Idealized antenna patterns for communication satellite interference studie

Noble, J. L.

Rice, P. L.

Thompson, W. I., III

English

NASA Technical Reports Server

E r / ~ s ,  R- 6 f 
'Idealized Antenna Pat terns  for use in Communication- 
Sat ell  i te Inter f e r enc e S tudie s 
I?. L. Rice, W.  I. Thompson, I11 and J. L. Noble 
Institute for Environmental Research 
Envir onomental Sc ienc e S ervic e s Rdminis tr a t ion 
Boulder, Colorado 
Abstract 
Antenna patterns to represent earth station antennas of cornmunica- 
I .  I , * . ,  
L l u I L - b d ~ l : l l l ~ C  ~ , y a L t : l ~ l a  c~~ t: Jttl'ivecl 1'1 C J ~ L ~  ~ L v C L ~ I ~ L ' U ~ ~ :  pciblisllcci &~i.a. 
patterns include an analytic expression describing the main beam and 
f i r s t  side 1-obe. 
smoothed rrlean power levels of tlicse side lobes. 
Tilt: 
Higher order  side 1Gbes a r e  spccificd in terms of 
Key Words I 
Aiitenna, c omniunic ation- satellite earth station, int erf e r  enc e 
Ic!e ali z e d r adia t i  on pat t c r n . 
I I  N67 13020 a 8 I (ACCESSION 7 7 ~ 1  ITHRU) e / 
https://ntrs.nasa.gov/search.jsp?R=19670003691 2020-03-16T17:21:12+00:00Z
ii. 
Table of Contents 
TITLE PAGE 
ABS TR AC T 
TABLE OF CONTENTS 
INTRODUCTION 
ANTENNA GAIN CHARACTERISTICS 
NORMALIZING PROCEDURE 
RESULTS 
CONCLUSION 
REFERENCES 
LIST OF CAPTIONS 
LIST OF TABLES 
i 
i 
ii 
1 
1 
5 
5 
6 
9 
11 
12 
0 
. 
1. 
Introduction 
Recent work has shown that scattering from precipitation may be an 
important factor in determining the probability of interference between 
an earth station and a te r res t r ia l  radio-relay station operating on the 
same frequency [l, 2 3. The authors have discussed a procedure for  
calculating rain-scattered radio wave power levels between such stations 
[ 3 3. 
polarization characterist ics of each antenna in any direction from which 
a signal may be expected. 
polarization gain patterns for comparing various interference models 
when no particular antenna characterist ics a r e  specified. 
These calculations require a knowledge of the power gain and 
This art icle presents idealized principal 
Antenna Gain Characterist ics 
Figure 1 shows a set  of polar coordinates, $ and e , with$ the angle 
between the axis of the main beam of an antenna and any given direction 
and e the azimuth angle measured in the xy plane from the positive x axis. 
The idealized antenna pattern is assumed to have axial symmetry about 
the main beam axis and hence the gain is independent of 8 and may be 
expressed a s  a function of 45 alone. 
on antenna diameters,  D, and operating wavelengths, x , i t  turns out 
that $is not the most convenient coordinate in which to specify the gain. 
Since antenna gains a r e  dependent . 
* A  more  natural  parameter  is derived f r o m 6  by the relation 
(1) 
TfD 
x sin +. - u --- 
This parameter  is more  useful because the entire antenna pattern can 
now be expressed in terms of one variable and the normalizing procedure, 
discussed below, is simplified considerably. 
The idealized antenna pattern has  a main beam and first side lobe 
described by 
2. 
2 
'1 =(+) (sin u/u> 2 . 
A graph of this function is shown in figure 2 which was taken from Silver 
[ 4 1. 
ing for the first major  side lobe in an analytic way. 
A s  the curve indicates, the antenna pattern w i l l  be  capable of allow- 
The function used to express the higher order  side lobes was deter- 
mined from studying graphs of smoothed mean power levels of currently 
