A simple procedure is described for determining the excitation coefficients of an array feed which compensates for the surface distortion of a reflector antenna to improve the radiation pattern in such a way as to approximate the performance of the undistorted antenna. A computer simulation for a practical feed array is presented as an example of compensation for the distortion of an actual antenna

Bailey, M. C.

Cockrell, C. R.

Staton, L. D.

English

NASA Technical Reports Server

NASA Technical Memorandum 100652 
Electronic Compensation For 
Reflector Surface Distortion To 
Improve Radiation Pattern 
Characteristics Of Antennas 
M. C. Bailey, C. R. Cockrell, and Lo D. Staton 
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A b l E L b A S  (NASA. Lanqley  6escarcb Center) Unclas 
February 1989 
NASA 
National Aeronautics and 
Space Ad mi n is t ra t ion 
Langley Research Center 
Hampton, Virginia 23665-5225 
https://ntrs.nasa.gov/search.jsp?R=19890012618 2020-03-20T02:19:57+00:00Z
ELECTRONIC COMPENSATION FOR REFLECTOR SURFACE DISTORTION 
TO IMPROVE RADIATION PATTERN CHARACTERISTICS O F  ANTENNAS 
Abst rac t  
A simple procedure is described for determining the excitation coefficients of an 
a r r a y  feed which compensates for the surface distortion of a reflector antenna to 
improve the radiation pattern in such a way a s  to approximate the performance of the 
d i s t o r t e d  antenna. A computer simulation for a practical feed array is presented 
as an example of compensation for the distortion of an actual antenna. 
, 
Introduction 
Large ref lector antennas are commonly used for high-gain and low-sidelobe 
applications. However, distortions in the reflector surface due to thermal gradients, 
g r a d  ty loads, manufacturing tolerances,  etc. ,  can s ignif icant ly  degrade the 
performance of the antenna. Large deployable reflectors for space applications may 
also be distorted due to errors in the deployment mechanism. Mechanical adjustment 
of the reflector surface can improve the performance, provided the proper adjustment 
mechanisms have been designed into the antenna. An array feed with adjustment 
capability of the amplitude and phase excitations of the array elements can provide 
an alternative (or supplement) to the mechanical meens of improving the radiation 
performance of a d i s tor ted  re f lec tor  antenna. Improving the performance of a 
distorted reflector antenna by adjustment of the array feed excitation is sometimes 
referred to a s  "electronic compensation". The purpose of this paper is to describe a 
simple method of determining the amplitude and phase excitations of an array feed to 
compensate for the surface distortion of a reflector antenna in order to approximate 
the performance of the "smooth" reflector. 
2 
Feed Array Excaitatlon 
The problem i s  to determine the amplitudes of N number of individual functions 
superimposed to approximate a desired fmction of x and y at discrete points in the 
x,y plane. In the present application, the function to be approximated is the complex 
field distribution in the aperture of a reflector antenna and the individual functions 
are the r e f l e c t o r  a p e r t u r e  f ie ld  d is t r ibu t ions  f rom individual radiators of an 
N-element array feed. Actually, the far-field of the reflector antenna in discrete 
angular directions could be taken as the desired function to be approximated and the 
far-field of the reflector due to each element of the array feed would then become 
the individual functions. The procedure is the same for both applications. 
The d e s i r e d  a p e r t u r e  f ie ld  in  the x,y plane is represented by the complex 
function, F(x,y), and the a p e r t u r e  f ie ld  due t o  the  r t th  array feed element is 
represented by the function, fn(x,y), with complex amplitude, An. The superposition 
