The topics of mesh reflectors, methods of analysis, measurements, problems of current interest, and future research, are those which should be addressed in assessing the current state of metallic mesh technology for spaceborne reflector antennas. The study of the properties of the conducting mesh material is discussed. To calculate the radiation patterns of antennas with conducting mesh reflectors, the electromagnetic properties of the mesh material must be integrated into an appropriate reflector antenna computer code. Such a code would take into account such factors as the curvature of the reflector surface, the radiation pattern(s) of the feed(s), etc. Many organizations have developed their own codes for these calculations. An excellent example of such a code is the one developed by Rahmat-Samii and Lee

Kauffman, Frank

English

NASA Technical Reports Server

MESH SURFACES FOR REFLECTOR APPLICATIONS
/7 _
N90- 19268
Frank Kauffman
Department of Electrical and Computer Engineering
North Carolina State University
Raleigh, North Carolina
PRECEDING PAGE. BLANK NOT FILMED
295
https://ntrs.nasa.gov/search.jsp?R=19900009952 2020-03-19T22:54:54+00:00Z
OUTLINE
The topics _listed in Figure 1 are those which I believe should be addressed in assessing the
_ current_ state of metallic mesh technology for spaceborne reflector antennas. The work I shall
: -discuss ]fivolves only the study of the properties of the conducting mesh material. To calculate
the radiation patterns of antennas with conducting mesh reflectors, the electromagnetic proper-
ties of the mesh material must be integrated into an appropriate reflector antenna computer
code. Such a code would take into account such factors as the curvature of the reflector surface,
the radiation pattern(s) of the feed(s), etc. Many organizations have developed their own codes
for these calculations. An excellent example of such a code is the one developed by Rahmat-
Samii and Lee (ref. 1).
I. Why Mesh Reflectors?
!I. Methods of Analysis
HI. Measurements
IV. Problems of Current Interest:
V Future Research_
Figure 1
296
MESH REFLECTORS BECAUSE
Listed in Figure 2 are three major reasons why metallic mesh materials are attractive for
use as the reflector surface in large aperture reflector antennas in space.
1. Weight
o Relative ease
aperture size
of deployment for required
3. Provides a
adjusted in
reflector
orbit
surface which can be
Figure 2
297
METHODS OF ANALYSIS
Figure 3 lists the methods which have been developed by various workers to calculate the
electromagnetic properties - transmission and reflection coefficients as a function of angle and
polarization - of infinite, periodic, rectangular wire grids.
The "average boundary condition" method (refs. 2 and 3) gives results which agree well
with other methods as long as the grid opening is electrically small - less than 0.1 wavelength.
Rahmat-Samii and Lee (ref. 1) have studied the mesh material using two different methods
of analysis. They used the average boundary condition method to model the mesh as a rectangu-
lar wire grid. They also modeled the mesh as "strip-apertures" - an infinite periodic array of
apertures cut in a thin perfectly conducting plate. The analysis of the strip-apertures was car-
ried out using a moment method technique similar to that reported by Chen (ref. 4). The wire-
grid mesh formulation and the strip-aperture mesh formulation are not in agreement for all
values of the mesh parameters. In particular, they found that the wire-grid mesh model did not
obey reciprocity and, hence, the strip-aperture formulation was the more accurate of the two.
The Fourier series method of Hill and Wait (ref. 5) is very slowly converging for some values
of mesh parameters.
The Spectral Domain Conjugate Gradient (SDCG) technique develol3ed by Christodoulou
and Kauffman (ref. 6) is an iterative technique for which convergence is guaranteed. The iterates
are chosen so as to minimize the number of iterations required. This formulation can also
accommodate grids with arbitrary surface impedance.
° Average Boundary Conditions
Kontorovich, 1963
Astrakhan, 1968
, Moment Methods - Strip Apertures
Chen, 1970
Rahmat-Samii & Lee, 1985
3. Fourier Series Expansion
Hill & Wait, 1974
, Spectral Domain Conjugate Gradient
(SDCG)
Christodoulou _ Kauffman, 1986
All treat rectangular mesh openings
Figure 3
298
ACTUAL MESH SURFACE
Figure 4 is a line drawing of the actual woven mesh material magnified many times. Note
the many small openings and loop contact points in addition to the large openings which
correspond to the rectangular apertures in the mathematical models.
The meshes which have been fabricated have been woven using gold-plated molybdenum
