Beam-waveguide (BWG) antennas provide multiple frequency band operations and other operational benefits for large ground-station antennas. Present design practices use diffraction analyses that ignore the presence of the BWG enclosure and may be inaccurate at lower frequency bands for ground-station antennas operating over multiple frequency bands. Introduced here is a new analysis approach that considers the presence of the BWG enclosure. Results based on the new analysis have revealed new understandings of the performance degradation mechanisms in a BWG antenna and have provided direction for potential design improvements

Cha, A. G.

English

NASA Technical Reports Server

r- - N89-27886
TDA Progress Report 42-97 January-March 1989
A New Analysis of Beam-Waveguide Antennas Considering
the Presence of the Enclosure
A. G. Cha
Ground Antenna and Facilities Engineering Section
Beam-waveguide (BWG) antennas provMe multiple frequency band operations and
other operational benefits for large ground-station antennas. Present design practices use
diffraction analyses that ignore the presence of the BWG enclosure and may be inaccurate
at lower frequency bands for ground-station antennas operating over multiple frequency
bands. This article introduces a new analysis approach that considers the presence of the
BWG enclosure. Results based on the new analysis have revealed new understandh_gs of
the performance degradation mechanisms in a BWG antenna and have provided direction
for potential design improvements.
I. Introduction
Beam-waveguide (BWG) technology offers wide frequency-
band coverages, improved gain/temperature (G/T) performance
for ultra-low-noise ground antennas by providing a more stable
operating environment for masers, advantages in maintenance
and operations, and reduced life-cycle cost for ground-station
antennas. For these reasons, there has been a trend towards
adopting the BWG design in new ground-station antenna proj-
ects. Examples are the Japanese 45-m and 64-m antennas at
Nobeyama and Usuda, and various 30-m class lntelsat and
Comsat ground antennas. Additionally, the Deep Space Net-
work (DSN) is building a 34-m BWG antenna at Goldstone,
California.
The BWG feed operating principle is based on geometric
optics (GO). By using a pair of properly shaped and positioned
mirrors, the radiation pattern of a feedhorn can be reproduced
at a point in space that is some distance away from the physi-
cal location of the feedhorn. For finite-size BWG systems and
at finite frequencies, some loss and some pattern distortions
are experienced. At present, such effects are predicted from
diffraction analysis developed for mirrors in open space. Com-
mon analysis techniques are Gaussian mode analysis and physi-
cal optics (PO) analysis. In actuality, the BWG mirrors are en-
closed by metal walls for safety when transmitting, and for
sensitivity (noise temperature) and protection against radio
frequency interference (RFI) when receiving. The absence of
the metal wall in the current analysis models leads to an error
whose magnitude is not well understood, especially at lower
frequencies when the wall diameter is 20 wavelengths or less.
In practice, this means one is forced to make decisions about,
for example, building a 6-ft- or 8-ft-diameter BWG system
based on weak assumptions. Such decisions often have major
impacts on antenna microwave/structural performances and
project cost tradeoffs.
This article presents a new analysis of BWG antennas which
considers the presence of the wall. This analysis is based on
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replacing the free-space Green's function used in PO analysis
with the dyadic Green's function for a cylindrical waveguide,
satisfying the boundary condition at the metallic BWG wall.
The results from this analysis have revealed some new under-
standings of the performance degradation mechanisms in a
BWG antenna and have pointed to potentially significant de-
sign improvements. Some of these ideas are discussed here.
Full realization of all benefits from BWG wall analysis and
design concepts will take some time. It is hoped that the dis-
cussions in this article will induce further innovative ideas and
designs.
II. The Optics of BWG Systems
Figures l(a) and l(b) show the microwave optics of BWG
systems. A basic cell consists of a pair of curved mirrors
(reflectors). In practice, a pair of flat mirrors is often added to
form a four-mirror system. However, the BWG characteristics
are largely determined by the pair of curved mirrors. The
conditions for distortionless transmission of feedhorn patterns
based on GO are discussed in [1]. It is shown that a parabo-
loid pair oriented as shown in Fig. l(a) is one choice that
meets the Mizusawa condition. This case is used here to discuss
the diffraction effects.
The Mizusawa condition guarantees distortionless trans-
mission of the feedhorn pattern from focus FI to focus F2 at
infinite frequency where GO is valid. The only loss is at the
first mirror as it does not collect all the GO rays. In practice,
BWG antenna designs must consider diffraction effects which
cause further degradations as shown in Fig. l(b). Figure l(b)
illustrates how the diffraction effects are presently modeled.