of a l l  a p e r t u r e  f i e lds  due to the array feed elements is equated to the desired 
aperture fjeld a t  discrete points (xi,yi) in the aperture plane as 
N 
where I i s  the total number of discrete 
Fo(i,YJ i=l,2,3 ,..., I (1) 
points in the aperture plane where the desired 
field is to be approximated. The complex amplitudes, An, are determined such that 
the desired aperture field i s  approximated in a least-squared sense by the N-element 
array feed. This is accomplished by defining the quantity, G, as 
and minimizing G with respect to Am, for m=1,2,3,  ..., N 
whlch results in N equations with N unknowns. 
3 
By making tfx following definitions: 
I 
A2 I:: *N 
I 
s = c fm(Xi,Yi) f n ( X p Y J  
mn i=i 
the problem can be expressed in convenient matrix notation as 
1 
'2 * * '  '2N I 
. .  . .  ' I  . .  
'N2 . a *  'NN J 
The complex values, An, for the excitation coefficients of the array feed elements 
a re  then determined from equation (6) by matrix inversion. 
The feed array excitation determined by this method neither maximizes the peak 
gain of the r e f l ec to r  antenna nor  minimlzes  the sidelobes of the antenna, but 
approximates  the  des i red  ape r tu re  f ie ld  distribution and therefore the desired 
radiation pattern in all angular space wlthin the limitations of the N-element array 
feed. If the excitation coefficients were determined by applying the procedure to tfle 
far-f ie ld  of the r e f l ec to r  antenna, as mentioned earlier, then the approximation 
would apply to the radiation pattern in the specified discrete angular directions, 
(t3i,+i), with no restrictions on the radiation pattern in other directions. However, 
specifying closely spaced within some far-field angular region of interest 
might be useful in some applications. Applying the procedure to either the aperture 
f ie ld  o r  the far-f ie ld  may also be useful i n  determining the initial excitation 
coef f ic ien ts  in an  i t e r a t ive  optimization scheme and thus reduce the number of' 
i t e ra t ions  requlred.  
4 
Example  
The 15-meter hoop/column mesh deployable antenna is used to illustrate through 
computer s imula t ions  tha t  adjustment  of array feed excitations can achieve an 
appreciable improvement in the radiation pattern characteristics by compensating 
f o r  the su r face  distortion. The surface distortion used in the simulation is the 
deviation from a paraboloid as measured by a metric camera while the antenna was 
deployed in the Martin-Marietta Near-Field Facility In July 1985. 
The a r r a y  feed used In the simulation is a triangular-grid array of multi-mode 
conical horns,  which w a s  or ig ina l ly  designed a s  a reconfigurable feed for a 
commer ica l  s a t e l i t e  antenna. Th i s  array feed was selected for the simulation 
because it possessed the capability. of computer controlled adjustment of amplitude 
and phase f o r  16 e l emen t s  and w a s  being made available for testing with the 
hoop/column antenna. The calculat ions were performed to determine whether 
suf f ic ien t  performance improvement could be achieved in order to justify an 
experimental test in the near-field facility. The calculations were performed with 
7, 19, and 37 elements in a hexagonal array with the possibility of expanding the 
original array to include the additional elements if necessary. Subsequently, due to 
de te r iora t ion ,  the beamforming network for the original array was found to be 
unusable and the experimental tests were cancelled. However, the results of tfle 
computer  s imula t ions  do show significant improvement in performance. The 
calculations were performed a t  6.4 CHz with 3.5 inch center-to-center spacing of 
the a r r a y  e l emen t s  using the measured radiation pattern of a single horn as the 
array element illumination of the distorted surface to calculate the geometric-optics 
aperture fields of the reflector. 
