The spherical reflector at the Arecibo Observatory (AO) offers great advantages for the design of simple and inexpensive high performance steerable antennas at VHF. Light and small feeds have the added benefit that they can be quickly installed in the Arecibo platform. It is important to evaluate the performance of any given feed including the effects of the spherical reflector. The optimization is emphasized of two parameters, namely, the distance below the focal point of the reflector and the beam width of a point feed. For the design of the feed at 46.8 MHz at the AO there were other requirements independent of MST (mesosphere stratosphere troposphere) work. The design of the primary array is discussed along with its performance with the AO spherical reflector

Hagen, J. B.

Ierkic, H. M.

Rottger, J.

Zimmerman, R. K.

English

NASA Technical Reports Server

420 /_
/
7.6.3
N87-10510
METHOD TO DETERMINE THE OPTIMAL PARA}_TERS OF THE
ARECIBE 46.8-MHz ANTENNA SYSTEM
INTRODUCTION
H. M. lerkic, J. Rottger, J. B. Hagen, and R. K. Zimmerman
Areclbo Observatory
P.O. Box 995 _ 6+ _)kArecibo, Puerto Rico
J
The spherical reflector at the Arecibo Observatory (AO) offers great
advantages for the design of simple and inexpensive high performance steerable
antennas at VHF. Light and small feeds have the added benefit that they can be
quickly installed in the Arecibo platform causing almost no interruption to
other experiments that may be in progress. Acceptable (primary) antennas are,
for example, dipoles with reflectors, Yagis, loops etc. It is important to
evaluate the performance of any given feed including the effects of the
spherical reflector. In this paper, we will emphasize the optimization of two
parameters, namely, the distance below the focal point of the reflector and the
beam width of a 'point' feed. For the actual design of the feed at 46.8 MHz at
the AO we had other requirements (e.g., best performance possible over a i0 MHz
bandwidth around the carrier frequency for application in ionospheric
modification experiments) independent of MST work. Details on the antenna
mounting constraints and a comprehensive description of the new VHF radar can
be found in ROTTGER et al. (1986).
DESIGN OF (PRIMARY) ARRAY
Numerical simulation codes were used to facilitate the exhaustive
evaluation of the characteristics of the primary feeds, thus facilitating their
design. The Numerical Electromagnetic Code (BURKE AND POGIO, 1981) obtains the
solution of integral field equations that describe the currents flowing over
wires and surfaces that the user has specified. The description of the program
and the limitations that the approximations, impliclt in the algorithms, create
can be found in the reference above.
We modelled several types of feeds and decided on a simple dipole with a
reflector. To minimize spillover out of the surface of the reflector by the
illuminating feed after installation (for large zenith angles) and also to
s_newhat improve against clutter from the horizon, we decided to form an array
of two feeds side by side separated by about half a wavelength. We call this
array a twin Yagi feed. The numerical simulation provided us with the
radiation pattern in the E and H planes and the impedance. The dimensions
deemed appropriate are 3.8 m for the reflectors, 3.1 m for the driven elements
with a separation of 1.5 m and with a radius for all the elements of 1.33 cm.
The two antennas composing the array are separated by 3.2 m and fed with a
parallel transmission of 100 _impedance. The radar system requires 50 _ for
optimum matching.
https://ntrs.nasa.gov/search.jsp?R=19870001077 2020-03-23T14:41:10+00:00Z
421
We summarize the performance of the array in the following table.
Table 1
F Gain Beam width Impedance
(MHz) (DB) E H (_)
42 8.I 75.2 53.1 54- i37
45 7.8 75.7 57.6 45 - i19
47 7.6 77.7 61.3 43 - i4
49 7.5 79.2 62.0 44 + ill