Mirror 1 is illuminated by the feedhorn and radiates into the
whole space. Assuming mirror 2 is in the near-field zone of
mirror 1, one can visualize mirror 2 intercepting the bulk of
the rays bounced off mirror 1, but there is a small amount of
energy loss due to the divergence of the beam of rays. In addi-
tion, it can also be expected that the rays reflected from mir-
ror 2 will now not be focused to a single point F2. This implies
that the image pattern at F2 compared to the real feedhorn
pattern at F1 will have amplitude and phase distortions. If the
real feedhorn pattern at F1 is the ideal pattern needed to
illuminate a reflector antenna, then the distorted pattern at F2
gives rise to further performance degradations in addition to
the spillover loss at each mirror.
Such mechanisms of performance degradation are predicted
from present analytical techniques, including Gaussian mode
analysis [2], physical optics [3], and geometrical theory of
diffraction (GTD). It is generally accepted that these tech-
niques yield good results under the very near-field approxima-
tion.
where L is the distance between mirrors 1 and 2, D is the
mirror diameter, 3, is the wavelength, and C is a constant gen-
erally taken as between 0.1 and 0.2 [3]. None of the above
analyses recognizes the presence of the wall and thus they are
likely to lead to errors in BWG antenna performance analysis
when the condition in Eq. (1) is not met. The following intro-
duces a new analytical approach that recognizes the wall pres-
ence. The new analysis is theoretically more satisfactory and
should in time lead to significantly better analysis and design
of BWG antennas.
III. New BWG Antenna Analysis That
Considers the Wall Presence
The new BWG wall analysis presented in this article is con-
ceptually similar to the PO analysis used in reflector antenna
analysis; Fig. 2 shows this analogy. The PO analysis and the
BWG wall analysis can each be conceptualized as a superposi-
tioning process whereby the radiation field of a current dis-
tribution is found by integrating the radiation field of point
sources. Assuming a time dependence e j_t, the PO far field is
written as
E(R ) = 10 ff + I¢_ _ (2)
where
T = -/,_ufK(R')gtn,R') ds' (3)
and
e-/klR - R'I
g(R, n') - (4)
4rtlR -R'J
In Eqs. (2), (3), and (4), _ is the angular frequency, ta is the
permeability,/_ is the position vector of the observer,,_' is the
position vector of a point source, and g(K',/_') is the free-
space Green's function. The integration is over the surface
current as determined from the PO approximation, i.e.,
K(R') = 2n'× fitnc(_,)
where _ is the unit normal vector and _c is the incident mag-
netic field. For BWG analysis, the approach in this article is
based on a very elegant dyadic Green's function formulation
163
discussed in [4]. For the one-mirror BWG system, the field
scattered by the BWG mirror in the waveguide can be written
as
E = -/_//f_,(R, n') x as' (5)
where G 1 (R, R') is the dyadic Green's function that satisfies
Maxwell's equations and the boundary conditions of the BWG
metal wall, i.e., no field exists outside the BWG wall. For a
cylindrical waveguide, the dyadic Green's function has been
derived and is given in Eq. (15) of [4] as
I=i n=O m=l
E __ _
x (-k)
// 2 [j. t k onm
+
X2Ixk x Nenmo (kx)N'enmo (-kx)
1
- -- zz _ (R - R'), z > 0 (6)
k z
where 6 (R -R') is the Dirac delta function, 6o is the Kro-
necker delta, 60 = 0 if n ¢ 0 and _o = 1 if n = 0, and the
1-summation is over even and odd modes. Note that in Eq. (6),
//, I_, k u, )t, Ix, and k x are understood to have double indices
m and n.
0J(//r) cos nC_]e_/n zMe (h) = -T-nJ(//r) sin n¢?-
o nra r COS ar sm j
(7)
-- 1 I- aJn(Lr) cos.,,,(h)=¥ /h ar sin
o
n¢_7
COS ^]
±jhnJn(Xr)r cosSin_+ h2j(kr) si n nCzJ e-/hz
(8)
lx = J;(')'' =-- Jn 2X 2 r=a (9)
j2 (//r) r dr a2 n2
n 2//2
(10)
In Eqs. (9) and (10), a is the radius of the waveguide, k is the
free-space wave number, and "In is the Bessel function of the
first kind.
