a spherical earth, except at short ranges

and with very rough seas.

If it is desired that, instead of statistical prediction, field-strength at a

particular point or in a particular region be more accuratedly predicted, it is

necessary to examine the dependence of the field-strength upon the geographical

contour, particularly upon the propagation path profile. While a complete analysis

of such dependence has not been made, and such analysis is not within the

scope of the present paper, it should be mentioned that LaGrone114 has proposed

to analyze such dependence in terms of relatively simple path-profile parameters;

and the method, though yet unsatisfactory at times, seems promising.

It is well known that electromagnetic waves with frequencies above 30 mc/s

are considerably attenuated by buildings. For example, Young35 found, for

450 and 900 mc/ s, a median field-strength ranging between 20 and 40 decibels

below the calculated values for a transmitting antenna height of 150 meters.

He also found a divergence as great as -25 decibels for 150 mc/ s at times. His

measurements were mainly confined to the densely built-up area of New York.

The data in Table I show results of measurements of attenuation of VHF

and UHF over built-up areas (cities) by various investigators.

Trees may be considered as a kind of surface irregularity, and thus give

considerable attenuation of field-strength beyond or in woods in the frequency

range considered. The degree of the attenuation depends upon the frequency

and polarization of th electromagnetic waves.B6 For moderately thick woods in

full leaf with the antenna below tree-top level, the average attenuation at 30

mc/ s is 2 to 3 decibels for vertical polarization and 0 decibel for horizontal

polarization. At 100 mc/ s, the average attenuation is 5 to 10 decibels for

vertical polarization and 2 to 3 decibels for horizontal polarization. As the

frequency increases, the average attenuation increases. At 1000 mc/ s, trees

16 T. lNAMI

Table. I. Attenuation over built-up areas.

Frequency Polarization Attenuation Reference mc/ s Decibels -- ----- · ---- - - ----· -· - -- -

61.75- 102.6 Less than 6+ 7 67.25 - 2+ 27 90 .8 Vertical 12* 33 90 .8 Horizontal 10* 33

288 12+ 27 450 20- 40+ 35 505 .25 24+ 28 510 16+ 27 530.25 13- 19+ 30 593.6 15* 26 600 10- 30+ 7 850 17-25+ 30 900 20- 40+ 35 910 19+ 27

-- - -------------- · * Below the mean-value of signal level at the corresponding distance

for propagation over areas not replete with buildings. + Below theoretical signal level for spherical earth.

that block vision are almost opaque to the electromagnetic waves. Waves reach­

ing the receiver must then diffract over or around the woods. Above 300 to

500 mc/s, there is little difference in the attenuation for vertically and horizontal­

ly polarized waves.a4

Measurements of attenuation through woods have been reported for 100

mc/ s, 540 mc/ s and 1200 mc/s by Saxton and Lane,37 for 500 mc/s by Trevor,~8

and for 540 mc/ s and 3260 mc/ s by McPetrie and Ford.3 9

The results of these measurements are given in Table II and Fig. 8. In

these experiments no effort has been made to investigate dependence of the

attenuation on thickness of the woods. From these data, the average attenuation

of field-strength due to woods, L, in decibels per kilometer is given approximately

by

log L = 2.61logfmc -5.435 for vertical polarization

log L = 0.912log f mc -3.347 for horizontal polarization

for 30::;; f mc ::;; 4000.

The graphs of these equations are plotted in Fig. 8.

An interesting investigation of the effect of trees between the receiver in

the clear and at varying distances has been reported by A. D. Ring and asso­

ciates.40 Results from this experiment indicate that field-strength received

beyond a wood varies, when expressed in decibels, logarithmically with distance.

For instance, at 485 mc/ s field-strength is 37 decibels below spherical earth value

at 0.01 mile from the wood, and reaches 10 decibels below the theoretical value

at about 1 mile from the wood.

Microwave Propagation Characteristics

Table II. Attenuation due to trees.

