The dichroic plate considered in this article is a metal plate perforated with arrays of apertures such that electromagnetic waves of certain frequencies pass through the plate and other frequencies are reflected. The shape of the apertures is an important contributor to the performance of the dichroic plate. An S/X dichroic plate, which passes X-band (8.4-8.45 GHz) and reflects S-band (2.0-2.32 GHz), is chosen for a case study. A comparison of the performance of dichroic plates of the same thickness and array pattern is presented for three different aperture shapes: circular, Pyleguide, and rectangular

Chen, J. C.

English

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TDA Progress Report 42-111
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/
._.- ,LL-_
November 15, 1992
Study of Narrow-Band Dichroic Plates With Circular,
Rectangular, or Pyleguide Apertures
J. C. Chen
GroundAntennasand Facilities EngineeringSection
The dichroic plate considered in this article is a metal plate perforated with ar-
rays of apertures such that electromagnetic waves of certain frequencies pass through
the plate and other frequencies are reflected. The shape of the apertures is an im-
portant contributor to the performance of the dichroic plate. An S/X dichroic plate,
which passes X-band (8.4-8.45 GHz) and reflects S-band (2.0-2.32 Gtlz), is cho-
sen for a case study. A comparison of the performance of dichroic plates of the
same thickness and array pattern is presented for three different aperture shapes:
circular, Pyleguide, and rectangular.
I. Introduction
Consider an S/X dichroic plate illuminated by a circu-
larly polarized wave; this wave is formed as a combination
of two orthogonal linearly polarized waves (TE and TM
polarizations). If the apertures on the dichroic plate are
symmetric, such as circular or square shapes, and the cir-
cularly polarized wave travels in the direction normal to
the plate, then the relative phase difference of the two
linearly polarized waves remains the same after the wave
hits the plate. This means that the transmitted and the
reflected waves are still circularly polarized, On the other
hand, for oblique incidence, the relative phase difference
between TE and TM polarizations will be changed after
the wave leaves the plate, resulting in the transmitted
and reflected waves being elliptically rather than circu-
larly polarized (depolarization). Since oblique incidence is
required in the Deep Space Network, an incident angle of
30 deg from the normal direction of the plate was chosen
for this case study (Fig. 1).
The S/X dichroic plate on the DSS-14 70-m antenna
was originally designed with circular apertures. Then
the depolarization was improved by replacing the circu-
lar apertures with Pyleguide apertures by P. D. Potter
in 1973 [1]. The results of the circular- and Pyleguide-
aperture computations and measurements by Potter are
discussed below. Furthermore, results of a theoretical de-
sign study of a dichroic plate with rectangular apertures
are also included.
II. Circular Apertures
Circular apertures were originally used because they
were easy to machine and the characteristics of the circu-
41
https://ntrs.nasa.gov/search.jsp?R=19930009712 2020-03-17T07:20:59+00:00Z
lar waveguide modes were well known. The first design
of an S/X dichroic plate was a 3.576-cm-thick metal plate
perforated with 2.273-cm-diameter circular apertures on a
60-deg skew grid with 2.388-cm spacing [Fig. 2(a)] [1]. A
depolarization problem was found in this dichroic plate de-
sign. Calculations, using the C. C. Chen Holey Plate Com-
puter Program, showed that the plate resonant frequencies
were 8.481 and 8.363 GHz for TE and TM polarizations,
respectively. A differential phase shift of 11.3 deg and an
ellipticity of 1.75 dB were computed at the operating fre-
quency of 8.415 GHz. The actual measured ellipticity was
1.84 dB. The reflected energy' level was measured to be
-18.6 dB at 8.415 GHz.
III. Pyleguide Apertures
A Pyleguide, a circular waveguide with a pair of flats on
opposite sides, was introduced to solve the depolarization
problem. Because one dimension is shorter than the other
for a Pyleguide aperture, the cutoff frequencies are differ-
ent for TE and TM polarizations. Since there was no com-
puter program to analyze a dichroic plate with Pyleguide
apertures, the size of the apertures was determined from
the cutoff wavelengths of the Pyleguides, which corre-
