Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications
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33-1
0
TABLE
3.
SYSTEM PERFORMANCE
PREDICTIONS
1 JAN SSN
=
20 CH 5.029
LONDONDERRY
TO
CHELTENHAM AZIMUTHS N.MILES
55.00N
-
7.31W 38.75N
-
76.85W 280.5 46.3 2880.3
RHOMBIC 50H 168L 70DEG. ANT
=
0
DB
OFF AZIMUTH
0
DEG. MIN. ANGLE
=
0
DEG. OFF AZIMUTH
0
DEG.
PWR
=
200.00 KW
3 MHZ MAN. NOISE
=
-154 DBW
REQ. S/N
=
61 DB
OPERATING FREQUENCIES
GMT MUF
2 8.6 3 4 5 6 7 8 10 12 15 17
20
22 25 27
2F 2F 2F 2F
2F 2F
2F
-
- - - - -
-
MODE
7 5
5
5
5 6
7------- ANGLE
187 185 185 185
185 186
187
-
-
- -
- - -
DELAY
50 99
99 97
87 66
20
-
-
-
-
-
-
-
C.PROB.
89
59 71
78 83
86
94
-
- - -
-
-
-
S/N..DB
50 42
81 91
85 66
20
-
- -
-
-
-
-
REL.
4 8.4
2F 2F 2F 2F
2F 2F
2F
-
-
- -
-
- -
MODE
8
5
5 5
6 7
7------- ANGLE
188 185
185 185
186 187
188
-
-
- -
-
- -
DELAY
50
99
99 96
84 61
16
-
-
-
-
-
-
-
C.PROB.
89 58
69 77
82 87
95
-
-
-
-
-
-
-
SIN..DB
50
34 77
89 82
60
16
-
-
-
-
-
-
-
REL
.
6 8.3
2F 2F 2F 2F
2F 2F
2F
-
-
-
-
-
-
-
MODE
7 5 5
5
6 7
7------- ANGLE
187 185 185 185
186 187
187
-
-
-
- -
-
-
DELAY
50 99
99 94
81 57
10
-
-
-
-
-
-
-
C.PROB.
89 56
68 76
82 87
97
-
-
- -
-
-
-
S/N..DB
50
28 76
89 80
57
10
-
-
-
- -
-
-
REL.
8 7.3
2F 2F 2F 2F 2F 2F
- -
-
-
----
MODE
755567
_-------
ANGLE
187 185 185 185 186 187
-
-
-
- - -
-
-
DELAY
50 99 97 85 59 27-
-
-
-----
C.PROB.
84 56 69 78 83 87-
-
-
-----
S/N..DB
48 29 71 76 56 26-
- -
-----
REL.
lo
7.9
2F 2F 2F 2X 2X 2F
- - - -
----
MODE
644116
--------
ANGLE
186 184 184 181 182 186
-
- - - - - -
-
DELAY
50
99 99 98 87 47
-
-
-
-
----
C.PR0B.
87 56 70 77 84 87-
-
-
-----
S/N..DB
49 30 75 86 84 46-
- -
-----
REL.
12 14.5
2F 3E 4F 3F 2F 2F 2F 2F 2F 2F
- - -
-
MODE
4 31510 4 3 3 3 4 4---- ANGLE
DELAY
184 181 190 187
184 183
183 183 184
184
-
-
-
-
50 99 99 99 99 99 99 90 39
8
- -
- -
C.PROB.
101 5
53 67
75 81 91 93 101
103
-
-
-
-
S/N..DB
50
0
14
67 84 93
98 90 39
8
-
-
- -
REL.
then be as small as
100
hertz, but such multipath may
be minimized by operating near the muf. Operation at a
frequency within approximately
10%
of the muf is
necessary for paths less than about
600
kilometers to
obtain bandwidths greater than, say,
1
kilohertz. The
multipath reduction factor (mrf) is defined as the
smallest ratio of muf to operating frequency for which
the range of multipath propagation time difference is
less than a specified value. The mrf thus defines the
frequency above which a specified minimum protection
ELECTROMAGNETIC-WAVE PROPAGATION
33-1
I
PATH
DISTANCE
IN
KILOMETERS
L
Fig. 10. Multipath reduction factor as
a
function
of
path
distance.