Frequency Attenuation mc/s d/b meter

100 0.06

100 0.03

500 0.12

500 0.10

fioo· 0.08

540 0.20

540 0.18

540 0.15

540 0.25

1200 0.35

3260 0.6

* Vertical polarization. + Horizontal polarization.

Polarization

V.*

H.+

H. & V.

V.

H.

v. H.

Remarks

} Several hundred meters of a thick wood, mainly deciduous, in full leaf.

Full leaf } 150 m deep wood

} Leafless

} Summer. 85 m thick wood, mainly deciduous, in full leaf.

H. I V.

H. & V.

H. & V.

Four rows of lime trees about 27 m high, spaced about 6 m in both directions. Full leaf

Reference

37

37

38

38

39

39

37

37

37

39

17

It should be noted in the equation giving the terrain irregularity factor,

presented on page 23, that no terms indicating dependence of the terrain

irregularity correction factor on distance from transmitter or on terminal heights

is involved. Apparently, the influence of the degree of irregularity of the terrain

outweighs any such influences, if present. But it should be emphasized that

no rigorous, controlled experiment has been reported-so far as the author is

aware-on dependence of the correction factor on frequency, distance from

transmitter, or terminal heights. It is possible that further investigation might

reveal a significant dependence of the terrain factor on distance from the trans­

mitter or on terminal heights, or a dependence on a frequency different from

that given by the equation relating to terrain irregularity.

Data in Fig. 9 (Saxton14 ) show the field-strength over spherical earth and

over irregular terrain for various frequencies and transmitting antenna heights,

and for a constant receiving antenna height. The striking feature about these

curves is that, apart from the region near the interference extrema-which in

any case may well be blurred over irregular terrain-the median field-strength

is apparently almost independent of frequency over the range concerned.33

The whole of the advantage in the field-strength to be obtained for a given

radiated power by increasing the frequency, which is apparent in the spherical­

earth case, is absent in the case of propagation over irregular terrain. If any­

thing, the lower frequencies give slightly higher field-strengths, particularly as

the radio horizon is approached.R3

18 T. INAMI

Moreover, because of the slope of the distribution curve for the higher

frequency, the comparative independence from frequency that is observed for

median field-strengths is largely lost for field-strengths that are exceeded at

90 % of the locations. Thus the higher the frequency, the higher the value of

median signal strengths which will be required to provide the same value of

90 % field-strengths. 41

l.O

30 50 70 100

A Saxton~Lane X Trevor e McPetrie-Ford 0 Me Petrie -Saxton V Vertical Polarization H Horizontal Polarization

The·points not marked leafless are for trees in full leaf.

0.912 lug fmc - ] .347

200 500 700 1000 2000 Frequency of Radiati on in mc/D

Fig. 8. Attenuation of Field-Strength Due to Trees.

5000

6o

40

20

80

6o

4o

20

0

0

Microwave Propagation Characteristics

50 mc/s

(a)

20 40

Transmitter Height: 100 m Receiver Height: 10 m Effective Earth Radius:

= ~ Geometrical Earth Radius 3

Polarization: Arbitrary

Radio Horizon

For Smooth Spherical Earth

60 80 100

1

Radio Horizon

I

~--~ ,-:::--~ ",, __ 50 mc/s 100 mc/s

200 mc/s ' , ____ _ (b) For Irregular Terrain ',

..... ·--- 500 mc/s 800 mc/s

0 20 40 60 80 100 Distance from Transmitter in Kilometers

Fig. 9-i. Field-Strength Characteristics.

19

Reproduced with Permission of the Controller of Her Majesty's Stationery Office. Crown Copyright, United Kingdom.

