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TUlD-2
EM Based Design Of Large-scale Dielectric Resonator
Multiplexers By Space Mapping
M. A. Ismail, D. Smith, A. Panariello, Y. Wang and M. Yu
COM DEV Space Group, Cambridge, Ontario, N1R 7H6, Canada
Abstraci - A novel design methodology for multiplexer
design is presented. For the first time, finite element EM
based simulators and space-mappiug optimization are
combined to produce an accurate design for manifold
coupled output multiplexers with dielectric resonator @R)
loaded filters. Finite element EM based simulators are used
as a fine model of each multiplexer channel and a coupling
matrix representation is used as a coarse model. Fine details
such as tuning screws are included in the fine model.
Therefore channel dispersion and spurious modes are taken
into account. The DR filter channel design parameters are
kept hounded during optimization. Our approach has been
used to .design large-scale manifold coupled output
multiplexers and it has significantly reduced the overall
tuning time compared to traditional techniques. The
technique is illustrated through design of a IO-channel
output multiplexer with 5-pole DR fiter based channels.
1. INTRODUCTION
In this work, we exploit space-mapping optimization
technique [l] and [Z] to design large-scale manifold
coupled output multiplexers. In DR output multiplexer
design, accurate geometrical dimensions are required in
order to minimize the tuning time of every channel and
hence the overall tuning time of the multiplexer. Finite
element EM simulators can analyze general waveguide
structures and can model (if used carefully) fme details
such as tuning screws and probes. For this reason they are
used as a fine model of each multiplexer channel.
Coupling matrix representation of narrow bandpass filters
[ 3 ] is used as a coarse model. The channel parameters are
kept bounded during space mapping optimization. The
sparsity of the mapping between the design parameters
and the coupling elements has been exploited.
Several authors [4]-[6] have utilized coupling matrix
representation and full wave EM simulators for filter
design. Extension to DR filter or multiplexer design bas
not been considered. A hybrid circuit-full-wave approach
is presented in [7] to design manifold multiplexers without
tuning elements. Full wave optimization of the entire
multiplexer structure is performed in the final step. This
was feasible since the multiplexer considered can be
analyzed by mode matching technique. In case of DR
manifold multiplexer design, it is impractical to perform
full wave optimization of the entire multiplexer structure.
The multiplexer design procedure we propose follows a
hybrid EM circuit optimization approach. It starts by
optimizing the manifold electrical parameters as well as
the coupling elements of all channels to achieve the
required specifications. Then space-mapping optimization
is applied to every channel to evaluate the optimal channel
dimensions. Finally a more accurate multiplexer model is
obtained by replacing the circuit model of each channel
with the corresponding EM s-parameters sweep (at the
optimal channel ~dimensions) over the multiplexer
frequency hand.
The new multiplexer model then
includes channel dispersion and spurious modes. To
account for the effect of dispersion and spurious modes
the new multiplexer model is optimized (with respect to
the manifold dimensions) to achieve the required
specifications.
11. BASICCONCEPTS
A. Channel Models
The coarse model of each multiplexer channel consists
of a network model of a narrow bandpass coupled
resonator filter [ 3 ] (coupling matrix representation) in
addition to two inputioutput transmission lines for
reference plane adjustment (see Fig. 1). The parameters
L I , ZI, L2, Z2 are the lengths and the characteristic
impedances of the input and output transmission lines,
respectively. Ansoft HFSS [ 8 ] is used as a fine model of
the filter channel.
The coupling matrix that satisfies some required
specifications is referred to as the ideal coupling matrix.
It corresponds to the optimal coarse model solution in
space mapping terminology [I]. There exists a mapping
between coupling matrix elements and channel
geometrical parameters. This leads naturally to the use of
space mapping optimization to evaluate the channel
dimensions that correspond to the ideal coupling matrix.
29 1
0-7803-7695-l/03/$17.000 2003 IEEE
2003 IEEE MTT-S Digest
m = P(d)
I
Fig. 1.
(1)
The objective is to find the optimal design parameter
vector d corresponding to an ideal coupling vector m*.
This can be evaluated by solving the nonlinear system of
equations
Resonator
Filter Circuit
Model
p(d)-m* = O
The coarse model of a multiplexer channel.
(2)
As in [I] and [2] this nonlinear system of equations is
solved iteratively using linear approximation of the
mapping in (1).
...
Sh""
UrCYlt
A. Optimization Step Computation
Q
Q
...
The optimization step computation is modified from the
one in [2] to include upper and lower bounds on the
design parameters. The residual r is defined by
r(d)=p(d)-m*
(3)
At the i'th iteration the residual r(d;+s) ,where s is the
optimization step, is approximated by the first two terms
of Taylor series
r(d; +s) = r; + J ; s
(4)
where r,=r(d;),J; is an approximation of the Jacobian of
the mapping p. The optimization step s is obtained by
minimizing the 12- norm of the residual (4) subject to
bounds on the design parameters and a trust region on the
steps
1
2
s = arg min -Ilr,
J , sI12
0
Channel N
channel input5
Fig. 2.