operating ear th  station antennas given in an International Radio Consult- 
ative Committee (CCIR) document [5 ]. 
relating the gain versus  l o g $ .  
f rom ear th  stations located a t  Andover, Maine [6, 71, Goldstone, Calif.. 
ornia [ 8  ] 
Village, Nova Scotia [11 I ,  Raisting, Germany [12), Wallops Island, Va., 
and the West Ford antennas a t  Camp Parks,  California and Westford, 
Massachusetts [13 3. 
This document presents curves 
Data for these curves were obtained 
Goonhilly Downs, England [ 9  I., Holnidel, New Jersey  [ lo  1 ,  Mill 
Values of gain from the CCIR document were replotted as a function 
of log u. 
accepted as a good f i t  to the data: 
These curves were studied and the following function w a s  
where . 
2 K = u  3/4 (sin u > ( r D / h  l2 . 
0 0 
.The point u 
below and corresponds to the value of u where the gain g 
the gain g 
slopes of the plotted data. 
median of 2.75. The function g w a s  employed for  Q's out  to 90 . 
F r o m  90 to 180° the value of g2 at  90 w a s  employed as the gain function. 
i s  determined from the normalization procedure described 
0 
is replaced by 1 
The exponent of u in ( 3 )  w a s  determined by comparing the 
2' 
Exponents ranged from -2. 5 to -3 .  0 with a 
0 
0 
2 
0 '  
- -  . 
3. 
- .  
- -  
Fig.  1 
1 1 1 1 1 1 1 1  
0.002 - 
I I I I I  I 1  
2 
U- 
Fig. 2 
. .  . ”. ~ .. . .... . . . . . ... . .. 
I 
’ _  
1 .  
Normalizing P r o  c e dur e 
The three components of the idealized antenna pattern outlined in the 
previous section must  be combined smoothly over the entire range of +. 
The resulting antenna pattern must  then be  normalized over a l l  solid angles 
to insure that an antenna with a radiation efficiency, e, rad ia tes  tlhis fraction 
of the power, p, put into i ts  terminals. 
power )ep, radiated from the anteritla tlii.oilgh a sphere of unit radius 
centered a t  the origin must satisfy the relation 
Referring to figure 1, the total 
By integrating (6) w i t h  respect t o e  , the equation 
l g n  sin + d (p = 2. (7) 
is obtained . 
gain in (7) can be divided into three components. 
Using the gain functions given in th-e previous section 2, the 
Thus (7) becomes 
n/ 2 
( s i n +  1 d o  
-7/4 (sin ( T ~ D / x  ) s i n + )  2 d @  4- K(nD/k )-11’44e 
(8) sin + I” . .  
‘ where the gain functions a r e  expressed in t e rms  of I#I . 
fo r  any given D/h where 
The above 
equation can be solved for Q, 
0 
-1 u 
$0 = sin [.&I . ( 9 )  
Results 
Because of the complexity of the integrands in (8), the integration is 
doiie aii electr=nic cszni i tQr fnr various t r ia l  IS. Results of com- r - - - -  0 
puiaiions for --- *. ;, A.. c 5 / A  1s .re given in table 1 where the symbol eif 
e .  ? 
i t 
6. 
Table 1. 
Critical Values for Various D/X Is 
D/X 
- 
10 
20 
50 
70 
100 
200 
500 
700 
000 
U 
0 
5.7CO 
5.690 
5.666 
5.666 
5.666 
5.666 
5.666 
5.666 
5.655 
1. 824x10-1 
K 
3 
3 
4 
4 
5 
5 
6 
6 
7 
1. 104x10 
4 .545~10  
3 .036~10 
5 .951~10 
1 .214~10  
4 .858~10  
3 .036~10 
5 .951~10  
1 .250~10 
10 l o g K  
30.430 
36.575 
44.823 
47.746 
50.842 
56.865 
64.823 
67.746 
70.969 
eff 
0.7040 
0.7029 
0.7025 
0.7025 
0.7025 
0.7025 
0.7025 
0.7025 
0.7025 
G 
29.942 
35.964 
43.922 
46.844 
49.942 
55.964 
63.922 
66.844 
69.942 
c 
7. 
stands for  the aper ture  efficiency of the antenna, defined a s  the ratio of 
the radiated power for  @ < $3 
power. Using (7): 
(.the main beam) divided by the total radiated 1 
eff ( (ITD/X )2  (sin u / u ) ~  sin Od @ I  /2 I 