To satisfy the radiation condition, when k u
k = I(k 2 -//2)1/21
k x = [(k 2 - X2)1/21
and k x are real,
When they are imaginary (k 2 <//2 k 2 ,(X2),
k = (-]')1(//2 -k2)1/21
kx = (-/)I(X 2 -k2)1/2 I
qnm
// = ldnm a (11)
Pnm
x = x - (12)
nm a
In Eqs. (11) and (12), qnm and Pnm are the mth root ofJn(x )
and/n(x).
J(p.m) = 0
d4(x)
dx
X=qnm
2_
where )'o is the _e-space wavelength.
=0
164
Note that M and N in Eqs. (7) and (8) represent TE and TM
waves propagating in the +z direction. Individually, each mode
satisfies Maxwell's equation, the boundary conditions at the
wall, and the "radiation condition" as z-*"*. It is clear that
Eq. (5) is conceptually the equivalent of PO in the beam-wave-
guide world. The difference is in Green's functions, which
must meet different boundary conditions, including the radia-
tion condition.
IV. Numerical Results and Assessment
The results of the wall analysis of a 34-m antenna under
construction (designated DSS-13 in the DSN) are shown in
Fig. 3. The projected mirror diameter is approximately 2.4 m,
or approximately 19 wavelengths at the analysis frequency of
2.295 GHz. These initial results revealed some exciting poten-
tial for BWG antenna design improvement. A very important
finding is that there are only a few significant modes propagat-
ing between the two curved mirrors. This is despite the facts
that the waveguide diameter is 19 wavelengths, and that a
large number of modes are theoretically above their cutoff
frequencies. As shown in Fig. 3, the electromagnetic (EM)
field scattered from mirror 1 consists of mainly TEll and
TMI 1 modes. This is not surprising, as the incident field is
assumed to be from a horn with a symmetric radiation pat-
tern, similar to that of a corrugated horn. By normalizing the
mode power to the TEll mode, the third and fourth signifi-
cant modes TE21 and TM21 are already about 30 dB down in
power.
Given that hundreds of modes may propagate, this result
must be viewed with some caution. It is encouraging that the
results described above are in qualitative agreement with some
results in [2]. By expanding the reflected field from a curved
mirror in Gaussian modes, the field can be represented approxi-
mately by just two Gaussian modes, TEMoo and TEMol. Note
that the field line of the TEMoo Gaussian mode bears a striking
similarity to that of the aperture field of a dual-mode (TEl1
and TM t 1) horn, with the two modes in appropriate amplitude
and phase relationships. Furthermore, the TEMol Gaussian
mode field lines are similar to the TE21 cylindrical waveguide
mode. These observations are shown in Fig. 4. Thus the results
in [2] are in qualitative agreement with the present analysis
with regard to the scattered field from mirror 1 in the immedi-
ate neighborhood of mirror 1.
The major difference between a Gaussian mode analysis and
the present analysis is that Gaussian modes and cylindrical
waveguide modes propagate with distinctly different charac-
teristics between mirrors 1 and 2. One significant difference is
that the dominant Gaussian TEMoo is seen to be more like two
cylindrical waveguide modes. For large mirror separations,
there is phase slippage between the two cylindrical waveguide
modes not predicted by the TEMoo mode. Clearly, the Gaus-
sian mode analysis is appropriate for BWG systems not en-
closed by metal walls. When it is applied to an enclosed BWG
system, it is a good approximation only while Eq. (1) is valid.
The present analysis is valid when the BWG system is enclosed
in metal walls and does not appear to be bound by Eq. (1), at
least in principle.
A discussion follows of the mechanisms that cause perfor-
mance degradation in an enclosed BWG system. These are
(1) mode generation
(2) mode dispersion
(3) spillover loss at each mirror
(4) multiple scattering between mirrors
(5) dissipative loss in the wall
Assume that an HE11 mode horn or equivalently a dual
TEl i and TM l I mode horn illuminates mirror 1. Each curved
mirror may be viewed as a mode generator whose scattered
field contains unwanted higher-order modes in the sense that
at the output end of the BWG system, only the TEl i and TM_ l
modes in the correct complex ratio are desired. It appears that
mode dispersion is a limiting factor, i.e., propagation with
different phase velocities in the BWG causes the various modes
to appear in wrong phases at the output of the BWG system.
Undoubtedly, the present analysis provides the correct basis
for calculating mode dispersion in an enclosed system com-
pared to existing approaches such as Gaussian mode, PO, GTD,
or others. Mechanisms (4) and (5) listed above have not been
modeled, although a description of dissipative loss that ignores
mechanisms (3) and (4) is within reach in the context of the
present analysis. Ignoring the multiple-scattering mechanism
nonetheless yields good results, as it appears to be much less
important than mode generation and dispersion effects in a
first-order analysis.