The "desired" aperture field was obtained by illuminating the llsmwtfi' reflector 
with a 7-element cluster array with uniform phase for al l  element excitations and 
- 14dB amplitude excitation for the outer 6-element ring. This 7-element cluster 
excitation was selected because it  produces a secondary radiation pattern with -28dB 
maximum sidelobes f o r  one quadrant of the  hoop/column antenna. The initial 
7-element feed cluster configuration is shown in figure I with the array excitations 
indicated. The aperture distribution for  the "smooth" reflector Is shown in  figure 2, 
5 
and the radiation pattern is shown in figure 3. The aperture distribution (nmpiitude 
and phase) in figure 2 i s  the "desired" function to be approximated by the array feed 
when compensating for the distortion of the reflector surface. 
The measured su r face  distortion i s  plotted in figure 4 with the height of the 
distortion exaggerated so as to be visible on the plot. The r m s  of the distortion is 
0.061 inches, with extreme values of -0.598 inch end t0.210 inch. I t  should be 
noted that the surface distortion used in this paper is obtained from measurements 
of targets located at  the surface "tie-points" only. The actual mesh surface between 
the tie-points exhibits a "pillowing" effect relative to the paraboloidal surface and, 
due to the periodic nature of these "pillows", distinct wide-angle sidelobes will be 
produced in the secondary radiation pattern. However, the main beam and close-in 
sidelobe degradation a re  dictated by the distortion shown In figure 4; therefore, this 
distortion i s  used for the compensation calculations. 
Geometric optics is used to calculate the apertures fields of the reflector and, for 
small surface distortions, the primary effect on the aperture fields will be a change 
in the phase distribution in a direct relationship to the surface distortion, due to the 
change in ray path length. The aperture fields for the distorted reflector a r e  shown 
in figure 5 and the corresponding secondary radiation pattern is sfmwn in figure 6. 
Evaluating the excitetion coefficients for the 7-element array to compensate for the 
su r face  distortion yields an insignificant improvement in the radiation pattern and 
indicates that more array elements a re  required. 
Surface compensation calculations were performed with a 19-element hexagonal 
cluster of horns a s  shown in figure 7 with the excitation coefficients indicated. The 
aperture field from the distorted reflector with this 19-element feed is 'plotted in 
figure 8 and the secondary radiation pattern i s  shown in figure 9. An appreciable 
improvement in the main beam and close-in sidelobes was obtained by using this 
1 9-element array feed. 
A larger hexagonal array of 37-elements was also used to further improve the 
radiation pattern. The excitation coefficients of this 37-element array are shown in 
figure 10 and the aperture field distribution is plotted in figure 11. The secondary 
radiation pattern in figure 12 approach the lkmooth" reflector pattern performance. 
6 
Conclusion 
It has been shown that the radiation pattern performance of a distorted reflector 
antenna can be improved significantly by using an array feed. Using a least-squared 
procedure to determine the array feed element excitations which will approximate the 
smooth r e f l ec to r  aperture field can produce a secondary radiation pattern which 
approaches the performance of the d i s t o r t e d  antenna without mechanical adjustment 
of the distorted surface. This compensation procedure may also serve to "Fine-tune" 
the performance of a reflector antenna h l c h  has mechanical adjustment capability. 
7 
-14.0 
(0.0) 
. dB 
(deg) , ! 
Figure 1. 7-element ar ray  geometry and excitation coefficients. 
I 
8 
( Amp1 i tude 
F i g u r e  2. Smooth r e f l e c t o r  a p e r t u r e  d i s t r i b u t i o n  