where 
(11 )  
-1  
@1 = sin (1.5 X/D) 
is calculated f rom (2)  with u =  3 1 ~ / 2 .  In table 1 the maximum gain, G, of 
the antenna w a s  computed from the formula 
2 
G =  10 log (ITD/X ) dB. 
Note that the angle u 
for  all D/X . 
and the aperture  efficiency a r e  nearly constant 
0 
A sample idealized antenna pattern is represented as a function of u 
and for O< @< 90  . 0 in figure 3 for  a DLA of 100 
gain is the constant -18. 5 dB determined by ( 5 ) .  
F o r  90°< @ <  180° the 
Conclusion 
We have presented an idealized pattern suitable for  use  in mutual 
interference studies with an estimated r. m. s. e r r o r  for  a "typical1' 
antenna of 3-4  dB. 
imates  these d a t a  in the f a r  side lobe region more  closely than the 
curve rccommended in the CCIR document [5 1. 
is =nrmalizerl for each D/X so  that a l l  of the power radiated f rom an  
The pattern is based on available data and approx- 
. 
The proposed pattern 
c 
8 
s 
I I I I I I 
0 0 
. 
a t % R 0 
9 
!=l 
? 
Fig. 8 
b i 
0 
References - 1 
1. 
I 
2. 
I 
I 3. 
4. 
5. 
6. 
7. 
8. 
' 9. 
9 .  
Doherty, L. H. and Stone, S. A . ,  Forward scat ter  f rom rain, Trans. 
IRE, AP-8, 414-418, (1960). 
Dennis, A. S., Precipitation scatter a s  an interference source in  
communication satellite systems, IRE Inter. Convention Record, 
P a r t  1, 145-151, (1962). 
Rice, P. L., Thompson, 11, W. I. and Ku'oLle, J. L., Calculations 
of rain-scattered power in relation to satellite communlcation sys-  
tems, Rad. Sci. /@vier*r)- 
Silver, S., Microwave antenna theory and design, McGraw-Hill, 
New York, (1949). 
CCIR (1966), Radiation diagrams of antennae a t  communication 
satellite earth stations, for use in interference studies, Doc. IV/ 
1010-E. 
Curtiss,  H. E. ,  Satellite System Interference Tests a t  Andover, 
Maine, BSTJ, 42, 2715-2739, (1963). -
Hines, H. N., T. Li and R. H. Turrin, The Electrical  Char- 
acter is t ics  of the Conical Horn-Reflector Antenna, BSTJ, 42, 1187- 
1211, ( 1963). 
_. 
Potter ,  P., The Application of the Cassegrainian Principle to 
Ground Antennas for Space Communications, IRE Trans. Space 
Electron. Telemetry, 154-158, ( 1962). 
Bray, W. J., h p r o v e d  performance of the Goonhilly Satellite- 
communication earth-station aer ia l  system, Elec. Letters, - 1, 
108-110, (1965). 
10. Crawford, A. B., Hogg, D. C. and Hunt, L. E., A Horn-Reflector 
Antenna for Space Communication, BSTJ, _. 40, 1095-1116, (1961). 
11. Foldes, P., S. Komlos, N.K. Chitre, R. Schwerdtfeger, and T. 
Szir tes ,  A Cassegrdnian feed for  wide-band satellite coinmunica- - 
tiods, RCA Rev., 26, 369-3 (1965). -
I -‘ 
References -2 
10. 
12. Schznfeld, M., The ground station at  Raisting for telecommunication 
w ith communications s a t  ellit e s , Luf tf ah r ett e chnik Raumf ahrtte chnik , 
11, 230-237, (1965). 
I_ 
13. LaYaZe, B. E’. , E.  V. B l a i s d e l - 1  and T:. J .  R i c p r d i ,  ‘ “ e s t  
7, 2 o r 6  eYlteiina aid f e e d  s y s t e m ,  F r o c .  IEEX. 52, 589-598, - 
(1364) .  
. .  
, 
Figure 1. 
Figure 2. 
Figure 3. 
List of Captions 
Geometry used in describing and normalizing the 
antenna radiation pattern. 
11. 
1 ealized 
Secondary pattern of a uniformly illuminated rectangular 
aperture (after ref. 4). 
Idealized antenna pattern for  a D/’. UI 100. 
I List of Tables 
Table 1. Critical values for various D/h Is. 


Idealized Antenna Patterns for Use in Communication-satellite Interference Studies

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