20

100

8o

6o

40

20

(a)

T. lNAMI

Transmitter Height: 300m Receiver Height: 10 m Effective Earth Radius:

= t Geometrical Earth Radius

Polarization: Arbitrary

Radio Horizon

~1 ' ............ .._ ...... ,

For Smooth Spherical Earth

OL-----~----~----~----~--~~------------~ 0 20 40 6o 80 100

(b) For Irregular Terrain

0~----~----~-----L----~--~~------------~ 0 20 40 6o 8o 100

Distance fr~m Transmitter in Kilometers

Fig. 9- ii. Eield-strength Characteristics. ~::.:Reproduced with permission of the Controller of Her Majesty's Stationery Office. Crown Copyright, United Kindom.

100

~ Bo

~ H Q)

+' ~ H Q)

PI

> ~ 20

4o

20

(b)

Microwave Propagation Characteristics

Transmitter Height: 200 m Receiver Height: 10 m Effective Earth Radius:

= ! Geometrical Earth 3 Radius

Polarization: Arbitrary

Radio Horizon

(a) For smooth spherical earth

Radio Horizon

-:::-... ........ ........_--1~ ................

I ~ ...... ,, For irregular terrain "

50 mc/s 100 mc/s 200 mc/s 500 mc/s 8oo mc/s

Distance from Transmitter in Kilome~ers

Fig. 9-iii. Field-strength Characteristics.

21

Reproduced with permission of the Controller of Her Majesty's Stationery Office. Crown Copyright, United Kingom.

22 T. INAMI

The curves of Figs. 9-ib, 9-iib and 9-iiib are such that, at 100 mc/ s, for

example, 10 % of the receiving locations may have a median field-strength about

10 decibels greater than the curves indicate, while a further 10 % may have

median field-strength of 10 decibels less. A similar range of variations, perhaps

1 or 2 decibels less, will occur at 50 mc/ s. At 500-600 mc/ s the variation from

the median value indicated by the curves is about ±15 decibels for the most and

the least favored 10% of the receiving locationlil ;7 a slightly greater range of

variation is expected at still higher frequencies.

2.6 Local-variation of field-strength level for propagation over irregular terrain.

Sufficient experimental data do not yet exist to allow us to draw any definite

quantitative conclusion on space-distribution of field-strength for propagation

over irregular terrain, although significant advances have been made on the

matter recently.34 The following tentative statement, however, may be made

until further investigations are made on the subject.

Space distribution of field-strength level, expressed in decibels, for pro­

pagation over irregular terrain seems to follow a Rayleigh distribution when

data are taken over a small section of a given locality, at least in areas replete

with buildings, trees, etc.aa,as When data are taken over sufficiently wide areas,

the local variation appears to be of Gaussian distribution,&2•33 and thus it may

be described by its 50 percentile value and standard deviation. Some studies3~

indicate the local variation to be independent of frequency of radiation and

distance from transmitter and have normal distribution with a standard deviation

of 5.5 decibels.

Standard deviation is defined by

whereX,-X is a deviation of observation from the mean and N is the total

number of observations. For a Gaussian distribution, standard deviation is

the difference in levels where the percentile difference is 68.27 per cent.

Other studies indicate the local variation to be frequency dependent.7.33

For examp,e, Egli33 found standard deviation to be 8.3 decibels at 127.5 mc/ s

and 11.6 decibels at 510 mc/ s. Egli's paper gives curves for standard deviation

as a function of frequency in the frequency range of 40-1000 mc/s, but they

should be used with caution because they are derived from the two meager ex­

perimental results mentioned.

Curves that do not follow either Gaussian or Rayleighan distribution have

been reported by Epstein and Peterson.~1 These data, however, are based on

measurements at not more than 8 locations, and therefore their statistical value

Microwave Propagation Characteristics 23

is questionable.