52 7.4 79.3 61.0 56 + i38
The actual enviror,,nent where the array is installed in the platform
includes the AO 430-MHz line feed. Care was taken to locate the array far
enough (out of the Caustic region of influence of the line feed) to avoid
interference (ROTTGER et al., 1986). Almost no perturbation of the array
performance was found theoretically by modelling the AO feed with a set of
wires.
PERFORMANCE OF (PRIMARY) ARRAY WITH THE AO SPHERICAL REFLECTOR
The problem of finding the gain of an antenna in front of a spherical
reflector has been treated by many workers; we follow closely the development
by CONDON (1969). To simplify the algebra, we assume that the (primary) array
main lobe is rotatiormlly symmetric and thus can be characterized by one angle
only. This approximation simplifies the algebra and is enough for our
purposes.
The far field due to the electric field distribution over an aperture can
be written as
E(_) = I/_ 2 I E(x,y) exp (i2_xsin_) (i)
dx dy
aperture
where
E(x,y) = electric field on the plane immediately above the reflector
s urf ace.
X = path length difference
= zenith angle
We rewrite this equation in terms of polar coordinates (Figure 1) to take
advantage of the rotational symmetry of the radiation pattern,
rm
i; I cost__ j (2_r 2_ rdrl2 (2)
O
rm
o
.2_r 2_e 2
E(r) Jo(--_ sin_) sin-_- rdr I
422
B
i
R
T-,
R= 265m
rm = 152 m
a R
PP
P cl
Figure i. Geometry involved in the
computation of the antenrm gain
(adapted from CONDON, 1969).
where
e (r) = path length error of array reflected from a sphere.
rm = radius of the aperture of the reflecting surface.
Equation (2) can be readily evaluated once the primary antenna pattern is
specified since the rest of the quantities depend only on the geometry.
Following CONDON (1969), we have assumed that the primary pattern can be fitted
with a cosine square type of f_netion. This simplification makes it possible
to characterize an antenna by its beam width alone.
Using this procedure, we have computed the values of antenna aperture
shown in Table 2 for several beam widths and distances z to the paraxial sur-
face. Note from this table that for the array previously discussed with an
average beam width of about 70 °, the maximum aperture is 43000 m2 when
z = 9.3 m. The radiation diagram corresponding to this antenna is shown in
Figure 2. The half-power beam width (found from the figure) is 1.6 ° with a
sidelobe 2.6 ° off axis suppressed by about 17 dB. For comparison, the figure
also shows the diagram for the array in front of a parabolic reflector.
CONCLUSIONS AND FUTURE DEV_LOP_NTS
A straightforward procedure has been proposed to design and install simple
antennas in the AO platform facing the spherical reflector.
Further work will include relaxation of some of the constraints used in
this note (e.g., rotational symmetry, cosine square primary pattern, etc.). We
are also planning to design antennas that will allow us to monitor the same
scattering volume at two frequencies (i.e., concentrical to the 430-MHz line
feed).
423
g
N
F=
Z*HPBM
0.5
0.8
1.0
1.3
1.5
1.8
2.0
2.3
2.3
2.8
3.0
3.3
3.5
3.8
4.0
4.3
4.5
4.8
$.0
5.3
3.5
5.8
6.0
6.3
6.5
6.8
7.0
1.3
7.5
7.8
8.0
8.3
8.3
8.8
9.0
9.3
9.5
9.8
10.0
10.3
10.5
10.8
11.0
11.3
11.3
11.8
12.0
12.3
12.5
12.8
13.0
13.3
13.5
13.8
14.0
Table 2
Antenna aperture (x 10-4m 2)
Beam width (degrees)
47.0 HHZ
30.0 55.00 60.00 65.00 70.00 75.00 80.00 25.00 90.00 95.00100.0q
2.60 2.53 2.21 1.96 1.75 1.57 1.41 1.28 1.17 1.07 0.98
2.64 2.60 2.29 2.03 1.80 1.62 1.45 1.32 1.20 1.10 1.01
2.68 2.67 2.37 2.09 1.86 1.67 1.SC 1.36 1,23 1.13 1.04
2.71 2.73 2.45 2.16 1.93 1.72 1.55 1.40 1.27 1.16 1.07
2.75 2.80 2.53 2.24 1.99 1.78 1.60 1.45 1.32 1.20 1.10
2.78 2.86 2.61 2.31 2.06 1.84 1.66 1.50 1.36 1.25 1.15
2.81 2.93 2.70 2.39 2.13 1.91 1.72 1.$6 1.42 1.29 1.19
2.83 2.99 2.78 2.47 2.21 1.98 1,78 1.62 1.47 1.38 1.24
2.86 3.04 2.86 2.55 2.28 2.05 1.85 1.68 1.33 1.40 1.29