sponded to the resonant frequencies (8.481 GHz and 8.363
GHz) of the original circular-aperture plate. The Pyle-
guide aperture was 0.013 cm larger than the original circu-
lar aperture, and the flat depth was 0.043 cm [Fig. 2(b)].
The Pyleguide apertures were only a small change from
the original circular apertures. The Pyleguide holes were
made with a tolerance of +0.005 cm. The phase shift was
3 deg and the ellipticity was 0.4 dB. The reflected power
average level for the Pyleguide dichroic plate was -24.5 dB
at 8.415 GHz [1]. The performance was improved by using
Pyleguide rather than circular apertures.
IV. Rectangular Apertures
A dichroic plate with rectangular apertures has enough
degrees of freedom to minimize the depolarization of the
circularly polarized incident wave. A computer program
based on a modal matching method was written to cal-
culate the transmission and reflection coefficients of a
dichroic plate with rectangular apertures [2]. The exper-
iments on the test dichroic plates showed that calculated
and measured resonant frequencies of the dichroic plate
were within 0.3 percent, which indicates good accuracy of
the software. The study of the dichroic plate with rect-
angular apertures in this article was based on this com-
puter program, while the dichroic plates with circular or
Pyleguide apertures discussed above were built and tested
by Potter [1]. An optimization program was integrated
with the rectangular-aperture dichroic plate program to
accelerate the time-consuming process of optimizing the
size of the rectangular apertures.
The optimization program finds the minimum of a user-
defined cost function of several variables. Each variable is
constrained between an upper bound and a lower bound.
The function is first evaluated at the initial values of vari-
ables given by the users. Then the function is recalculated
at different values of the variables. The program continues
to search for a new set of variables until the local minimum
of the function is found or until any one of the variable
boundary constraints is broken. In this case, the variables
were the dimensions of the apertures and the cost func-
tion was a function of the reflection loss of both the TE
and TM polarizations, and the relative phase shift between
them. Since several local minima may exit, the optimiza-
tion process should be repeated with different initial values
in order to find the absolute minimum.
The dimensions of the rectangular apertures were de-
termined using the following method. First, the boundary
constraints for the dimensions of rectangular apertures Ax
and A_ were found. The aperture should be larger than
the cutoff size for the lowest frequency of the passband,
and smaller than the unit cell:
C
< Ax <_ D_ - Wmin2f_
e
2-'-_ < A_ < Du, sin fl - Wmin
where c is the speed of light, ft is the lower frequency of
the passband, and Wmin is the minimum wall thickness of
the apertures. The wall of the aperture has to be thick
enough to support the plate. _ is the skew angle, and Dx
and Du, are the dimensions of the unit cell (Fig. 1).
Second, the aperture was set to be square, Ax = A_, so
only one variable was optimized. The program searched
for the optimized square aperture A1 = Ax = Ay.
Third, Ax was fixed to the optimized square aperture
dimension A1, and A_ was varied as the optimization vari-
able. The optimized value of Ay was As.
Finally, using A1 and As as the initial values, both
Ax and A u were optimized (Fig. 3). The optimization
program searched for only the local minimum; therefore
it was necessary to repeat the procedure (starting from
the second step) to assure that optimum aperture size was
achieved.
42
A 1.925-cm by 1.951-cm rectangular aperture was found
using the optimization program for a 3.576-cm-thick di-
chroic plate on a 60-deg skew grid with 2.388-cm spacing
[Fig. 2(c)]. Figures 4 through 6 show the transmission co-
efficients for TE and TM polarizations, the relative phase
shift between TE and TM polarizations, and the ellipticity
from 7 to 9 GHz. The calculations show a reflection loss
of 0.000 dB for TE polarization and 0.001 dB for TM po-
larization, a relative phase shift of 2.0 deg, and ellipticity
of 0.3 dB at 8.415 GHz. The conductivity loss was esti-
mated to be 0.01 dB based on a 3.576-cm-long, 1.925-cm
by 1.951-cm rectangular waveguide.
V, Summary and Conclusion
The results of this case study show that the apertures of
unequal dimensions (rectangular or Pyleguide) produced a