(From Salaman, R.
K.
“A
New Ionospheric
Multi-
path Reduction Factor
(MRF).”
0
1962,
Institute
of
Radio
Engineers.)
against multipath is provided. Fig.
10
shows the mrf for
various lengths of path.
*
Diversity?
It has been shown that if two or more high-frequency
radio channels
are
sufficiently separated in space,
frequency, angle of arrival, time, or polarization, the
fading
on
the various channels is more or less indepen-
dent. Diversity systems make use of this fact to improve
the overall performance, combining or selecting sepa-
rate radio channels
on
a single high-frequency circuit.
Satisfactory diversity improvement can be obtained if
the correlation coefficient of the fading
on
the various
channels does not exceed about
0.6,
and experiments
*
Salaman, R.
K.
“A
New Ionospheric Multipath Reduc-
tion Factor (MRF).”
IRE Transactions on Communication
Systems,
Vol. CS-10,
June
1962; pp. 220-222.
‘l
“Bandwidth and Signal-to-Noise Ratios
in
Complete
Systems,” CCIR, Geneva, 1982,
Vol.
111,
Report 195.
Grisdale, G.
L.,
Morriss,
J.
H.,
and Palmer, D.
S.
“Fading
of Long-Distance Radio Signals and
a
Comparison
of
Space
and Polarization Diversity Reception
in
the 6-18 Mc
Range,”
Proceedings
of
the IEE,
Part
B,
No. 13, Jan. 1957,
pp.
39-51.
NORTH POLE
EQUATOR
have indicated that a frequency separation of the order
of
400
hertz gives satisfactory diversity performance
on
long high-frequency paths. Spacing between antennas
at right angles to the direction of propagation should be
about 10 wavelengths. Polarization diversity has been
found to be about equivalent to space diversity in the
high-frequency band. Measurements have indicated that
times varying from
0.05
to
95
seconds may be neces-
sary
to obtain fading correlation coefficients as low as
0.6
in high-frequency time-diversity systems. Angle-of-
arrival diversity requires the use of large antennas
so
as
to obtain the required vertical directive characteristics.
Differences in the angle of arrival of
2”
have been shown
to give satisfactory diversity improvement
on
high-
frequency circuits.
Great-Circle
Calculations
With reference to Pig.
11,
A
and
B
are
two places
on
the surface of the earth the latitudes and longitudes of
which
are
known.
In
the figure,
B
=
place of greater
latitude (nearer the pole),
LA
=
latitude of
A,
LB
=
latitude of
B,
and
C
=
difference of longitude between
A
and
B.
Angles
X
and
Y
at
A
and
B
of the great circle
passing through the two places and the distance,
Z,
between
A
and
B
along the great circle can be calculated
as follows:
sin
4
(L~
-
L~)
tan
4
(Y
-
X)
=
cot
f
c
cos
;
(LB
+
LA)
and
give the values off
(Y
-
X)
and
i
(Y
+
X)
from which
;(Y
+X)
+
$(Y
-
X)
=
Y
and
NORTH POLE
NORTH POLE
EQUATOR
e
CB
SOUTH POLE SOUTH POLE SOUTH POLE
(A)
Both
polnts
located
In
northern hemlsphere.
(5)
In
opposlte hemispheres.
(C)
Both
pofnts
located
In
southern hemlsphere.
Fig.
1
1.
Three globes representing points
A
and
B.
33-1
2
REFERENCE
DATA
FOR ENGINEERS
1
(Y
+
X)
-
(Y
-
X)
=
x
In the above equations, north latitudes are taken as
positive and south latitudes as negative. For example, if
B
is latitude
60"
N and
A
is latitude 20"
S,
20"
LB
+
LA
=
60
+
(-20)
-
60
-
20
-
40
2 2 2 2
40"
L,
-
LA
=
60
-
(-20)
-
60
+
20
80
2
2 2 2
--=-=
If both places are in the southern hemisphere and
LB
+
LA
is negative, it is simpler to call the place of
greater south latitude
E
and to use the above method for
calculating bearings from true south and to convert the
results afterward to bearings east of north.
