Automatic design using FD TD simulator in an optimization loop

1
Automatic design using FD TD simulator in an
optimization loop

• Presented by Wojciech K.Gwarek
• with contributions from Malgorzata
  Celuch-Marcysiak, Przemyslaw Miazga, Maciej
  Sypniewski and Andrzej Wieckowski
• the authors are with

Institute of Radioelectronics Warsaw University
of Technology 00-665 Warszawa, Nowowiejska 15/19
Poland E-mail gwarek_at_ire.pw.edu.pl
2
Abstract We discuss the elements of a general
optimization scheme consisting of 1. A
parametric shape editor 2. An FD-TD simulator 3.
An optimizer 4. A goal function calculator The
aim is to discuss the possibilities provided to
engineers by general-purpose tools available
commercially. In particular we examine the
possibilities provided by QWEDs QuickWave-3D
FD-TD simulator and widely used Matlab
toolbox. We discuss particular features of the
FD-TD method applied in electromagnetic
simulations for automatic design purposes, the
sources of errors of analysis and ways to make it
more efficient. We show the results of
automatic design on 5 examples a coaxial
connector, a microstrip to waveguide transition,
a waveguide diode mount, a septum polarizer and a
waveguide filter. In each case we discuss the
sources of errors, the ways to speed up the
optimization process and to enhance the chances
of convergence to a satisfactory solution. We
also provide hints on practical applications.
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General scheme for automatic design using FD TD
simulator in an optimization loop
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General requirements 1. Simulator which -
is fast enough to produce the single simulation
results in seconds or minutes, not in
hours - allows smooth change of the results as a
function of the change in dimensions 2.
Parametric shape editor which is -
universal, allowing a large variety of shapes and
media - easy to use 3. Comprehensive and
programmable goal function calculator 4.
Optimizer which - is relatively insensitive
to rough goal function and preferably -
is able to skip local minimum to look for the
global one.
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Why should we use FD-TD method

• When applied to linear circuits with pulse
  excitation it permits to extract wide-band
  circuit parameters after just one simulation
• It is very fast especially when applied to a wide
  scope of deterministic problems concerning
  S-matrix or radiation pattern extraction. It
  produces acceptable computing times even for
  relatively large problems.
• It has clear physical interpretations giving good
  insight into the operation of the circuit
• It is easy to apply with a variety of media
  forming the analyzed structure
• There are practically no problems with parasitic
  solutions and the algorithms are not sensitive to
  computer round-off errors
• Disadvantages to be fought
• Fast, explicit integration schemes used in time
  domain enforce additional restrictions on meshing
  flexibility
• High-Q circuits (like narrow band filters) need
  special consideration

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Hints how to use FD-TD electromagnetic simulation
in automatic design and/or optimization processes

• whenever possible reduce the number of considered
  dimensions or use symmetry conditions
• if possible perform segmentation and assign
  specific goals to optimization of the specific
  segments
• check carefully the number of needed FD-TD
  iterations avoid exciting off-band resonances
• check the accuracy of the FD-TD approximation
  and continuity of the goal function with respect
  to change of variables
• try to avoid the situation when the change of a
  dimension drastically modifies meshing in
  sensitive areas
• try to economize the computing time by taking
  into account systematic errors
• prior to final setting of the set of variables
  and scaling factors run sensitivity analysis
  and/or grid search to see the type of dependence
  on major variables

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Whenever possible reduce the number of considered
dimensions. Problems presented below are all 2-D
( or more precisely vector 2D)
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Example 1 Optimisation of N to LCM20 coaxial
connector for 0-8GHz band Original commercial
design
Optimised design
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Comparison of the simulated S11 for the original
and the optimized design
ReferenceP.Miazga, W.Gwarek, IEEE Trans MTT, May
1997, pp.858-861
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Example 2 Object Microstrip to waveguide
transitionDesign goal Lowest possible S11 in
the band 10-12 GHz
Microstrip-to-waveguide transition considered in
Example2. Picture shows half of the structure
assuming magnetic symmetry plane in the middle.
Upper and lower waveguide walls are not shown for
clarity of the picture.
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Example 2 (cont)The optimized variables in 2
optionsA One variable optimization with
respect to lstlst1lst2lst3 B Six variable
optimization with respect to lst1,lst2,lst3,hs2,hs
3,sis
Side and upper view of the microstrip to
waveguide transition with parameters as they are
used in optimization
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Example of a parser type parametrized input of a
3-D shape Editor for optimization purposes
aacomment"Microstrip to waveguide
transition" bitmap"nobitmap.bmp" PAR("Name
",oname,"mstowg") PAR("wg width
(wga)",wga,23) PAR("wg height (wgb)",wgb,11) PAR
("ms width (msw)",msw,3.75) PAR("ms height
(msh)",msh,1.27) PAR("ms substr.
width",mssw,30) PAR("ms substrate",med,substr) P
AR("ref. dist. (rd)",rd,7) PAR("length of step1
(lst1)",lst1,6) PAR("length of step2
(lst2)",lst2,6) PAR("length of step3
(lst3)",lst3,6) PAR("height of step2
(hs2)",hs2,7) PAR("height of step3
(hs3)",hs3,3) PAR("substrate insert
(sis)",sis,0) ENDHEADER msl
rd3 wgllst1lst2lst3rd2 wgahwga0.5 mswh
msw0.5 msswhmssw0.5 ltotmslwgl hs1wgb-msh
OPENOBJECT(oname) sis10 if sislt0 do
sis1-sis endif
Microstrip-to-waveguide transition described in
the UDO language by QWED. Header appearing in the
Editor (below) and parts of the UDO code (right)
ELEMENT(z,msh,0,med,substr,IN)
NEWLINE(x,y,xmsl-sis1,y) ADDY(msswh)
ADDX(-mslsis1) CLOSELINE ENDELEM if sisgt0
do ELEMENT(z,msh,0,med,substr,IN)
NEWLINE(xmsl,y,xmslsis,y) ADDY(wgah)
ADDX(-sis) CLOSELINE ENDELEM endif ELEMENT
(zmsh,0,0,metal,strip,IN) NEWLINE(x,y,xmslls
t1,y) ADDY(mswh) ADDX(-msl-lst1)
CLOSELINE ENDELEM .... .... PORT(z,wgb,INPTEMPL
ATE,UP,inpms,rinpms) NEWLINE(x,y,x,ymsswh)
NEWLINE(x,y0.5mswh,x,y) PORTEXC(msh,msh)
GETIOPAR("mstowgi.iop") ENDPORT

