2.5
UNIFORM THEORY OF DIFFRACTION ANALYSIS FOR
CONDUCTIVE STRIPS W I T H CONSTANT AND TAPERED
RESISTIVE LOADS
Mark C . Heaton- and Philip J . Joseph
Department of Electrical and Computer Engineering
Air Force Instilute of Technology
Wright-Patterson Air Force Base OH 45433
Randy L. Haupl
Department of Electrical Engineering
United States Air Force Academy CO 80840
I.
INTRODUCTION
Resistive edge loading of perfectly conducting surfaces can reduce the backscattering sidelobe levels from those surfaces with little increase to the maiii backscattering lobe. A constant resistive load provides some control over the backscattering
sidelobes, but a tapered resistive load provides significantly improved performance.
Traditionally, these geometries have been analyzed using integral equations and
pliysiral optics (1’0).Tlie integral equation approach limits calculations to electrically small or mid-sized objects, while the physical optics approach has limited
accuracy.
This paper explores tlie use of a uniform theory of diffraction (UTD) approach
t o tlie analysis of conductive strips with constant and tapered resistive loads.
IJTD diffraction coeflicients are found for resistive edges and junctions using the
geometrical optics ( G O ) reflection and transmissioii coefficients of resistive strips.
Tlie UTD radar echo-length predictions for edge-loaded strips agree well with
moment Inetliod (Mhl) predictions and with measurements.
11.
U T D DIFFRACTION COEFFICIENTS FOR RESISTIVE LOADS
Figure 1 illustrates the more general case of a conductor with tapered resistive loads. The taper is approximated by a sequence of constant resistive loads
(typically LO per wavelength), as shown. Diffraction coefficients are thus needed
for resistive edges and juiictions (the conductor/resistive junction is treated as a
special case of the resistive junction).
Tlie G O reflection and transmission coefficients for a resistive sheet are derived
in [ I ] using tlie resisbive boundarv condition. These determine the G O field discoutinuities associated with the resistive edge and junction geometries. The needed
diffraction coeflicients are found by scaling the UTI1 solutiou for tlie perfectly COIIducting case according to tlie GO field discontinuities (analogous to the approacli
of (21 for a dielectric half-plane), then empirically modifying the scaled result.
U.S. Government work not protected by U.S. copyright
18
Figure 2 shows tlie model of the junction of two resistive half planes, or of
the edge of a single resistive llalf plane if material B is ignored. The diffraction
coefficient for resistive edge diffraction is given by
05''
I
= (1 - I;q)D(9 - 9') t R;D(9 t 9')
(1)
while the diffraction coefficient for the resistive junction is given by
where
The subscripts s and 11 indicate soft and hard boundary conditions, respectively, R
and T are the (modified) GO reflection and transmission coeflicienls, respectively;
the superscripts A and B diflerentiate between materials A and B, when necessary.
q is the sheet resistivity normalized to that of free space. Finally, 8 = 8' = 8" for
backscatter while 8 = (8'+8")/2 for bistatic scatter, where 8' and 8' are the angles
made by the incident and scattered rays with respect to the surface normal. Note
that the angles ,$,,$' are measured from material A.
111.
RESULTS
UTD calculations are compared with hIM and PO calculations, and with experimental results. Figure 3 shows the E-polarized (electric field parallel to the
edge of the strip) backscattering patterns from a 4A strip with the center 2A highly
conductive and I X resistive loads (q=0.320tj0.120) on either edge. The resistivity
value was deternlined through waveguide reflection measurements with a network
analyzer. Calculations and measurements show very good agreement.
Figure 4 sliows the E-polarized backscattering patterns from a 4A strip with
an ?a taper I A from either edge. The M M and PO solutions differ from the UTD
solution in tlie null and far-out sidelobe regions. Similar comparisons made for
II-polarized scattering and bistatic scattering yield like results.
IV. CONCLUSIONS
This paper presetits a UTD approach for calculating the scattering patterns
of resistively edge-loaded conducting strips. The approach shows good agreement
with method of moments calculations and with measurements.
19
References
[I]
R.. L. Haupt, Synthesis
of Resistive Tapers to Control Scattering Patterns of
Slrrps, PhD Dissertation, The University of Michigan, 1988.
(21 W. D. Burtiside and K. W. Burgener, “High Frequency Scattering by a Thin
Lossless Dielectric Slab,” IEEE Trans. on Antennas and Propagatiou, 1‘01 AP31, NO 1, pp. 104-111, 1983.
Load
Conductor
Z(x>
Load
______
Actual Resistance
Resistance Model
Figure 1: Loaded strip and quantized model of resistive taper.
Incident
Plane Wave
Observer
,’.
”mmrm
Figure 2: UTD geometry for resistive junction (also for resistive edge if material
I? is ignored).
20
,
20
0
10
20
30
I
I
40
50
70
EO
90
0 (Degrees from Broadside)
Figure 3: E-polarized backscattering patterns of a 2A conducting strip with 1A
resistive edge loads (q=0.320tj0.120). (measurement -, AIM - - -,UTD
.
e)
20
rl
-10
tn
C
rl
-20
&I
a)
U
U
(d
-30
v)
-40
i o io io do so i o 7’0 i o i o
,
0 (Degreee from Broadside)
Figure 4 : E-polarized backscattering pattwns of a 2A conducting strip with 1 A
resistive edge loads, z z tapcr. (h4II -, UTD - - -,PO . . .)
21