The distance
Z
(in degrees) along the great circle
between
A
and
E
is given by the following:
tan
4
z
=
tan
4
(LB
-
LA)
x
[sin
(Y
+
~)l/[sin
4
(Y
-
x)]
The angular distance
Z
(in degrees) between
A
and
B
may be converted to linear distance as follows.
Z
(in degrees)
X
11 1.12
=
kilometers
Z
(in degrees)
X
69.05
=
statute miles
Z
(in degrees)
X
60.00
=
nautical miles
In multiplying, the minutes and seconds of arc must
be expressed in decimals of a degree. For example,
Z
=
37'45'36" becomes 37.755'.
Exumple:
Find the great-circle bearings at Brent-
wood, Long Island, longitude 73'15
'
IO'W,
latitude
40"48'40"N, and at Rio de Janeiro, Brazil, longitude
43"22'07'W, latitude 22"57
'09"s;
and the great-circle
distance in statute miles between the two points. Refer
to Chart
1.
Great-circle initial courses and distances
are
conve-
niently determined by means of navigation tables such
Navigation Tables for Navigators and Aviators
Dead-Reckoning Altitude and Azimuth Table
Large Great-Circle Charts:
HO Chart No.
-HO NO. 206.
-HO NO. 21
1.
1280-North Atlantic Ocean
128 1 -South Atlantic Ocean
1282-North Pacific Ocean
1283-South Pacific Ocean
1284-Indian Ocean
The above tables and charts may be obtained at a
nominal charge from the United States Navy Depart-
ment Hydrographic Office, Washington, D.C.
EFFECT OF NUCLEAR
EXPLOSIONS ON RADIO
PROPAGATION*
Nuclear explosions below an altitude of about 15
kilometers have little effect on radio transmission.
However, a detonation occurring at an altitude between
15
and
60
kilometers can produce blackout in the
low-frequency
,
medium-frequency
,
and high-frequency
bands over a radius of several hundred kilometers. This
effect lasts only for a few minutes except in an area close
to the site of the explosion. In general, it can be said that
the effect of nuclear explosions
is
greatest near the site
of the detonation, but the effects of ionization and
shock waves do not last longer than a few minutes at
distances greater than a few hundred kilometers from
the site of the explosion.
High-altitude nuclear explosions (at altitudes greater
than about 150 km) increase the electron density in the
upper atmosphere by orders of magnitude. As a result,
the propagation of signals at frequencies as high as
100
GHz between satellites and from satellites to earth is
impaired. The impairments take the form
of
large
attenuation and time delays together with rapid variation
of signal strength and frequency-selective fading which
can limit the available bandwidth and data rates.
IONOSPHERIC SCATTER
PROPAGATION?
This type of transmission permits communication in
the frequency range from approximately 30 to
60
megahertz and over distances from about
1000
to
2000
kilometers. It is believed that this type of propagation is
due to scattering from the lower
D
region of the
ionosphere and that the useful bandwidth is restricted to
less than
10
kilohertz. The greatest use for this type of
transmission has been for printing-telegraph channels,
particularly in the auroral regions where conventional
high-frequency ionospheric transmission is often unreli-
able.
The median attenuation over paths between
800
and
1000 miles in length is about
80
decibels greater than
the free-space path attenuation at 30 megahertz and
about 90 decibels greater than the free-space value at
50
megahertz.
*
Glasstone,
S.
The Effects
of
Nuclear Weapons.
Washing-
ton:
US
Government Printing Office, 1962.
Middlestead, R.
W.,
et al. "Satellite Crosslink Vulner-
ability in
a
Nuclear Environment."
ZEEE Journal
on selected
areas
of
communications, Vol. SAC-5, pp. 138-145, Febru-
ary 1987.
Mohanty,
N.,
ed.
Space Communication and Nuclear
Scintillation.
New York: Van Nostrand Rheinhold, 1991.
"Ionospheric Scatter Transmission,"
Proceedings
of
the
IRE,
Vol. 48, No. 1, 1960; pp. 5-29. CCIR XVth Plenary
Assembly, Geneva, 1982, Vol. VI, Report 260-3, and
Vol.
111,
Report 109-2.