w i t h  7-element c l u s t e r  a r r a y  feed .  
9 
2. 
1. 
8 
-1 
-2. 
0 (degrees) 
F i g u r e  3.  R a d i a t i o n  p a t t e r n  contours  f o r  smooth r e f l e c t o r  
w i t h  7-element c l u s t e r  a r r a y  f e e d .  
10 
F i g u r e  4.  Measured d e v i a t i o n  from p a r a b o l o i d a l  s u r f a c e  
f o r  one quadrant  of hoop/column r e f l e c t o r  antenna.  
Amplitude 
F i g u r e  5. D i s t o r t e d  r e f l e c t o r  a p e r t u r e  d i s t r i b u t i o n  
w i t h  7-element c l u s t e r  a r ray  feed .  
12 
n IvI I I 
8 (degrees) 
I 1 1 1 1 1  
B6.0  89.0 90. 0 91.0 92.0 
F i g u r e  6. R a d i a t i o n  p a t t e r n  contours  f o r  d i s t o r t e d  r e f l e c t o r  
w i t h  7-element c l u s t e r  a r r a y  f e a d .  
13 
-24. I 0 (-65) 
-23.0 
(-7 1) 
-25.5 
(- 154) 
-20.7 
(-1 I I )  
dB 
(deg) 
0 
F i g u r e  7. 19-element a r r a y  geometry and e x c i t a t i o n  c o e f f i c i e n t s  
fo r  sur face  d i s t o r t i o n  compensation. 
F i g u r e  8. D i s t o r t e d  r e f l e c t o r  a p e r t u r e  d i s t r i b u t i o n  
a f t e r  s u r f a c e  d i s t o r t i o n  compensation 
w i t h  19-element a r r a y  f e e d .  
F i g u r e  9. R a d i a t i o n  p a t t e r n  contours  f o r  d i s t o r t e d  r e f l e c t o r  
a f t e r  s u r f a c e  d i s t o r t i o n  compensation 
w i t h  19-element a r r a y  f e e d .  
16 
F i g u r e  10. 37-element a r r a y  geometry and e x c i t a t i o n  c o e f f i c i e n t s  
f o r  sur face  d i s t o r t i o n  compensation. 
17 
F i g u r e  11 .  D i s t o r t e d  r e f l e c t o r  a p e r t u r e  d i s t r i b u t i o n  
a f t e r  sur face d i s t o r t i o n  compensation 
w i t h  37-element array  feed .  
F i g u r e  12. R a d i a t i o n  p a t t e r n  contours  f o r  d i s t o r t e d  r e f l e c t o r  . 
a f t e r  s u r f a c e  d i s t o r t i o n  compensation 
w i t h  37-element a r r a y  f e e d .  
19 
Report Documentation Page 
1. Report No. 2. Government Accession No. 
I 
4. Title and Subtitle- 
19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 
Unc lass i f i ed  Uncl ass i  f i ed 20 
E lec t ron i c  Compensation f o r  Re f lec to r  Surface 
D i s t o r t i o n  t o  Improve Rad ia t ion  Pa t te rn  Charac te r i s t i cs  
o f  Antennas 
22. Price 
A03 
1. Author(s) 
M. C. Ba i ley ,  C. R. Cockre l l ,  and L. D .  Staton 
9. Performing Organization Name and Address 
NASA Langley Research Center 
Hampton, VA 23665-5225 
12. Sponsoring Agency Name and Address 
Nat ional  Aeronaut ics and Space Admin is t ra t ion  
Washington, DC 20546-0001 
15. Supplementary Notes 
3. Recipient's Catalog No. 
- 
5. Report Date 
February 1989 
6. Performing Organization Code 
8. Performing Organization Report No. 
10. Work Unit No. 
506-44-21-03 
11. Contract or Grant No. 
13. Type of Report and Period Covered 
Technical Memorandum 
14. Sponsoring Agency Code 
16. Abstract 
A simple procedure i s  descr ibed f o r  determin ing the  e x c i t a t i o n  c o e f f i c i e n t s  o f  an 
a r ray  feed which compensates f o r  t he  sur face d i s t o r t i o n  o f  a r e f l e c t o r  antenna t o  
improve the  r a d i a t i o n  p a t t e r n  i n  such a way as t o  approximate the  performance o f  the  
und is to r ted  antenna. A computer s imu la t i on  f o r  a p r a c t i c a l  feed a r ray  i s  presented 
as an examp e o f  compensation f o r  the  d i s t o r t i o n  o f  an ac tua l  antenna. 
17. Key Words (Suggested by Authork)) 
antenna 
r e f  l e c t o r  
r a d i a t i o n  
18. Distribution Statement 
Unc lass i f i ed  - Un l im i ted  
Subject  Category 32 
1 


Electronic compensation for reflector surface distortion to improve radiation pattern characteristics of antennas

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