2.88 3.10 2.95 2.64 2.36 2.13 1.93 1.75 1.60 1.47 1.35
2.90 3.15 3.03 2.72 2.45 2.21 2.00 1.82 1.67 1.53 1.41
2.91 3.20 3.11 2.81 2.53 2.29 2.08 1.90 1.74 1.61 1.48
2.93 3.24 3.19 2.90 2.62 2.38 2.17 1.99 1.82 1.68 1.56
2.93 3.28 3.27 2.98 2.71 2.47 2.26 2.07 1.91 1.76 1.64
2.94 3.32 3.34 3.07 2.81 2.37 2.36 2.17 2.00 1.85 1.72
2.95 3.35 3.41 3.16 2.90 2.67 2.43 2.26 2.09 1.94 1.81
2.95 3.38 3.48 3.25 3.00 2.77 2.56 2.37 2.19 2.04 1.90
2.94 3.40 3.54 3.33 3.10 2.87 2.66 2.47 2.30 2.14 2.00
2.94 3.42 3.60 3.42 3.19 2.97 2.77 2.58 2.40 2.24 2.10
2.93 3.44 ].66 3.50 3.29 3.08 2.88 2.69 2.51 2.35 2.21
2.92 3.45 3.70 3.38 3.39 3.19 2.99 2,80 2.63 2.46 2.31
2.91 3.45 3.75 3.66 3.48 3.29 3.10 2.92 2.74 2.58 2.43
2,89 3.45 3.79 ].73 3.37 3.40 3.21 ].03 2.86 2.69 2.54
2.87 3.45 3.82 3.80 3,66 3.50 3.33 3.15 2.98 2.81 2.66
2.83 3.44 3.84 3.86 3.75 3.60 3.44 3.27 3.09 2.93 2.77
2.83 3.43 3.86 3.92 3.84 3.70 3.55 3.38 3.21 3.05 2.89
2.80 3.41 3.88 3.97 3.92 3.80 3.66 3.30 3.33 3.16 3.00
2.77 3.38 3.88 4.02 3.99 3.89 3.76 3.61 3.44 3.28 3.12
2.74 3.36 3.88 4.06 4.06 3.98 3.86 3.71 3.56 3.39 3.23
2.71 3.32 3.87 4.09 4.12 4.06 3.Q6 3.82 3.66 3.50 3.34
2.68 3.29 3.85 4.12 4.18 4.14 4.05 3.92 3.77 3.61 3.45
2.64 3.23 3.83 4.13 4.22 4.21 4.13 4.01 ].86 3.71 3.35
2.60 3.20 3.80 4.14 4.26 4.27 4.21 4.10 3.96 3.81 3.63
2.56 3.15 3.77 4.14 4.29 4.32 4.27 4.17 4.04 3.89 3.74
2.51 3.10 3.72 4.13 4.32 4.37 4.33 4.24 4.12 3.98 3.82
2,47 3.05 3.67 4.12 4.33 4.40 4.39 4.31 4.19 4.05 3.90
2.42 2.99 3.61 4.09 4.33 4.43 4.43 4.36 4.25 4.11 3.97
2.38 2.93 3.55 4.05 4.32 4.44 4.46 4.40 4.30 4.17 4.02
2.33 2.86 3.48 4.01 4.31 4.43 4.48 4.43 4.34 4.21 4.07
2.28 2.79 3.41 3.95 4.28 4.44 4.48 4.45 4.36 4.25 4.11
2.23 2.73 3.33 3.89 4.24 4.42 4.48 4.46 4.38 4.27 4.14
2.18 2.65 3.24 3.82 4.19 4.39 4.46 4.45 4.38 4.28 4.15
2.13 2.58 3.15 3.74 4.13 4.35 4.44 4.44 4.38 4.28 4.16
2.07 2.50 3.06 3.65 4.06 4.29 4.40 4.41 4.36 4.27 4.15
2.02 2.43 2.96 3.56 3.98 4.23 4.34 4.36 4.32 4.24 4.13
1.97 2.35 2.86 3.45 3.89 4.15 4.25 4.31 4.28 4.20 4.10
1.91 2.27 2.76 3.34 3.79 4.07 4.20 4.24 4.22 4.15 4.06
1.86 2.19 2.66 3.23 3.69 3.97 4.12 4.17 4.15 4.09 4.00
1.80 2.11 2.55 3.11 3.57 3.86 4.02 4.08 4.07 4.02 3.93
1.75 2.03 2.44 2.98 3.45 3.74 3.91 3.98 3.98 3.03 3.85
1.69 1.95 2.33 2.85 3.32 3.62 3.79 3.87 3.87 3.84 3.77
1.64 1.87 2.22 2.72 3.18 3.48 3.66 ].78 3.76 3.73 3.67
1.39 1.79 2.11 2.59 3.04 3.34 3.53 3.62 3.64 3.62 3.56
1.33 1.72 2,00 2.45 2.89 3.20 3.35 3.48 3.51 3.49 3.44
1.48 1.64 1.89 2.31 2.74 3.04 3.23 3.33 3.37 3.36 3.32
424
45.
35.
on
n
w
25.
>-
15.
>
H
L) 5.
LU
rr
I--I
r-_ -5.
-15.
F ,. 46. 8 P4_Z
Z = 9.30 M
HPBW (P) = 70. O0 DEGREES
RPERTURE = O. 434E÷05 MmM
DIRMETER = 235.0 M
HPBW (S] = 95. t MINUTES
\_-/ \
\
,/ \
li rw
!1 /11
I, I
.I
;i i
11 i
f td
!
O. 30. 60. 90. 120.150.180.210.
ZENITH (MINUTES)
Figure 2. Radiation pattern for AO array in
front of spherical reflector (solid line)
and parabolic reflector (dashed line).
Primary beam width is 70 ° and distance =
from paraxial surface 9.3 meters.
REFER_q CE S
Burke, G. J., and A. J. Pogio (1981), Numerical electromagnetic code, Lawrence
Livermore Laboratory, Technical Document 116, 1-3.
Condon, J. J. (1969), Theory of point fed spherical reflectors, Cornell-Sydney
University Astronomy Center, CSUAC 182.
Rottger, J., H. H. Ierkic, R. K. Zimmerman, and J. B. Hagen (1986), Investiga-
tions of the lower and middle atmosphere at the Arecibo Observatory and a
description of the new VHF radar project, this volume.


Method to determine the optimal parameters of the Arecibo 46.8-MHz antenna system

Ierkic, H.

Röttger, J.

Hagen, J.

Zimmerman, R.

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Method to determine the optimal parameters of the Arecibo 46.8 MHz antenna system

Method to determine the optimal parameters of the Arecibo 46.8-MHz antenna system

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