wire about 1 mil in diameter. The plating is typically around .25 Ixm thick. Meshes have been
woven with anywhere from 10 to 32 openings per inch.
Figure 4
299
WIRE-GRID MESH AND STRIP-APERTURE MESH MODELS
The sketches shown in Figure 5 define the geometries used in the mathematical analysis of
the conducting mesh material.
--------J I------_ T
J
i i
Wire-grid mesh with rcc[angular llttic¢.
l " :ml ," I
_-_ • b
2 x_ ',
a
LATTICE
(a)
Ym
y, i ix'
APERTURE "_I
a _-- CONDUCTOR
A UNIT CELL
{b)
(c) (all (c)
Strip-aperture mesh model with different lattice configurations. ,
Figure 5
300 ORIGINAL PAGE IS
OF POOR QUALITY
TRANSMISSION COEFFICIENTS USING WIRE-GRID
AND STRIP-APERTURE MODELS
The mesh transmission coefficients versus angle of incidence, calculated using both the
wire-grid and the strip-aperture formulations,are shown in Figure 6. Notice that To, b :# T,b 0 for
the wire-grid model indicating that the formulation does not obey reciprocity.
a:O. 547 mm a-O. 547 mm
b:l. 449 mm b:l. 449 mm -
2 ro=O.03 mm a-.__c_c= b-d
FREQ-12GHz 2r 0 2ro=F -
_1,90°
£/2=00
I I 1 I I I I I 1 I 1
5 10 15 20 25 30 35 40 45 50 55 60
-33
-35
-37
-39-
-41 -
-43
0
8 i (deg)
Figure 6
301
REFLECTION COEFFICIENT VS. MESH OPENING - TM POLARIZATION
Figure 7 shows a comparison of the reflection coefficient vs. mesh opening in wavelengths
calculated by the method of Hill and Wait (ref. 5) and by the SDCG method of Christodoulou
and Kauffman (ref. 6). As can be seen in the figure, the agreement between the two methods is
quite good. This can be said of all of the analytical methods discussed earlier with the exception
of the average boundary condition, which gives poor results for large mesh openings.
1.O
Z a8
LU
LL
U_
LU O.6
O
0
Z
0 o.4
I-
c.)
uJ
...J
LL 0,2
LU
C_
0.0
"\ T.tvl -_--_--×- WAIT I5"]
s.o.c.G
®=70° _'_.
I i 1 1
0.1 0.2 0.3 0.4 Q5 ,,. (_L/_
,3=70 deg., and _.o=0 deg.
Figure 7
302
REFLECTION COEFFICIENT VS. MESH OPENING - TE POLARIZATION
Figure 8 shows the reflection coefficient vs. mesh opening for the orthogonal polarization.
The same remarks made in discussing Figure 7 apply to Figure 8. Also, seeing comparisons with
other calculations but not with measurements points toward one of the areas very much in need
of further work: careful measurements of reflection and transmission coefficients as a function of
angle of incidence, frequency, polarization and mesh opening. Our calculations agree well with
one another but do they do a good job of modeling the actual mesh material?
I.O
w
C_
u__
W
O
C) 0.6
Z
0
I--
L_) o.4
LLJ
._J
Lu
LLJ
C3_
0.2
0.0
i
..... WAI T S
METHOD
%
C/C[-- 0.02 _
@= 70 °
d=b
|
0.1
I I _, I
0.2 0.3 0.4
@=70 and _:0 degrees
Figure 8
0.5 -----_ 0./2
303
SKETCH OF THE 5.2 GHZ BUCKET RADIOMETER SET-UP
We leave now the discussion of the analytical methods which have been developed and turn
our attention to the measurements which have been made.
Radiometer techniques offer a means of determining the ohmic losses of the mesh material.
These measurements are power measurements: power reflected - reflectivity, power transmitted
through the mesh - transmissivity, power absorbed - emissivity. The power emitted, or radiated,
by the material is equal to the power absorbed if one neglects scattering. Measurements have
shown this to be a good assumption. Conservation of energy requires that the sum of these three
quantities, expressed as fractions of the incident power, be equal to one.
Knowledge of ohmic losses is very important if the material is to be used in a reflector
antenna in a radiometer system. Such losses cause the brightness temperature measured by the
system to be in error if they are not calibrated out or accounted for by some other means.
Figure 9 is a sketch of a system used by Harrington and Blume (ref. 7) to measure the emis-
sivity, transmissivity and refiectivity of the gold-plated molybdenum mesh at 5.2 GHz. Four
measurements with four different test configurations are required.
TSFMR
/
/// Radlornetrlc buc_
__AI lined
/
308K_ \ 7K
I
I
l
I k--Far-Field Antenna Pattern
I I SFMR
I
\ l
\
Figure 9
304
2.65 - GHZ CLOSED RADIOMETER
Figure 10 is a sketch of the radiometer used by Harrington and Blume (ref. 7) to measure
the emissivity of the gold-plated molybdenum mesh at 2.65 GHz. Both of these systems and the
measurements required are discussed in detail in the reference cited.
Frame with mesh-.._.Cu plate
Sect,on A-_,-_.//I -'--
,orn.n,.°°.Cold
"_-'_ .......... "_.,,. Dry air In
II_//L ;I I_ II I_ I' L ......
I_"1" I , ! I _ I I ! !! _ ALU-Tlaps
Ecco foam-_ _' ': ': t, V _' ',L_L_f f f !
Cryoload N
2
2.65-GHz
Radiometer
I
J
Figure 10
305
RADIOMETERIC TEST RESULTS