Obviously, local variations depend upon the type of local terrain and fre­

quency of radiation. Local variations are greater and wider in range for the

higher frequencies of radiation. Local variations are relatively small (about 2-4

decibels at 100-600 mc/ s) 7 in open sites, and if the locality is flat it may not

exceed ±1 decibel.31 A few isolated trees and buildings which are not very

close (say, 20 feet) to the receiving antenna do not affect the local site field­

strength variations appreciably at frequencies less than 100 mc/ s, but they

increase local site field-strength variations up to 8 to 10 decibels at 600 mcj s.1

In regions which are well built up, the field-strength variations are further in­

creased-being some 15 decibels at 600 mc/ s and 6 to 8 decibels at 100 mc/ s.

Variations are increasingly greater (15-20 decibels)7 at 600 mc/ s with the

presence of trees in leaf amongst the houses, banks of leafy trees and large build­

ings, and may become as large as 25 decibels under certain conditions. (See

section 2.5.)

Local variations are, in general, very irregular, often consisting of small

fluctuations superimposed upon larger ones.

2.7 Time variation of field-strength level for propagation within horizon. In

the foregoing material, time variations in the field-strength level relative to time

variations in the refractive index over the propagation path have been neglected.

In fact, in none of the experiments referred to previously-except those by Day

and Trolese,2u and Epstein and Peterson30-has the subject been investigated.

Simultaneous refractive index measurements were not made in any of the experi­

ments. In this section, the time variation of the field-strength level will be

discussed.

For distances less than about 60 miles, or within the radio horizon (which­

ever is smaller), variations in field-strength level of VHF signals arising from

changes in atmospheric refraction are normally not of great importance. For

UHF, the maximum range at which time variation of signal level in neglible

is smaller-say, 40 milesa0-for normal propagation conditions. At still higher

frequencies, the range is even smaller. For instance, Day and Trolese25 found

2 month mean diurnal variation of field-strength levels to be less than ±2.5

decibels for frequencies of 170 mc/s, 520 mc/s, 1000 mc/s, 3300 mc/ s, and 9375

mc/ s and ±13 decibels for 24,000 mc/ s, for a 26.7-mile path in a desert in winter.

On this path, however, field-strength level variations are larger than average

because of the large diurnal changes in refraction peculiar to the propagation

path.

Under certain conditions signal level variation may be very great. This

happens when one of the following conditions is met:

24 T. lNAMI

1. When receiving antenna is near standard radio horizon. The normal variation of refraction may be sufficient to put the receiver in the diffraction region for some time, thus reducing the field-strength received considerably.

2. When the propagation path is such that an unstable duct or elevated reflecting layer may be formed.

3. When one of the terminals is considerably elevated above the mean level of propagation path. When variations in effective earth radius factor k cause a modification in the effective earth radius, the effective terminal heights are altered and may thus bring waves travelling the direct and ground-reflected paths into phase opposition, with consequent fading. This only happens when the effective path difference is any multiple of a wavelength. For most optical paths subject to normal variations in effective earth radius factor k (1 to 2, say), the path difference is less than a wavelength in the VHF range, and fading due to this cause is rare.

For example, in experiments by Gough at Lake Victoria, East Africa,4~

the condition 3 above is satisfied (Fig. lOb) and a severe fading is observed at

169 mc/s (Fig. lOa). For this path phase opposition of ground-reflected and

direct waves should occur when modified earth radius factor k=l.46 for 169 me,

assuming a reflection coefficient of water of -1 for the grazing angle in question,

but no phase opposition for 77 me. Such signal variation can be eradicated in

the VHF range (for the normal variation in k) by lowering the terminal heights

or reducing the operating frequency. When these measures are not possible, the

depth of fading can, theoretically, be reduced by the use of vertical polarization;

because the reflection coefficient for water, even near grazing incidence, is then

significantly less than unity owing to the very small pseudo-Brewster angle in

the VHF range.