ELECTROMAGNETIC-WAVE PROPAGATION
33-1
3
CHART
1.
EXAMPLE
OF GREAT-CIRCLE CALCULATIONS
Longitude Latitude
73"15"10"W 40°48"40"N
L8
Rio de Janeiro 43'22'07"W (-)22'57 '09"s
LA
Brentwood
29"53'03"
C
17'5 1 '3
1
"
+
LA
63"45 '49"
-
LA
i
C
=
14"56'31"
5
(LB
+
LA)
=
8"55'45"
1
(LB
-
LA)
=
31"52'54"
log cot 14"56'31"
=
10.57371
log cot 14"56'31"
=
10.57371
plus log cos 31"52'54"
=
9.92898
0.50269
minus log sin X"55'45"
=
9.19093
log
tan
i
(Y
+
X)
=
1.31176
4
(Y
+
X)
=
87"12'26"
plus
log
sin 31"52'54"
=
9.72277
0.29648
minus log cos 8'55'45''
=
9.99471
log tan
(Y
-
X)
=
0.30177
4
(Y
-
X)
=
63'28'26''
Bearing at Brentwood
=
i
(Y
+
X)
+
f
(Y
-
X)
=
150"40'52" East
of
North
Bearing at Rio de Janeiro
=
5
(Y
+
X)
-
(Y
-
X)
=
X
=
23"44'00" West
of
North
5
(LB
-
LA)
=
31"52'54"
(Y
+
X)
=
87"12'26"
log tan 31'52'54''
=
9.79379
plus log sin 87"12'26"
=
9.99948
(Y
-
X)
=
63"28'26"
9.79327
minus
log
sin 63'28'26''
=
9.95170
log tan
f
Z
=
9.84157
4
Z
=
34'46'24''
Z
=
69O32'48"
69"32'48"
=
69.547'
Linear distance
=
69.547
X
69.05
=
4802 statute miles
METEOR-BURST
PROPAGATION
*
Frequencies
in
the very-high- and ultrahigh-fre-
quency bands may be propagated by reflection from
columns
of
ionization produced by meteors entering the
lower
E
region. Experimental single-channel two-way
telegraph circuits have been operated
in
the frequency
range from
30
to
40
megahertz
over
distances of
600
to
1300
kilometers with transmitter powers
of
1
to
3
kilowatts. One-way transmission of
voice
and facsimile
have
also
been made with transmitter powers
of
1
kilowatt and
20
kilowatts, respectively.
The frequency range from about
50
to
80
megahertz
has
been found best suited for meteor-burst transmis-
sion.
*
"Communication by Meteor-Burst Propagation," CCIR
XVth
Plenary Assembly, Geneva, 1982, Vol. VI, Report
251-3. Oetting, J. D., "An Analysis
of Meteor Burst
Communications for Military Applications,"
IEEE
Transac-
tions
on
Communications,
Vol. Com-28, Sept. 1980.
PROPAGATION ABOVE
30
CONDITIONS*
MEGAHERTZ, LINE-OF-SIGHT
Radio Refraction?
Under normal propagation conditions, the refractive
index of
the
atmosphere decreases with height so that
radio rays travel
more
slowly near the ground than at
higher altitudes. This variation in velocity with height
*
Bullington,
K.,
"Radio Propagation at Frequencies
Above 30 Megacycles,"
Proceedings
of
the IRE,
Vol. 35,
October 1947, pp. 1122-1 136.
Ken,
D.
E.,
Propagation
of
Short Radio Waves.
New York McGraw-Hill Book Co.,
1951. CCIR XVth Plenary Assembly, Geneva, 1982,
Vol.
V.
i
Bean, B. R., and Dutton,
E.
J.
Radio
Meteorology.
Monograph 92, Institute
for
Telecommunication Sciences
and Aeronomy, Environmental Science Services Administra-
tion
(ESSA).
Washington: Superintendent
of
Documents,
1966.
33-1
4
REFERENCE
DATA
FOR ENGINEERS
results in bending of the radio rays. Uniform bending
may be represented by straight-line propagation, but
with the radius of the earth modified
so
that the relative
curvature between the ray and the earth remains
un-
changed. The new radius of the earth is known as the
effective earth radius, and the ratio of the effective earth
radius to true earth radius is usually denoted by
K.