N-channel manifold-coupledoutput multiplexer
B. Multiplexer Model
The multiplexer considered in this work is a manifoldcoupled output multiplexer (see Fig. 2). It comprises a
number of narrow bandpass filters (channels) connected to
a waveguide manifold. The symbol "T-J" denotes either
an H-plane or E-plane waveguide T-junction and "C"
denotes a circuit model of a waveguide transmission line.
In our design procedure the T-junctions are analyzed by
exact mode matching technique. Each channel is either
represented by its coarse model (Fig. 1) or by the sparameters block obtained from the EM simulator. The
algorithm presented in Section IV will make use of both
representation to get the optimal physical dimensions of
all the channels and the manifold
3 2
+
subject to
(5)
IIsII- 5 Ai
I 5di+s <u
where 1 and U are vectors of lower and upper bounds,
respectively and A; is the size of the trust region at the i'th
iteration. The problem in (5) is a quadratic optimization
problem with simple bound constraints. It can be solved
efficiently by the gradient-projection method in [9]. As in
[2] the solution (d;+s) is accepted only if it results in a
reduction in the residual r. Tbe trust region is also
updated according to the criteria in [2]. Broyden formula
[I] is also used to update the Jacobian J. The initial value
of the Jacobian J is approximated by fmite difference
around the initial design parameters.
111. BANDPASS
FILTERCHANNEL
DESIGN
The channel design procedure follows the algorithm in
[2] with some key modifications. In the optimization step
computation we impose lower and upper bound
constraints on the channel design parameters. These
bounds reflect geometrical constraints on the channel
parameters. The sparsity of the mapping between cbannel
geometrical parameters and coupling elements is also
maintained.
Let the vector d of dimension n represent the channel
geometrical parameters. Let the vector m of dimension m
contain all the coupling elements including inputloutput
couplings. We assume that for a channel with a design
parameter vector d there exists a unique coupling vector m
such that the s-parameters of the channel coarse model
(Fig. 1) match those obtained by the EM simulator. There
exists a mapping between m and d
B. Sparsiry of the Matrix J
In waveguide filters changing one geometrical
parameter affects only some specific coupling values and
has little effect on the other couplings. This observation
indicates that mapping p in (1) is sparse (hence the
Jacobian J in'(4).is also sparse). We incorporate this
observation in our technique by keeping the matrix J
292
sparse during Broyden update. The sparsity features can
be deduced from the following practical observations:
1) Changing the inputhutput irises (or probes) affects
only the inpuffoutput couplings and the resonant
frequency of the nearest resonator.
2 ) Changing the parameters of a resonator results only in
changing the resonant frequency of this resonator.
3) Changing an iris (or a probe) between two cavities
results in changing the coupling between the cavities
and the resonant frequencies of the two cavities.
R d coupling for M23
Fig. 3. 5-pole DR filter structure (top view).
1V. MANIFOLD
MULTIPLEXER
DESIGN
Assume that the multiplexer has N channels (see Fig. 2 ) .
The design procedure to evaluate the manifold dimensions
and the channel geometrical parameters are as follows
Step 1. Optimize the overall circuit model of the
multiplexer (manifold parameters and coupling
elements of all channels) to meet the required
specifications. The resulting coupling values are
denoted as ideal couplings.
Step 2 For i = I , 2 , ..., N apply the technique in Section
Ill to evaluate the optimal design parameters of
the i'th channel.
Comment: The starting point for the (i+l)'th
channel can be obtained by extrapolating the
mapping information of the i'th channel.
Step 3 Get a more accurate model of the multiplexer by
replacing the circuit model (coupling matrix) of
each channel with the corresponding sparameters sweep block (computed hy the EM
simulator at the optimal channel design
parameters over the multiplexer frequency band
of interest). Notice that the resulting multiplexer
model takes into account the effect of channel
dispersion and spurious modes.
Step 4 Evaluate the manifold parameters by optimizing
the new multiplexer model to meet the required
specifications. The optimization variables at this
stage are the manifold spacing between channels
and the lengths of the waveguides connecting the
channels to the manifold.
Comment: Notice that by optimizing the new
multiplexer model obtained in Step 3 we adjust
the manifold parameters to compensate for
channel dispersion and spurious modes.
When designing a channel using space mapping
technique a number of EM simulations is needed in order
to get an initial approximation for the Jacobian J in (4).
From experience we notice that the same Jacobian
approximation can be used for adjacent channels as long
as they have comparable normalized coupling values and
bandwidth. Hence the overall number of EM simulations
is significantly reduced.
