AP13-8
SPECIPYING SCATTERING SIDELOBES FOR A RESISTIVE STRIP
Randy L. Haupt
Air Force Institute of Technology
The University of Michigan
Ann Arbor, Michigan 48109
Valdis V. Liepa
Radiation Laboratory
Dept of Electrical Eng and Computer Science
The University of Michigan
Ann Arbor, Michigan 48109
Introduction
The current on an antenna can be tapered in order to generate a
desired far field
pattern. This same principle may be applied to scattering
problems as well. Consider a
resistive strip inwhich the resistivity is tapered in such a way that an incident plane wave
induces a prescribed current distribution on the strip. Then, the current produces the
desired scattering pattern. In this paper we use Physical Optics and the Taylor aperture
distribution t o demonstrate a technique to
lower the bistatic scattering and backscattering
sidelobes of a resistive strip.
Synthesizing Resistive Tapers
Senior and Liepa[l] placed a parabolic resistive taper on a half plane to reduce the
edge currents. A similar taper on both
edges of a strip tapers the current on the strip,
which in turn lowers the sidelobes of the scattering patterns. A parabolic taper, however,
does not allow one the capability of specifying the sidelobe level over a given angular
region. Specifications of this type are common in antenna theory (e.g. Chebychev, Taylor,
Baylis).
Haupt and Liepa[Z]have shown that the Physical Optics currentclosely approximates
the true current on a smoothly tapered
resistive strip. Consequently, it is possible to derive
a resistive taper that produces a desired cnrrent distribution by inverting the Physical
Optics equation for the current on the strip. The steps for synthesizing a tapered
resistive
strip that has scattering patterns characteristic
of the Taylor current distribution are
outlined below.
STEP 1 We relate the desired far field pattern to a current distribution on the strip.
phase control
Since the strip is extremely thin and resistive, only amplitude, and not
of the current is possible. Thus, unsymmetric bistatic patterns at normal incidence are
not feasible. Also, the resistive taper will not be able t o exactly reproduce the necessary
current distribution, since the exact resistive taper has real and imaginary values. In this
analysis we have chosen to use the Taylor amplitude taper to relate the f a r field pattern
to the current on the strip. This taper l i m i t s the h t E-1sidelobes on either side of the
main beam t o a height of q dB below the peak of the main beam, while the remaining
sidelobes fall-off exponentially.
STEP 2 Next, the desired current distribution must
be related to the resistivity. The
Physical Optics current when the electric field is parallel t o the edge of the strip is given
bv
CH2435-6/87/0000-0542$01.000 1987 IEEE
542
where
J - PhysicalOpticscurrent
4, - angle of incidence relative the the surface of the strip
7 - normalied resistivity = R/Z,
Z,,is the impedance of free space
E, - is the amplitude of the incident field
Solving Eq(1) for q
(+o
= 0)leaves
q(z)= Eo - .5
J(x)Zo
q is real and approximate since J is real and approximate.
STEP 3 We verified the result by numericallysolving the followingequationfor
the
current.
-E
incident
E
---total
=E
or
+
Eoeikzeos*o = q ( z ) J ( z )
_.
zo
-8cattered
!la
J ( z ’ ) H p ) ( k l z- z‘l)dz‘
4
(3)
(4)
--D
where
k = 2 ”
wavelength
H p ) = Hankel function
This equation is solved for J using equally spaced collocation points with pulse basis
functions and PLU decomposition and backsubstitution.
Results
Figure l a shows the resistive taper derived for a 30dB, E=2 Taylor distribution on a
6 wavelength strip. The following figures show the current (Fig lb), the bistatic scattering
pattern for normal incidence (Fig lc) and the backscattering pattern (Fig Id). The next
set of figures demonstrate the synthesis technique for even lower sidelobes. Bistatic and
backscattering patterns for a50dB Taylor taper appear in Figs 2a and 2b respectively. In
both cases, the sidelobes are 50dB and lower.
References
1. T. B. A. Senior and V.V. Liepa, “Backscattering from Tapered Resistive Strips,”
IEEE Bans. AP, vol 32, no 7, July 1984, pp 751-754.
2. R.L. Haupt and V.V. Liepa, ‘The validity of approximating currentson a resistive
strip using physical optics” IEEE 1986 AP-S‘Intl Sym Digest, pp 137-140.
543
CURRENT
$1
88
=%
\
\
-3.00
POSITION ON
ST%F
/
,
/
2
0
3.00
I N WRVELENGTHS
STRIP
A
EITION
a. Synthesized Resistive Taper
ON
ON S T K P NI
W R V E L E ~ ~ ~ ~ S
b. StripCurrent
BRCKSCRTTERING
SCRTTERING
BISTRTIC
d. Backscattering Pattern
c. Bistatic Scattering Pattern
Figure 1. Results from a 30dB E=4 Taylor Taper
544
EISTRTIC SCRTTERING
BRCKSCQTTERING
0
RNG~LO~O~INOEG%?S
b. Backscattering Pattern
a. Bistatic Scattering Pattern
Figure 2. Results from a 50dB E=5 Taylor Taper
545
90.00