The
average value of
K
in temperate climates is about 1.33;
however, values from about
0.6
to
5.0
are
to be
expected.
The decrease in the refractive index with height may
at times be
so
great that the ray is bent down with a
radius equal
to
that of the earth
so
that the earth may
then be considered to be flat.
A
further increase in the
refractive-index gradient results in the radio ray being
bent down sufficiently to be reflected from the earth.
The ray then appears to be trapped in a duct between the
earth and the maximum height of the radio path.
Under certain atmospheric conditions, the refractive
index may increase with height, causing the radio rays
to bend upward. Such inverse bending results in a
decrease in path clearance
on
line-of-sight paths.
h,
=
RECEIVING-ANTENNA
HEIGHT IN FEET
v
2000
1500
1000
700
500
300
200
RADIO
GEOMETRICAL HORIZON
“HORIZON“ DISTANCE
IN MILES IN MILES
vv
120
110
1oc
90
60
50
The distance to the radio horizon over smooth earth,
when the height,
h,
is very small compared with the
radius of the earth, is given with a good approximation
by the expression
d
=
(3Kh/2)lI2
where,
h
=
height in feet above the earth,
d
=
distance to radio horizon in miles,
K
=
ratio
of
the effective to the true radius of the
earth.
Over a smooth earth, a transmitter antenna at height
h,
(feet) and a receiving antenna at height
h,
(feet)
are
in
radio line-of-sight provided the spacing in miles is less
than
(2/~,)”~
+
(2h,)”*
(assuming
K
=
1.33).
The nomogram in Fig. 12 gives the radio-horizon
distance between a transmitter at height
h,
and a
receiver at height
h,.
Fig. 13 extends the first nomo-
gram to give the maximum radio-path length between
h,=TRANSMITTING-
ANTENNA HEIGHT
IN FEET
v
2000
-
1800
-
-
-
-
-
-
-
1600
-
-
-
-
1400
-
-
-
-
1200
-
-
-
-
1000
-
-
-
-
800
-
-
-
-
Fig.
12.
Nomogram giving radio-
horizon
distance
in
miles
when
h,
and
h,
are known. Example
shown:
Height
of
receiving
antenna
60
feet;
height
of
transmitting
antenna
500
feet;
maximum radio-path length
=
41.5
miles.
(K
=
1.33)
600
-
ELECTROMAGNETIC-WAVE PROPAGATION
33-1
5
MAXIMUM
TANGENT~AL
RADIO.
RECEIVING-ANTENNA
GEOMETRRICAL
PATH TRANSMITTING.
IN MILES
h,=
FEET
IN MILES
IN MILES
h,
=
FEET IN MILES
HEIGHT DISTANCE DISTANCE ANTENNA HEIGHT
14
000
12
000
10 000
2.5
2.0
v
600
500
400
v
16
14
80 000
70
000
12
60
000
1000
600
200
0.02
path for Fig. transmission length 13. Nomogram and tangential between giving two distance radio- air-
l.i\
6000
‘\
\\\\
3oi400
planes at heights
h,
and
h,.
Example
na airplane
8500
feet (1.6 miles);
height
of
transmitting-antenna air-
plane
4250
feet
(0.8
mile); maxi-
mum radio-path distance
=
220
300
shown: Height
of
receiving-anten-
10
4000
3000
200
2000
\
‘\
05
miles.
(K
=
1.33)
200
\
7000
03
4000
two airplanes whose altitudes are known. Both figures
assume a value of
K
=
1.33.
Path Plotting and Profile-
Chart Construction
Path
Plotting-When laying out a microwave sys-
tem, it is usually convenient to plot the path
on
a profile
chart. Such charts are scaled to indicate the departure of
the curvature of the earth from
a
straight line. With
reference
to
Fig.
14,
D2
+
R2
=
(h
+
R)2
=
h2
+
2Rh
+
R2
D2
=
h2
+
2Rh
where,
D
=
distance,
R
=
radius
of
earth
(3960
miles),
h
=
altitude.