V. MULTIPLEXER
DESIGNEXAMPLE
To illustrate the multiplexer design procedure we
consider a IO-channel manifold-coupled output
multiplexer in the frequency hand 3.5-4.25 GHz. Eight
channels have a bandwidth of 1.5% and the remaining two
have a bandwidth of 0.8%. Every channel is a 5-pole DR
filter shown in Fig. 3. The input/output waveguides are
coupled to the first and fifth resonators, respectively
through double ridged irises. All couplings are realized
by rectangular irises except the coupling M2,3 which is
realized by a rod coupling [IO] (see Fig. 3) for power
handling consideration. AnsoA HFSS [8] is used as a fine
model of every channel and the network model in Fig. 1 is
used as a coarse model. Tuning screws are added to a
nominal depth to maximize the tuning range. The Tjunctions connecting the channels to the manifold are
analyzed by mode matching.
Ideal channels coupling values are obtained in the fust
step of the design procedure in Section 1V. Spacemapping optimization (Section 111) is then applied to each
channel to get the optimal channel dimensions. For
example, the results of applying space-mapping
optimization to the first channel are shown in Fig. 4 (7
iterations are required). Each channel is then replaced by
the corresponding s-parameters sweep obtained by HFSS
at the optimal channel dimensions. As a result the new
multiplexer model includes channel dispersion and
spurious modes. Finally the manifold parameters are reoptimized to meet the required specifications. Fig. 5
compares between the multiplexer ideal response and the
EM response where every channel is replaced by its
simulated s-parameters (by Ansoft HFSS). The measured
response of the multiplexer is shown in Fig. 6. The
spurious modes predicted by EM analysis in Fig. 5
correlate very well with the measurements in Fig. 6.
~
293
VI. CONCLUSION
-60
A new design methodology for DR based channel
output multiplexers has been presented. Space-mapping
optimization has been used tn design the multiplexer
channels. Finite Element EM based simulators are used as
a fine model of every channel and coupling matrix
representation is used as a coarse model. Fine details such
as tuning screws are included in the design process. The
design procedure results in accurate design of DR
A IO-channel output multiplexer is
multiplexers.
presented to illustrate the multiplexer design procedure.
~
ACKNOWLEDGEMENT
The authors would like to thank R. Granlund and S.
Lundquist, COM DEV Space Group, Cambridge, Canada,
for useful discussions during the course of this work.
0
REFERENCES
[I]J.W. Bandler, R.M. Biemacki, S.H. Chen, R.H. Hemmers
and K. Madsen, “Electromagnetic optimization exploiting
aggressive space mapping,” IEEE Trans. Microwave
Theory Tech., vol. 43, 1995, pp. 2874-2882.
[2] M.H. Bah, J.W. Bandler, R.M. Biemacki, S.H. Chen and
K. Madsen, “A trust region aggressive space mapping
algorithm for EM optimization,” lEEE Trans. Microwave
Theory Tech., vol. 46,1998, pp. 2412-2425.
[3] A.E. Atia and A.E. Williams, ‘Warrow-handpasswaveguide
filters.” IEEE Trans. Microwave Theon, Tech.. vol. MTT20, 1972, pp. 258-265.
141
. _P. Harscher. E. Ofli. R. Vahldieck and S . Amari. “EMSimulator based parameter extraction and optimization
techniaue for microwave and millimetre wave filters.”
IEEE h - S Int. Microwove Symp. Digest (Seattle, WA),
2002. DD. I 1 13-1116.
[5] W. Hauth. D. Schmitt and M. Guglielmi, “Accurate
modeling of narrow-band filters for satellite
communication,” IEEE MTT-S Inf. Microwave S y ” .
Digest, 2000, pp. 11671770.
[ 6 ] S.F. Peik and R.R. Mansour, “A novel design approach for
microwave planner filters,” IEEE MTT-S Int. Microwave
Symp. Digest, 2002, pp. 1109-1112.
[7] L. Accatino and M. Mongiardo, “Hybrid circuit-full-wave
computer-aided design of a manifold multiplexers without
Nnina elements,” IEEE Trans. Microwave Theory Tech.,
vol. CO, 2002, p 2044-2047.
.181. AnsoA HFSS . Ver. 8.0.25. AnsoA Comoration, Four
Station Square Suite 200, Pittsburgh, PA 15219-1119.
[9] J. Nocedal and S.J. Wright, Numerical Optimization. New
York Springer-Verlag, Inc., 1999.
[IO] D. Smith, “Filter utilizing a coupling bar,” USA Patent,
Pat. N. US 6,255,919 BI, 2001.
-20
B
I
-40
2
-60
-80
3.55
3.75
3.95
4.15
Frequency (GHr)
4.35
4.5
Fig. 5. The ideal response of the 10-channel DR multiplexer
(solid line) versus the EM response (doned line).
0
-20
B
S -40
2
R.
-60
-80
3.55
3.75
3.95
4.15
Frequency (Om)
4.35
4.5
Fig. 6. Measured response of the IO-channel DR multiplexer.
294
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