69-1
RESISTIVE TAPERS THAT PLACE NULLS IN THE
SCATTERING PATTERNS OF STRIPS
Randy L. Haupt
Department of Electrical Engineering
Unikd States Air Force Academy
Colorado Springas,CO 80840
Valdia V. Liepa
Radiation Laboratory
Department of Electrical Engineering and Compukr Science
The Univemity of Michigan
Ann Arbor, Michiian 48109
Introduction
The mattering patterns of a perfectly conducting strip may be modified by d i g part
of the strip from resutive materisb. Thk paper dacribcm a method of deriving a complex
resistive taper that will place multipk nulla in the bistatic scattering patkrn or one null in
the backscattering pattern of a strip.
Equation.
The first step is to solve the strip integral equation for the normalired rabtivity (q) at
an incident angle broadaide to the strip. Only the &polariaation result. are given here.
where
J, =s-directed current density
k
=
2*
wavelength
20 =Length of strip in wavelengths
If:')
t
=hankel function of second kind order zero
=distance along strip in wavelengths
The next step usen the ShorcSteyakd [R.A. Shore and E.Steyskal, "Nulling in l i e = CAIray patkrns with minimiration of weight perturbations," RADGTRr82-32, (ADAll8695),
Feb 1982.1 n u k g technique to find a current density that rill produce a null in the far
field pattern. Tke current distribution on the strip that generates n& at specified angles in the biatatic scatkring pattern M represented by the qukscent current, Jo(x), plus a
perturbation, J.(t)6(+).
J,(+)
= J,o(z)(l+ a(+))
In the far field, this new current produces nulla at M locations
where S(9) is the relative far field pattern. The above integral may then be solved using
mid point integration
N
N
Jndk**co'*m
= A c ( 1 + 6n)J0neJkrsc0'*m = 0
=A
S(9,)
n=l
(4)
n=l
where
Jn = current that produces nulla in the far field
Ja = quiescent current
6, = perturbation to the quiescent current
A = = length of current segment
S = far field pattern
,
Rearranging ( 4 ) into a form amenable to matrix solution yields
N
A6n J
a
dkS.CO#*m
"4
=-
c
N
A J adk*.COS)m = -So($,), m = 1,2,...,M
(5)
n=l
where So is the quieacent relative far field pattern.
Now that (4) is in the form of M equations with N unknowna, where M<N, a le&
solution to the matrix equation is
given by
squares solution is paaible. Usually,the minimum norm
( A t A ) z = A'b
If the current perturbations are minimized in a least mean square sense
N
16,1'
= minimum
(7)
n=l
then the components of (
where
6) take the form
is the transpose of the vector. The minimization in (7) is not unique.
ResultI
Figure 1 in an example of placing a null in the far field backscattering pattern of
a perfectly conducting strip at 75'. The quiescent pattern is superimposed on the nulled
pattern. Figure 2 shows a null placed in the backecattering pattern of a tapered resistivestrip
at 2W. In both examplesthe resistive taper is complex and the current density perturbations
are small.
1181
,
,r
9
c -20
-2.0
x
0.0
~UAVELENGTHSI
20
0.0
x
20
NAVELDIGTHS)
b. NarnUzed reshtlvr t q a for
dllng
P
I
3.1
v
Figure 1. Nulls are placed in the Epolarired backscattering pattern at 75”. The strip is 4X
wide and was originally perfectly conducting. The solid line is the nulled pattern and the
line with circles is the quiescent pattern.
1182
1
--
-
NULL
OUIESCENT
RERL PART
-1Iyu;ItMY
PART
i s !
-
O J
-2.0
0.0
20
X (UAVELENGTHS)
a !lagnltudc of lnduced current
h l t y on rtrlp. #.=90'
-
-NULL
WESCENT
b. Norrallzed reslstlvr taper for
nUlllW
I
-
- M u
MmscENT
n
0,
-?
0
IS
90
135
180
p0
c. Blrtstlc rstterlnp psttrm. p.40'
d. Backrwttalnp m t f m
Figure 2. A null is placed in the Epolarized backscattering pattern at 20". The strip is 4X
wide and has a low sidelobe resistive taper . The solid line is the nulled pattern and the
line with circles is the quiescent pattern.
1183
I