Since
h
<<
R,
D
=
(2Rl~)l/~,
and
inserting the true
earth radius with
R
and
D
in statute miles
and
h
in feet
10
6
20
000
3
50
000
30
000
lolloo
00
D
=
[(3/2)h]”2
h
=
(2/3)D2
for true earth, where
D
is
in miles and
h
in feet.
For
a value of
K
=
1.33
D
=
[(3/2)h]”2(4/3)1’2
=
(2h)’/2
h
=
D2/2
Fig.
14.
Straight line tangent to surface
of
earth.
33-1
6
REFERENCE
DATA
FOR ENGINEERS
c
U
Y
5
10
15
20
25
0
10
20
30
40
50
MILES
t;
Fig.
15.
profile
scale.
Typical
paper,
413-earth
1000-foot
Or more generally
h
=
2D2/3K
Profile
Paper-If a
4/3
effective-radius factor is
used, the departure from a horizontal tangent line is
h
=
D2/2
where symbols are as above. By using this equation, a
template can be made for convenient drawing of profile
paper (Fig.
15).
For instance, if the horizontal scale is
10
milestinch, the vertical scale
100
feevinch, and a
width corresponding to
40
miles is desired, the points in
Table
4
may be plotted.
A
typical example of a template constructed accord-
ing to these figures is given in Fig.
16.
If a different
scale is desired than is provided on available profile-
chart paper (for example, if a 50-mile hop is to be
plotted on 30-mile paper), then the scale
of
miles may
be doubled to extend the range of the paper to
60
miles.
The vertical scale in feet must then be quadrupled; i.e.,
TABLE
4.
POINTS
FOR
CONSTRUCTING TEMPLATE
Distance Distance
From
Center From Horizontal
(Horizontal) (Vertical)
0
miles
=
0
inches
0
feet
=
0
inches
5
miles
=
Yz
inch
12%
feet
=
YE
inch
10
miles
=
1
inch
50
feet
=
YZ
inch
15
miles
=
1%
inches
112Yz
feet
=
1%
inches
20
miles
=
2
inches
200
feet
=
2
inches
100-foot divisions become 400-foot divisions, as on the
right in Fig.
15.
Fresnel Zones
The Fresnel-Kirchhoff theory was originally devel-
oped to account for the diffraction of light when
obstructed by diaphragms, and when transmitting
through apertures of various shapes and sizes. This
theory may be applied to radio and sound waves and is
based on the concept that any small element of space in
the path of a wave may be considered as the source of a
secondary wavelet, and that the radiated field can be
built up by the superposition of all these wavelets
(Huygens principle).
Consider a transparent screen between a distant
transmitter,
T,
and a receiver,
R,
with the distance from
screen to transmitter being at least 10 times the distance
from screen to receiver, and with the plane of the screen
perpendicular to direction
T-R.
Concentric circles may
be drawn on this screen, with the centers at the point
where line
T-R
intersects the screen at
0,
the radius
of
the first circle being such that the difference in length
between path
0-R
and the path from the circumference
of this circle to
R
is
4
wavelength
(A).
The radii of the
other circles are such that the corresponding path-length
differences are integral multiples of
A.
The radius of
the first circle is
(dh)”’,
where
d
is the distance from
0
to
R,
and the radius
of
the second circle is
(2dh)”*,
of
the third
(3dA)’”,
etc. The area within the first circle is
called the first Fresnel zone, and the other ring-shaped
areas are the second, third, etc., Fresnel zones. The
fields from the odd-number zones are in phase at
R,
and
the fields from the even-number zones are also in phase
at
R
but are opposite in phase to the fields from the
ELECTROMAGNETIC-WAVE PROPAGATION
33-1
7
Fig.
16.
Construction
of
a
template
for
profile charts.
DISTANCE
IN
MILES
0
5
10
15
20
25
30
35
/
t
0
5
10
15
20
25
30
35
odd-number zones.