Figure 11 shows the test results at both 5.2 GHz and 2.65 GHz (ref 7).
TEST RESULTS-RADIOMETRIC BUCKET
(5.2 GHz)
SAMPLENO. GOOO1 QO002
EMISSIVITY .004B_.0002 .0050_.0003
.0041±.0003 .0054 ±.0012
.0049±.0003 .O050 3.0003
,0051 _.0003 .OO50±.O003
.0046 ±.0004 .0059 _.0004
MEAN: .0047 ±.O004 ,0053 ±.0004
REFLECTIVITY .9724 _,OOO5 .9743 _.OOO5
.9716 ±.OOO8 .9693 ±.O006
TRANSMISSIVITY ,0266 ±.0006 .O190 ±.0006
.0213 ±.0008 .0233!.0003
(a)
TEST RESULTS-CLOSED SYSTEM(2.65 GHz)
SAMPLE NO. GDO01 GD002
EMISSIVITY 0.0185
0.0287
0.0134
0.0129
0,0137
0.0130
MEAN: 0,0167 0.0062
(b)
O.0156
O.0167
0.0255
O.0183
O.0168
0.0186
Figure 11
0.004
306
ADVANTAGES/DISADVANTAGES OF THES.2 GHZ AND 2.65 GHZ
RADIOMETERIC MEASUREMENTS
Figure 12 lists the quantities measured and the problems encountered using the two sys-
tems.
A COOPERATIVE LaRC/NRL PROGRAM HAS DEVELOPED TWO DIFFERENT
METHODS FOR MEASUREMENT OF THE ELECTROMAGNETIC PROPERTIES
OF MESH MATERIAL.
(1) Radiometric bucket method
Measures reflectivity, emissivity and transmission
Problems: RFI, solar interference, weather, multiple
measurements
(2) Closed system
Measures emissivity directly
Problems: Limited intergration time, heating/cooling
rate limitations
Figure 12
307
PROBLEMS OF CURRENT INTEREST
Listed in Figure 13 are problems which have come to the attention of workers in this area
which must be solved if mesh utilization for spaceborneantennas is to reach its full potential.
The first problem listed comes from observations on shuttle missions in which gold-plated
materials, when exposed to the plasma discharge around the vehicle in low earth orbit, would
oxidize in such a way as to form a Schottky barrier junction. These observations are discussed
by Blume (ref. 8). If the contact points of the woven wire mesh form junctions of the type, its
reflection and transmission properties and its ohmic losses would be altered dramatically. I will
discuss this problem in more detail using the next two figures. However, before I do, let me men-
tion briefly the second and third problems on the list.
The second problem comes from a desire for a mesh Which performs well at higher frequen-
cies - above 60 GHz. Such a mesh must be much smoother, with smaller ceil size, than the
current technology can provide. Some cooperative work between LaRC and a textile mill in
North Carolina is being done to address this problem.
The third problem is listed simply to provide the information that Chase Hearn at LaRC
has developed a resonant cavity technique for measuring the ohmic losses of these mesh materi-
als.
1. Modeling Wire Mesh Contact Points
2. Woven Mesh Technology
o Cavity-type Mesh Measurements
Figure 13
(Power)
308
GOLD - MOLYBDENUM OXIDE ' GOLD JUNCTION
Figure 14 provides a sketch of the Schottky barrier junction which may be formed by the
oxidation of the material due to the action of the plasma discharge around the spacecraft in low
earth orbit. Dr. Blume is currently planning an experiment to determine whether or not the
gold/molybdenum mesh oxidizes as have similar materials during earlier space flights.
Au
Mo 03
Mo 03- _
,
t.......roT' ............'...............' ::: ....;:TT;;TT/Y1
x_- Substrat e
Figure 14
309
CAPACITANCE VS. TEMPERATURE FOR A $CHOTTKY BARRIER. JUNCTION
Figure 15 is a graph of capacitance of the diodeversus temperature. Such variation is a
cause for concern because spaceborne antennas are subjected to extreme temperature changes
alid thermal gradients. If the mesh contact points behave in this fashion, the reflection,
transmission and loss properties of the mesh will undergo wide fluctuations with temperature.
,_ 102
I.I.
I0
7O
R 0 =
C b =
Cs =
130
Cp (High)
Cp (Low)
3.15 x tO-2 .0_
8-5 nF
320 nF
104 rad (sec -1)
0.5?eV
I
I
/
/
/
/.
/
/
/
/
I
I
I
I
I
I
I
I
I
Ro expl_/2kT)
Cs cb Cs
190
I
250
I I I
310 370430
T (OK)
Figure 15
310
FUTURE RESEARCH
Figure 16 offers a list of those problems which, in my opinion, require further research.
A comprehensive set of measurements is needed not only to expand our knowledge of the
mesh material but also to judge the adequacy of our analytical techniques.
The first gold - mobybdenum oxidation experiments are now being planned by Dr. Blume at
LaRC with assistance from faculty and students at Old Dominion University.
Very limited tests are now under way on weaving tighter conducting mesh materials. Much
more must be done if these materials are to be used at millimeter wavelengths.
Xe Measurement of Wave Properties
tion, Transmission, Polarization
- Reflec-
2. Gold- Molybdenum Oxidation Experiments
3. Smoother, Tighter Woven Meshes
Frequencies
Figure 16
for Higher
311



Mesh surfaces for reflector applications

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