7-8
TAPERED RESISTIVE CYLINDRICAL PARABOLIC ANTENNA
Randy L. Haupt
Dept of Electrical Engineering
United States Air Force Academy 80840
Introduction
The sidelobes of a reflector antenna may be lowered by strategically loading
the reflector with lossy material. Placing lumped and tapered impedance loads a t the
edges lower the sidelobe level with a minimal reduction in gain [l]. Making the
reflector from a tapered resistive material provides more control over the sidelobe level
but produces a greater reduction in the gain. This paper examines methods of
synthesizing low sidelobe reflectors by tapering the resistivity of the reflector.
Pabolic lleflecton with Resistive Loads
The antenna is a cylindrical parabolic reflector lying in the x-y plane with a
single line feed parallel to the z-axis a t the focal point. A plane wave incident at an
angle of bo measured from the positive x-axis excites a current on the reflector surface
that flows in the z-direction. This current in turn radiates a scattered field, pact of
which is detected by the feed. The total electric field a t the feed is given by
where
(x,
, ym) are the segment midpoints
on the parabola
(9, yf) are the locations of the feed elements
1 when 0 5 bo
S(40,f) is the blockage factor = 0 otherwise
bo is the incident field angle
sibland bb2< Qo
<?T
The first term in (1) is the field scattered by the reflector surface. The second term is
the incident field which is only present when not blocked by the reflector surface. The
blockage angles for the feed are
The endpoints of the reflector are given by xend , yend
(
).
Consider a reflector that has a diameter of l O X , a focal length of 5 X (h=O.5),
90CH2776-310000-015hS1.00 01Y90 IEEE
156
iiiiil
:L
fml
will1
an electric field pattern given by
elsewhere
(3)
far field pa1,tern for this antenna with a perfectly conducting reflector surface
irr Fignre 2. Its first sidelobe is 22 dB below its main beam peak. A rather
I;irgr sidelobc occurs a t 114", because the feed radiation spills over the reflector edge a t
t 11:i point.
'I'lit.
:iojmirs
(I
The goal is to develop a resistive taper for the reflector surface t h a t will
priduce desirable sidelobe levels. If the reflector were flat, then many techniques exist
1.0 tlcrivc a current distribution on the reflector that will produce desired sidelobe
Icvcls. Taking such a current distribution and projecting it back onto the parabolic
rrllctrtor surface gives a current distribution for the parabolic reflector. This projected
cirrrent distribution does not produce the same sidelobe levels as for the flat reflector
I ) t ~ a i i s cthe rcflector is curved.
The projected current distribution on the reflector can be related to a resistive
h p c r via a physical optics equation [ 2 ] .
wlirrc
J, = projected current density on reflector surface
7 = normalized resistivity
(xm,ym)= points on the reflector surface
4' = do - 4 s
&, = angle of incident field from feed
Tlie reflector is divided into N segements each A long.
(xi , yi) and (xi+l , yi+l) are the endpoints of the segments.
Once tliis resistive taper is found, the far field pattern is calculated using the method
of momcnts.
COMPUTED RESULTS
The examples shown here project a Taylor current distribution onto the
rcflcctor surface, calculate the resistive taper using physical optics, then calculate and
plot. the far field pattern. Figure 2 shows the calculated values for the resistive tapers
corresponding to Taylor current distributions with ii=9 and sidelobe levels of -30, -40,
iintl -50 tlB below the peak of the main beam. T h e corresponding far field patterns are
shown in Figure 4. Note that the far field patterns have maximum sidclobe levels that
arc nearly 10 d B lower than the taper predicts. This result is expected, because the
uiiiform taper on the reflector has a maximum sidelobe level nearly 10 d B below that
of a uniform flat reflector. Figure 2 also shows a rather large spillover/transmission
sidelobe between looo and 180'.
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C 0N C L U SION S
Resistive tapers may be placed on reflector surfaces to control the sidelobe
level of the reflector. T h e tapers have the disadvantages of lower gain and a large
spillover/transmission sidelobe. However, the price of lower sidelobes is loir.er gain.
and sometimes the spillover/transmission sidelobe is not important. Obviously feed
blockage will cause a deteriation in the designed sidelohe level of a reflector. This
factor was not included in this analysis.
This type of antenna causes a significant reduction in gain. Thus, it should be
used carefully. One alternative is t o synthesize edge tapers that produce the desired
IOW sidelobe levels. Another possibility is to design the feed to obtain an illumination
t h a t is close to the desired illumination and only use a small amount of taper to get
the desired illumination. Also, this method could be used on subreflectors to obtain
the desired illumination on the main reflector.
REFERENCES
1. 0. M. Bucci, et. al., “Control of reflector antennas performance by rim loading,“
IEEE Trans. Ant. and Prop., vol. AP-29, no. 5, Sep 81, pp. 773-779.
2. R. L. Baupt and V. V. Liepa, “Synthesis of tapered resistive strips,” IEEE Trans.
Ant. and Prop., vol. AP-35, no. 11, Nov 87, pp. 1217-1225.
Figure 1. Tlicse are the resistive tapers derived for an fi=9 Taylor distribution and
sidelobe levels of 30 dB (solid), 40 dB (dashed), a n d .50 dB (dot-dash).
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Figure 2. Antenna patterns of a twedimensional parabolic reflector having a diameter
of 101, focal length of 51, and feed pattern given by (3). The reflector has a resistive
tapers that correspond to the tapers shown in Figure 1: 30 dB Taylor (solid), 40 dB
Taylor (dashed), 50 dB Taylor (dot-dash), and perfectly conducting reflector (dotted).
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