It
can be shown that the effect at R
of each zone is nearly equal. If an infinitely absorbing
screen
is
provided with an aperture of the same diarne-
teras the first Fresnel zone, it will be found that the field
at
R
is twice as great as the unobstructed or free-space
field. If the aperture is increased to include the second
zone, the field at
R
will then be nearly zero, since the
fields from zones
1
and
2
are nearly equal in amplitude
and opposite in phase. With a continued increase in the
diameter of the aperture, further maxima and minima
appear; the amplitude of these oscillations decreases
very gradually until eventually the field at
R
approaches
the free-space value, which is half that due to the first
Fresnel zone. If the distance from the screen to the
transmitter is
dl
,
and from the screen to the receiver is
dz,
then the general expression for the radius of the nth
Fresnel zone is
Required Path Clearance
A
criterion to determine whether the earth is suffi-
ciently removed from the radio line-of-sight ray to allow
mean free-space propagation conditions to apply is to
have the first Fresnel zone clear all obstacles in the path
of the rays. This first zone is bounded by points for
which the transmission path from transmitter to receiver
is
greater by one-half wavelength than the direct path.
Let
d
be the length of the direct path and
dl
and
d2
be
the distances to the transmitter and receiver from a
point,
P.
The radius of the first Fresnel zone at
P
is
approximately given by
R12
=
h(dldz/d)
where all quantities are expressed in the same units.
first Fresnel-zone radius in feet at
P
is given by
If
d
is in miles and frequency
F
in megahertz, the
R,,
=
2280(d1d2/Fd)1’2
The maximum occurs when
dl
=
d2
and is equal to
R,,
=
114O(d/F)’/*
While a fictitious earth of
4/3
of true earth radius is
generally accepted for determining first Fresnel-zone
clearance under normal refraction conditions, unusual
conditions that occur
in
the atmosphere may make it
desirable to allow first Fresnel clearance
of
an effective
earth radius of
0.7
to
0.5
of the true radius.
Fig.
17
shows the effect of path clearance on radio
transmission.
*
Interference Between Direct
and Reflected Rays
Where there is one reflected ray combining with the
direct ray at the receiving point (Fig.
18),
the resulting
field strength (neglecting the difference in angles of
arrival, and assuming perfect reflection at
T)
is related
to the free-space intensity, irrespective of the polariza-
tion, by
E
=
2Ed
sin
2~(6/2h)
where,
E
=
resulting field strength,
S
=
geometrical length difference between direct
same
Ed
=
direct-ray field strength,
1
units
and reflected paths, which is given to a close
approximation by
6
=
2h,,h,,/d,
where
h,,
and
h,,
are the heights of the antennas above a
*
Bullington,
K.
“Radio Propagation Fundamentals,”
Bell
System
Tech.
J.,
Vol. 36, No. 3,
1957,
pp. 593-626.
33-1
8
REFERENCE
DATA
FOR
ENGINEERS
reflecting plane tangent to the effective earth. (See Fig.
18.)
The following cases are of interest:
E=O
for
ha,ha,
=
dA12
E
=
2Ed
for
ha,ha,
=
dAl4
E
=
Ed
for
ha,ha,
=
dM12
In case
hat
=
ha,
=
h,
E=O
for
h
=
(dh/2)’/2
E
=
2Ed
for
h
=
(dh/4)1’2
E
=
Ed
for
h
=
(dA/12)’/2
All these equations are written with the same units for
all quantities.
Space- Diversity Reception
When
h,,
is varied, the field strength at the receiver
varies approximately according
to
the preceding equa-
EFFECTIVE EARTH
Fig.
18.
Interference between direct and reflected rays.
Fig.
17.
Effect
of
path clearance
on
radio
transmission.
(From Bullington,
K.
“Radio
Prop-
agation Fundamentals.”
Bell System Tech.
J.,
Vol.
36,
No.
3,
Fig.
8,
01957
American Ele-
phone and Telegraph
Co.)
CLEARANCE/FIRST FRESNEL ZONE,
H/Ho
R
=
reflection coefficient of surface
H
=
clearance
M=
[HI/K’~){
[1+
(H~/H~~ihJ/2}2~F/4000~*~
H1,H2=antenna height
in
feet above a smooth sphere
F=
frequency in megahertz
K- (effective earth radius)/(true earth radius)
Ho= first Fresnel zone radius=
IW1.