better axial ratio than the symmetric apertures (circular)
for the case of oblique incidence with a circularly polar-
ized wave. The performance of a dichroic plate with rect-
angular apertures was easier to optimize than that with
Pyleguide apertures since an accurate computer program
for a dichroic plate with rectangular apertures was avail-
able. Table 1 shows insertion loss, relative phase shift,
ellipticity, and maximum reflected power of the dichroic
plate with circular, Pyleguide, and rectangular apertures
at 8.415 GHz. The maximum reflected power level at
8.415 GHz for the dichroic plate with rectangular aper-
tures is expected to be slightly better than -24.5 dB. The
grating lobes depend on the array pattern of the dichroic
plate. Since in this case study the array pattern remains
the same, the grating lobes are the same for these three
configurations.
The reflected power from the dichroic plate resulted in
increased temperature in the antenna system. The max-
imum noise temperature contribution from ground radia-
tion was 0.7 K at 8.415 GHz for the 70-m antenna. While
in the beam-waveguide-antenna pedestal room (300 K for
DSS 13), the maximum noise temperature contribution of
the dichroic plate was 1.06 K. The horn radiation pattern
is not a perfect plane wave. Part of the horn radiation
strikes the plate at angles other than the design angle; as
a consequence extra reflections are created which result
in an increased noise temperature. Further study using a
plane wave expansion of the horn pattern would allow the
reflected power to be predicted theoretically.
References
[1] P. D. Potter, "Improved Dichroic Reflector Design for 64-m Antenna S- and
X-Band Feed Systems," The Deep Space Network Progress Report, JPL Techni-
cal Report 32-1526, vol. XIX, Jet Propulsion Laboratory, Pasadena, California,
pp. 55-62, February 15, 1974.
[2] J. C. Chen, "Analysis of a Thick Dichroic Plate with Rectangular Holes at Arbi-
trary Angle of Incidence," TDA Progress Report _2-105, vol. October-December
1990, Jet Propulsion Laboratory, Pasadena, California, pp. 9-16, February 15,
1991.
[3] T. Y. Otoshi and M. M. Franco, "Dual Passband Dichroic Plate for X-band,"
TDA Progress Report _2-g4, vol. April-June 1988, Jet Propulsion Laboratory,
Pasadena, California, pp. 110-134, August 15, 1988.
43
Table 1. The performance of S/X dlchrolc plates at 8.415 GHz.
Parameter
Aperture
Circular Pyleguide Rectangular
Insertion loss, dB
TE -- 0.009 _ 0.010 b
TM -- 0.004 0.011
Relative phase shift, deg 11.3 c 3.0 2.0
ERipticity, d8 1.84 0.4 0.3
Reflected power
level,d dB (max) -18.6 -25.4 --
• The insertion loss of the dichroic plate with a Pyleguide aperture is achieved
by experiments [3].
b The calculated insertion loss of the dichroic plate with rectartgular aper-
tures includes the reflection loss and conductivity loss, but not the loss
due to surface roughness.
c The relative phase shift and elliptlcity of the dichroic plate with circular
or PyleguJde apertures are determined experimentally [1].
d The reflected power level is achieved by experiments.
44
I INCIDENT
Iil\ /' .I'
Flg. 1. Geometry o! X/Ka dlchrolc plate.
45
¢a) I----A'
......._-_--- 2.068 cm
(b) i__s, (o.o_3c_
..._'-_ 2.068 cm
(c)
F-_c'
T
1.925 cm
÷
1.951 cm _-
I--=,- C
2.068 cm
Fig. 2. Apertures: (a) circular; (b) Pylegulde; and (c) rectangular.
46
LET Ay = A x
OPTIMIZING A x
A x = Ay = A 1
LET A x = A 1
OPTIMIZING Ay
Ay = A 2
LET THE INITIAL VALUES OF A x
AND Ay BE A 1 AND A 2
OPTIMIZING A x AND Ay
Fig. 3. Method for finding an optlmlzed rectan-
gular aperture for a dlchrolc plats.
-5
nn
Z
_o-lo
O9
O3
_ -15
-20
-25
7.0
" 'h'-M'----:
..,S --" I"--PASSSANO
.-7
H -
-
I I I I I 1 I-'_ 1 I
7.2 7.4 7,6 7,8 8.0 8.2 8.4 8.6 8.8 9.0
FREQUENCY, GHz
Fig. 4. Transmission coefflclent versus frequency for )US dlchrolc
plate wlth rectengular apertures for TE and TM polarizations.
14
12
g' lo _
-o.
6
4
2
_-2
-4
-6
I J I I I I I 1
_PASSBAND -
l
1 I I L I I I I I
7.0 7.2 7.4 7.6 7.8 8.0 8.2 8,4 8.6 8.8 9.0
FREQUENCY, GHz
Fig. 5. Relative phase shift between TE and TM polarizations ver-
sus frequency for )US dlchroic plate with rectangular apertures,
o
.J
.J
UJ
2.5
2.0
1.5
1.0
0.5
0
7.0 7.2
I 1 I I I I PI l 1
7.4 7.6 7,8 8.0 8.2 8.4 8.6 8,8 9.0
FREQUENCY, GHz
Fig. 6. EIIiptlcity versus frequency for X/S dlchrolc plate with
rectangular apertures.
47


Study of narrow-band dichroic plates with circular, rectangular, or Pyleguide apertures

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