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Choice of optimizer Option A an optimizer
specially prepared to work with a particular
simulator (as exemplified belowby the one from
QWED)
Advantage simplicity in use with prepared
dialogues Disadvantage limited flexibility in
choice of the optimization method and the goal
function
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Choice of optimizer Option B a general
purpose optimizer (as exemplified below by the
one from Matlab Toolbox). The text on this and
next slide is a complete code for running a
minimax optimization on 6 variables of the
microstrip to waveguide transition using an FD-TD
Editor and Simulator activated from a DOS command
line
Microstrip to waveguide trans. minimax
method x07.7363 5.7097 7.0488 7.1318 2.8375
0.0578 global spar global start_ch global
best_ch global fbest global first global
iterac fbest1 first1 iterac1 OPTIONS(1)0
display intermediate results OPTIONS(2)0.0001
termination tolerance x OPTIONS(3)0.0001
termination tolerance F OPTIONS(14)2000 max
function call OPTIONS(16)0.003 min change for
grad OPTIONS(17)0.1 max change for
grad OPTIONS(18)1 step length grid
on minimax('ms2wgb',x0,OPTIONS)
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continuation of Matlab script for 6 variables
optimization of the microstrip to waveguide
transition
function w,g ms2wgb(x) global sparglobal
start_ch global best_chglobal fbest global
firstglobal iterac save 'c\3dex\matopt\ms2wgb\p
aramsb' x -ASCII dos('"c\Program
Files\Qwed\Qw_3d\Qw_edi\bin\zed.exe"
-p"c\3dex\matopt\ms2wgb\ms2wgb.pro" -m -o1000 -e
-q -i') dos('"c\Program Files\Qwed\Qw_3d\Qw_sim\
bin\ker1.exe" -t "c\3dex\matopt\ms2wgb\ms2wgb.ta3
"') sparload('c\3dex\matopt\ms2wgb\ms2wgb.spl')
wspar(4181,2)gzeros(1,41) if(first)
first0 start_chspar(,2) end
if(max(w)ltfbest) fbestmax(w)
best_chspar(,2) x fprintf('iterd
min6.2f dB\n',iterac,20log10(fbest)) end plot(
spar(,1)./109,20log10(spar(,2)),'k-',spar(,1)
./109,20 log10(start_ch),'b-',spar(,1)./109,20
log10(best_ch),'g-') grid on iteraciterac1
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Example 2 (cont)The results of optimization of
S11dB versus frequency thin blue line -
initial solution medium green line - results of
one variable optimization thick magenta line -
results of six variables optimization
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Example 3 Matching of a driving point impedande
of a waveguide diode mount Half of the structure
is taken due to magnetic symmetry. We try to
match the impedance to 100 ? (corresponding to
50? for the entire structure) We consider two
cases A) a post made entirely of metal and
short-circuited to the waveguide base B) lower
part of the post made of teflon
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The case A (purely metal post) is resonant and
difficult to match wide band. Figure below
presents the results of calculation after 1000
iterations for two different distances from the
guide short. In the case of a resonant structure
we should assure that - the number of FD-TD
iterations is big enough to limit the ripples
caused by truncated Fourier transform - the step
for gradient calculation of the optimizer is big
enough to get out of the local minima formed by
the ripples Otherwise we are likely to finish
optimization at a local minimum as in the
presented case in which we tried to tune the
matching frequency from 11.6 to 10.44
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Prony Postprocessing One of the solutions to
smoothen the ripples is by using a special
postprocessing like for example the Prony
method. Picture below presents the result of
simulation of S11 versus frequency with 1000
FD-TD iterations of the structure from the
previous slides. The results of direct analysis
(blue) are compared to the results obtained using
QProny algorithm authored by M. Mrozowski .
Application of such a procedure is very valuable
in the analysis of resonators, filters and
multiplexers.
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Results of optimization of the diode mount for
the band 10.5-11.5 GHz
Initial (left) and optimized (right) dimensions
of the diode mount and comparison of their
characteristics of S11 versus frequency .
Optimization was performed on 2 variables
distance of the post from the waveguide short and
height of the teflon part of the post
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Optimization preprocessing - A grid search When
the character of the goal function is difficult
to predict or when we suspect to have multiple
minima, it may be is advisable to run preliminary
calculations on a predefined grid of a pair (or
several pairs) of sensitive variables and plot
the results on a 3-D or 2-D graph as exemplified
below for the Example 3. The waveguide short
distance was assumed to be (3,5,7,9,11) and the
height of the dielectric part of the post to be
(2,4,6,8). White spot on the right picture
presents the point where the minimum has been
found in the optimization process.