2.8 Correlation between median path attenuation and fading range of signals. Since there exists a definite relationship between path-length and path attenua­

tion and between path-length and fading range of signals, it is not surprising

to find that a certain relationship is observable between median path attenuation

and the fading range of signals. In fact, experiments4~ show that, for VHF

at least, the following things are true:

1. Fading is negligible if median path attenuation is less than about 100 decibels. 2. If path attenuation exceeds about 100 decibels, an approximately linear

increase of fading range with median path attenuation is observed. 3. With the exception of land paths subject to nocturnal surface ducts, land

paths give less fading than water paths having the same median attenuation. The reason for this is that atmospheric stratification is, in general, less marked over land than over water.

4. No significant differences between fading characteristics of lower and higher VHF are observed.

Figure 11 is a mass-plot of fading range versus median attenuation on 99

paths at 80 mcjs and 170 mc/s, based on 6 days' continuous measurments each.

10

140

6o

Microwave Propagation Characteristics

{

LAKE VICTORIA, EAST.AFRICA PATH Transmitter 700 feet above the lake

water Receiver 1800 feet above the lake

water Horizontal Polarization Radiated Power: 8 watts Yagis (Gain 8 db above dipole)

169 mc/s wave

20 L-----------~2~0~0----------~1~20~0~--------~2~0~0~~ 1951-4-9 1951-4-10

Local Time in Hours

..--, QJ >

100 ~ en

-----~ 0\

~ f.; 0 'H

110'-' en Qj ..0 •rl t)

~ :~

120 § •rl .., ~

.~ QJ .., ~

I ..<:1

130 ~

lig. lOa. Diurnal Variation of Field-strength at 77 and 169 mc/s

5500

5000

4500

Fig. lOb. Profile of Propagtion Path of Fig. lOa Reproduced with Permission of the Institution of Electrical Engineers.

25

26 T. lNAMI

These are based on Gough's experiments.42

In Fig. 11, (a) is for normal land paths; (b) is far tropical land paths sub­

ject to nocturnal surface duct; and (c) is for tropical over-water paths. Solid

and broken lines are conservative and optimistic fading-range estimates on a

weekly basis. In order to obtain field-strength level in decibels above 1

corresponding to a median path-attenuation desired, the abscissa value should be

subtracted from 150.

In subtropical and Mediterranean Sea areas, winter fading ranges are

probably somewhat less than the range indicated by Fig. 10-c. Moreover, it is

likely that paths in temperate and arctic regions will generally exhibit smaller

fading ranges than the ranges shown by Fig. 11.

The fading range, as computed from only a few days' record, is very sensitive

to the incidence of even a single deep fade; because of the fact that, by definition,

it is based on signal levels exceeded for 99.9 % of the time (all but llh minutes

a day). Thus the fading range is likely to fluctuate more widely when measured

over short periods than over long periods.

Stack-Forsyth43 reports a correlation similar to Gough's at a wavelength

of 10 centimeters.

2.9 Polarization dependence of field-strength level for propagation within radio

horizon. The theory of the propagation of radio waves over a spherical earth20

predicts that the propagation characteristics of horizontally and vertically

polarized waves will not differ significantly provided that (1) the heights of

transmitting and receiving antennas above ground are at least a few wavelengths,

and (2) the heights of transmitting and receiving antennas are very much less

than the distance between the antennas.

There is now considerable experimental evidence7•26•31 to indicate that the

above is generally true, although there are differences of detail between the

Each point is based on 6 Days' continuous measurement.

Frequency: 80 mc/s. 170 mc/s.

(a) For normal land paths

0 0

Microwave Propagation Characteristics 27

(b) For tropical land paths subject to nocturnal surface duct 0

0

0 0

U) oo 0 rl 0 (l)

..a ·rl

0 C) 0 (l)

'LJ

J:: oo oo 0 ·rl oo o

0 o/ (l) 0 0 tlO ol J:: 0 0 0 ro 7 H 0 0 tlO 0 0 0 0 0 / ~ 0 0

·rl 'LJ

& (c) For tropical over-water paths

Median path a~tenuation in decibels

Fig. 11. Mass-plots of Fading Range Versus Median Attenuation. Reprodced with Permission of the Institution of Electrical Engineers.