Z*)/(Zl
+Z2)Jlh
tion. The use of two antennas at different heights
provides a means of compensating
to
a certain extent for
changes in electrical-path differences between direct
and reflected rays (space-diversity reception).
The antenna spacing at the receiver should be approx-
imately such as to give a
AI2
variation between geo-
metrical-path differences in the two cases. An approxi-
mate value of the spacing is given by
Ad14ha,
when all
quantities are in the same units.
The spacing in feet for
d
in miles,
ha,
in feet,
A
in
centimeters, and
f
in megahertz is given by
spacing
=
43.4Ad/ha,
=
1.3
X
lo6
dlfh,,
Example:
A
=
3
centimeters,
d
=
20
miles, and
ha,
=
50
feet; therefore spacing
=
52
feet.
Variation
of
Field Strength
With Distance
Fig.
19
shows the variation of resultant field strength
with distance and frequency; this effect is due to
interference between the free-space wave and the
ground-reflected wave as these two components arrive
in or out
of
phase.
To compute the field accurately under these condi-
tions, it is necessary to calculate the two components
separately and to add them in the correct phase relation-
ship. The phase and amplitude of the reflected ray are
determined by the geometry of the path and the change
in magnitude and phase at ground reflection.
For
horizontally polarized waves, the reflection coefficient
can be taken as approximately
1,
and the phase shift at
ELECTROMAGNETIC-WAVE PROPAGATION
33-1
9
Fig.
19.
Variation of resultant field
strength with distance and frequency.
An-
tenna heights: 1000 feet,
30
feet;
power:
1
kilowatt;
ground constants:
LT
=
5
X
emu,
e
=
15
esu;
polarization: horizontal.
reflection as
180
degrees, for nearly all types of ground
and angles of incidence. For vertically polarized waves,
the reflection coefficient and phase shift vary apprecia-
bly with the ground constants and angle of incidence.
(See Fig. 24 of Chapter 32.)
Measured field strengths usually show large devia-
tions from point to point because of reflections from
ground irregularities, buildings, trees, etc.
For
transmission paths of the order of 30 miles and
for frequencies
up
to about
6000
megahertz, good
engineering practice should allow for possible increases
of signal strength of
f10
decibels with respect to
free-space propagation and should allow a fading mar-
gin depending
on
the degree of reliability desired
in
accordance with the following:
10 decibels-90 percent
20
decibels-99 percent
30
decibels-99.9 percent
40
decibels-99.99 percent
Fading and
Diversity*
Line-of-sight propagation at ultrahigh frequencies is
affected both by signal-strength variation due to multi-
path transmission and by bending of the beam due to
abnormal variation of refractive index with height in the
lower atmosphere.
At frequencies below about
8000
megahertz, and
on
paths having adequate clearance, the fading
on
line-of-
sight paths is due to multipath transmission. Multipath
fading may be divided into two main types; the first is
relatively rapid and is caused by interference between
two or more rays arriving by slightly different paths; this
is known as
atmospheric-multipath.
The second type of
fading is less rapid and is due to interference between
direct and reflected rays; this is referred to as
reflection-
multipath.
In general, the number of fades per unit time
due to atmospheric-multipath increases with path
length; however, the duration of a fade of a given depth
tends to decrease with increasing path length. Fig.
20
shows the typical fading characteristics of a terrestrial
line-of-sight path. See Chapter 27 for earth-to-space
paths.
Either frequency or space diversity may be used to
reduce the amplitude of multipath fading.
In
the case of
atmospheric-multipath fading
on
line-of-sight paths, it
*
Bullington,
K.,
“Radio
Propagation Fundamentals.”
Bell System Technical Journal,
Vol.
36,
No.
3,
1957;
pp.
593-626.
Pearson,
K.
W.,
“Method
for
the
Prediction
of
the
Fading Performance
of a
Multisection Microwave Link.”
Proceedings
of
the
ZEE,
Vol.
112,
No.
7, July 1965; pp.
1291-1300.
CCIR
XVth
Plenary
Assembly,
Geneva,
1982,
Vol.
V,
Report
338-4; pp. 279-314.
Transmission
Loss
Predictions for Tropospheric
Commu-
nication Circuits.
National
Bureau
of
Standards
Technical
Note
No. 101.