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Example 4 A septum polarizer This and the
following slide show a particular design by Saab
Ericsson Space. Next slides show a process of
automatic design of such a device using an
electromagnetic simulator in an optimization
loop.
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Comparison of measurements by Saab Ericsson Space
and simulations by QWED of the phase difference
between the output signal of horizontal and
vertical polarizations (below) and pictures
illustrating propagation of two polarizations at
center frequency (right)
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Segmentation of the polarizer permits to extract
the region of the septum which decides on the
most important parameter - the axial ratio of
circular polarization. Optimization is performed
on seven variables as indicated below.
Imperfect matching can be corrected outside the
septum region in the segment of rectangular
waveguide.
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sparload('c\3dex\matopt\septm3\septm3.spl') ang
difabs(rem(spar(,9)- spar(,12)360,360.0)-95)1
.745 modratabs(spar(,8)./spar(,11)-1)100 aux
zeros(1,61) aux1zeros(1,61) auxatan(angdif(71
131,1)./modrat(71131,1)) aux1abs(sin(aux)) au
xabs(cos(aux)) wangdif(71131,1).aux1(161,1)
modrat(71131,1).aux(161,1)
Matlab script for axial ratio as a goal function
phase difference between vertical and horizontal
polarizations of the optimized polarizer
amplitude ratio of vertical and horizontal
polarisations of the optimized polarizer
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S11 dB versus frequency of the septum part
(right) obtained from its optimization for the
best axial ratio. If the matching of the septum
part is not considered satisfactory it can be
compensated in the guide bent (below left)
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General scheme of segmentation
Attention Segmentation may be in general
multimodal with higher modes being evanescent. In
such a case we face problems of a) definition
of S-matrix with complex reference impedance b)
nonorthogonality of the incident and reflected
power waves Those problems have been thoroughly
treated in the recommended paper R.Marks,
B.Williams - A General Waveguide Circuit Theory,
Journal of Research of NIST, Vol97, No.5
Sept.-Oct. 1992, pp.533-562.
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Change of dimensions may result in modification
of meshing which causes some discontinuity of the
goal function even when conformal FD-TD methods
are applied. We should take care that with
changed dimensions the meshing of sensitive areas
does not change its character. Such sensitive
areas are metal corners like one of the corners
of a septum polarizer presented below. It is
better to use mesh snapping planes to reproduce
the corner always in a similar way (a and b)
than let the software make its arbitrary
decisions about its approximation (c) .Change
between a) and b) is not so drastic as the change
between a and c)a) b) c)
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Results of calculation of the phase difference
between horizontal and vertical polarization
produced by the septum polarizer. 1. thin blue
curve - initial dimensions of the polarizer,
FD-TD cell size 0.5 2. medium green curve -
initial dimensions of the polarizer, FD-TD cell
size 0.15 3. thick magenta curve - optimized
polarizer, FD-TD cell size 0.5 4. v.thick red
curve - optimized polarizer, FD-TD cell size
0.15 Optimization was conducted with cell size
0.5 and goal phase difference 950
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Illustration of the influence of the spectrum of
the exciting pulse on the convergence of the
FD-TD algorithm.
S11 versus frequency of the septum polarizer
excited by a wide-band (? type) pulse observed
after 2000, 3000 and 10000 FD-TD iterations
S11 versus frequency of the septum polarizer
excited by a narrow -band pulse observed after
1100, 1500 and 3000 FD-TD iterations
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Example 5 A 3-resonator waveguide filter The
images present the process of automatic design of
the filter with four variables by a minimax
method.
S11 (up) and S21 (left), both in dB of the
considered filter. Blue lines show the
characteristics for starting conditions and the
red lines the characteristics for final design.
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Conclusions The level of state-of-art
hardware and software has reached the stage, at
which automatic design of a variety of types
microwave circuits using a general purpose FD-TD
simulator and a general purpose optimizer is a
practical alternative for engineers determined
to get better design much faster than by the
classical approaches. However, the success of
such an operation is in many cases not a priori
guaranteed and requires a very conscious use of
both tools and careful choice of their
parameters.This underlines importance of the
exchange of experience of different users and
software vendors like that provided by
contributors to this workshop.