28 T. INAMI

characteristics of the two types of polarization when diffraction effects are in­

volved. For example, it has been found that vertically polarized waves are

attenuated less directly behind hills or deep in the shadow area of an obstacle

than horizontally polarized waves, and the opposite effect has been observed

for receiving locations beyond hills but just outside their shadow, or in locations

in the back of-but away from-the deep shadow of a hilJ.31,44 Local site varia­

tion of field-strength is found to be somewhat greater for vertical polarization

than for horizontal-polarization. 7,31

The effect of trees as screening or absorbing agents rather than as reflectors

is more emphasized for vertically polarized waves.31 Thus, the attenuation is

less for horizontally polarized waves in wooded areas.3l,35

For propagation over irregular terrain, the ratio of field-strengths for

vertically polarized waves to those for horizontally polarized waves varies from

one location to another for a particular propagation path and frequency; the

ratio of such field-strengths averaged over a sufficient number of points near

a particular location-say within 30 to 40 meters of the location-is independent

of distance from the transmitter.7 The value of such median ratio averaged over

a number of transmission paths is, according to Saxton and Harden,7 about 0.9,

and is apparently independent of frequency; the value of the 10-percentile ratio

is about three times the 90-percentile ratio.

2.10 Recovery-effect of ground-wave at a land-sea boundary. As Millington4"

has shown, when a ground-wave is propagated first over a ground-surface of

one value of conductivity, and second over that of higher conductivity, there is

a recovery in field-strength before the attenuation becomes characteristic of the

second ground-surface and the field-strength will increase, for a certain space

interval beyond the boundary, with the increase of distance from the trans­

mitter; while on crossing the boundary in the opposite direction, there is a

corresponding sudden decrease of field strength before the attenuation takes

the value corresponding to the earth-constant of the first ground surface,

provided:

1. The propagation path is sufficiently smooth to permit a spherical-earth ap­proximation.

2. The heights of the antennas are not large compared with the wavelength employed.

3. The wave is vertically polarized.

Such an effect is often ohserved in waves at medium or high frequencies. 40 ·UO

A similar effect is noticed in VHF waves propagating over a composite path,

especially when the difference in conductivity is large, e.g., at a land-sea boundary.

A result of experiments47·"1 at 77.575 mc/s is shown in Fig. 12, together with

Microwave Propagation Characteristics 29

a theoretical curve calculated on the assumption that f = 15 e.s.u and a=10-Ia

e.m.u. over land and E=SO e.s.u. and a =4X 10-11 e.s.u. over sea. Among the

experimental points, the X's are believed to be the most accurate. A remarkable

agreement of experimental results with the theory is apparent. It is to be

noted that the experiments are carried out for the specific purpose of con­

firming or disproving the theory, under controlled conditions, and, therefore,

must be considered the most accurate of the kind possible. The vertical discon-

100

~ 90 > ~

80 r-1

<lJ :> 0 .g 70 rn

r-1 <lJ

~ u

60 <lJ 'd

10:: 50 •rl

..c: +' 00 10::

40 <lJ H +' rn I

'd 30 r-1

<lJ •ri

"" 20

10 0

Flat La.nd

1

(a)

o, x, +: Experimental Points Theoretical Curve, Land & Sea Theoretical Curve, Land Only

Frequency of Radiation: 77.575 mc/s 3.9 meters

Vertical Power :·lo Watts

0.5 Meter

Wave-Length: Polarization: Effective Radiated Antenna Heights: Type of Antennas: Half-wave Dipoles

,~ .

I"""-........_

2

"""-........._ I 0 .......... I +

Sea

3

....._I 0 ,___ I I 1 Irregular Land

4 Distance from Transmitter in Kilometers

5

Fig. 12. Propagation Over Composite Path- Recovery Effect. Reproduced with Permission of the Institution of Electrical Engineers.