In terms of design improvements, the greater accuracy of
the wall analysis model at lower frequencies should lead to
more cost-effective designs of BWG antennas. Specifically, the
diameter of the BWG tube is determined by low-frequency
performance requirements. A less accurate analysis tends to
lead to an unnecessarily large BWG tube, which raises antenna
construction costs. Since a section of the BWG tube runs
parallel to the antenna elevation axis, a larger tube requires
the reflector and its backup structure to be raised higher,
increasing the moment of the reflector and backup structure
about the elevation axis. This reduces the antenna's pointing
performance in wind, which must be compensated for by a
165
heavier, more expensive design. The alternative is that a re-
duced antenna wind pointing performance must be accepted.
In addition, the analytical results showing that there are only a
few significant modes likely between mirrors 1 and 2 suggest
some further improvements to the BWG antenna and feed
design. Since most of the power is in the TEtl and TMll
modes and the differential propagating phase of the modes can
be computed, it appears possible to design a dual-mode or
multimode horn to compensate for the mode generation and
mode dispersion effects discussed above.
Acknowledgments
The author wishes to acknowledge Mr. R. C. Clauss of JPL for many stimulating dis-
cussions pertaining to the BWG wall effects and Mr. M. J. Gans of AT&T Bell Labora-
tories for allowing the use of Fig. 4 in this paper, which is from [2]. Also, J. Schredder
has helped tremendously with software development based on the wall analysis.
References
[1] M. Mizusawa and T. Kitsuregawa, "A Beam Waveguide Feed Having a Symmetric
Beam for Cassegrainian Antennas," IEEE Trans. Antennas and Propagation, vol.
AP-21, pp. 884-886, November 1973.
[2] M. J. Gans, "Cross Polarization in Reflector Type Beam Waveguides and Antennas,"
The Bell System Technical Journal, pp. 289-316, March 1976.
[3] K. K. Chan, "Some Aspects of Beam Waveguide Design," IEEProc., vol. 129, pt. H,
no. 4, pp. 203-210, August 1982.
[4] C. T. Tai, Dyadic Green's Functions in Electromagnetic Theory, Scranton, Pennsyl-
vania: Intext Educational Publishers, 1971.
166
(a)
F1
(b)
F1
J
F2
Fig. 1. Optics of BWG systems: (a) geometric
optics approximation; (b) diffraction analysis
with mirrors in open space.
METHODS OF SOLUTION
PHYSICAL OPTICS
MIRROr,/f_"
/ _--SURFACE CURRENT
57
WHERE
/ = -jwu f K (R') g (R , R') ds'
g(_,_,)= eJkl _ R'I
FREE-SPACE GREEN'S FUNCTION
BWG WALL ANALYSIS
MIRROR
SURFACE CURRENT
E- = -j_u .F_IK ds'
WHERE
_ (_,_,)
=_%_[aM(R) M(R'}+bN(R)N(R')]
_1 IS A SOLUTION OF MAXWE LL'S
EQUATIONS AND SATISFIES
BOUNDARY CONDITIONS
Fig. 2. Enclosed BWG system analysis approaches.
167
HORN ILLUSTRATION LEVEL
ATMIRROR EDGE- 20dB
DSS 13 GEOMETRY
FREQUENCY - 2,295 GHz
MODE POWER CONTENTS
MODE MODE COEFF ICIENTS
TEll 024 + j 0.88 0 d8
EVEN
TM11 0.25 j0.07 10.9 dB
ODD
TE21 -0.01 - j 0.03 -29,6 d8
EVEN
TM21 -0,02 - j 0.0 -33,2 dB
ODD
Fig. 3. Results of one-mirror BWG •y•tem wall analysis.
Y
EO0
FUNDAMENTAL
I
L-----4_
E00
FUNDAMENTAL
GAUSSIAN
MODES
TEMo0 _-
CYLINDRICAL WAVEGUIDE MODES
TEll +TMll
TEM01 _- __ TE21
FEEDHORN VERTICALLY POLARIZED
#Y #Y
I I
+ _.  \Ilf-
+ E01 ETOT
HIGHER ORDER TOTAL
EEEOHORNHOR,ZONTALLYPOLAR,ZED
#Y #Y
+ L -_ _ X
+ E01 ETOT
HIGHER ORDER TOTAL
Fig. 4. Two-mode decomposition of aperture field.
168


A new analysis of beam-waveguide antennas considering the presence of the enclosure

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