2009 IEEE MTT-S International Microwave Workshop Series on
Signal Integrity and High-Speed Interconnects (IMWS2009-R9)
A Simple ADS Schematic for Space Mapping
Qingsha S. Cheng, Member, IEEE, John W. Bandler, Life Fellow, IEEE, and
Slawomir Koziel, Senior Member, IEEE
Simulation Optimization Systems (SOS) Research Laboratory,
McMaster University, Hamilton, ON, Canada L8S 4K1, www.sos.mcmaster.ca
School of Science and Engineering, Reykjavik University, Kringlunni 1, IS-103 Reykjavik, Iceland
implicit or output SM are implemented as four separate
schematics: coarse model optimization, fine model simulation,
parameter extraction, and re-optimization of the surrogate.
In our new methodology, we combine the four schematics
into one schematic. The schematic is partitioned into different
functional blocks (Fig. 1). This way, the optimization results
are saved explicitly in the schematic and no temporary files
are required to transfer data between iterations, except for the
external fine model simulation. The new schematic design is
capable of calling either ADS Momentum or Sonnet em3 as a
fine model.
The new implementation also facilitates manual operation if
preferred. Simply disabling and enabling appropriate blocks
in each step will do the trick.
Depending on the application, extra steps to make the
optimization robust can easily be added into the schematics.
Abstract-In this paper we present a simplified space mapping
implementation in Agilent ADS. All the space mapping steps are
integrated into one ADS schematic. We also describe a generic
sequential optimization implementation method using the
Application Extension Language functions to activate and
deactivate certain design blocks or components to achieve the
necessary automatic iteration and looping. The methodology is
demonstrated through two microwave design examples.
Index Terms-space mapping, electromagnetics-based CAD,
circuit design, microwave modeling.
I. INTRODUCTION
Space Mapping (SM) technology [1] addresses the issue of
reducing the time-consuming full-wave electromagnetic (EM)
simulations of microwave structures with the help of a fast
physics-based model or surrogate for device modeling and
optimization. Many engineers have adopted SM [ 2 ] [ 3 ].
Because SM requires more than one model, implementation is
not straightforward. The first implementation was in OSA901.
A comprehensive Matlab-based framework, the SMF system,
was introduced in 2005 [4].
The purpose of this paper is to introduce a strategy to semior fully-automate the SM process in a simpler way than in [5].
We illustrate our strategy solely in Agilent ADS2, a widelyused Electronic Design Automation (EDA) system for highfrequency and microwave modeling and design applications.
The strategy allows for easy application expansion and
application-dependent algorithm adjustments.
surrogate
PE algorithm
model!
surrogate
fine model
coarse
Fig 1. An ADS schematic including 4 functional blocks.
III. ROBUST PARAMETER EXTRACTION AND COARSE MODEL
OPTIMIZATION
We take a few measures to improve the robustness of the
parameter extraction and surrogate model optimization. The
parameter extraction (PE) process matches the surrogate to the
fine model. In some cases, the traditional gradient-based PE
fails. Therefore, depending on the application, we implement
various two-state PE strategies. Normally, we use the ADS
II. AUTOMATIC SPACE MAPPING ADS IMPLEMENTATION
In [5] an automated four-schematic implementation of the
space mapping technique is described. The steps for input,
This work was supported in part by the Natural Sciences and Engineering
Research Council of Canada under Grants RGPIN7239-06, STGP336760-06,
and by Bandler Corporation.
Q.S. Cheng and J.W. Bandler are with the Simulation Optimization
Systems Research Laboratory, Department of Electrical and Computer
Engineering, McMaster University, Hamilton, ON, Canada L8S 4K1.
J.W. Bandler is also with Bandler Corporation, Dundas, ON, Canada
L9H 5E7.
S. Koziel is with the School of Science and Engineering, Reykjavik
University, Kringlunni 1, IS-103 Reykjavik, Iceland.
1 OSA90/hopeTM version 4.0, User's Manual, August 1997, Optimization
Systems Associates Inc. (now Agilent Technologies), P.O. Box 8083, Dundas,
Ontario, L9H 5E7, Canada.
2Agilent ADS 2005A, Agilent Technologies, 1400 Fountaingrove Parkway,
Santa Rosa, CA 95403-1799, USA.
978-1-4244-2743-7/09/$25.00 C2009 IEEE
optimizabon
algorithm
random search followed by the Quasi-Newton optimization. If
the random search leads to a poor match, we restart our SM
algorithm with a two-stage gradient and/or Quasi-Newton
optimization.
Surrogate optimizations are frequently performed by the
ADS Minimax optimization routine. Occasionally the routine
may get trapped in a local minimum, especially after a
parameter extraction process that brings the surrogate to a
3emTM Version 11.52, Sonnet Software, Inc., 100 Elwood Davis Road, North
Syracuse, NY 13212, USA.
35
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2009 IEEE MTT-S International Microwave Workshop Series on
Signal Integrity and High-Speed Interconnects (IMWS2009-R9)
frequency-shifted design. We use a specification tracking
technique to guide the path of surrogate optimization.
Step 1 Connect the specifications to form a piecewiselinear specification function.
Step 2 Match the piecewise-linear specification function
to the initial surrogate response using a discrete search.
Step 3 Shift the specification function back towards the
original specification in a few stages. In each stage, a
Minimax optimization is applied to the surrogate to satisfy the
intermediate specification. In other words, the piecewiselinear specification function guides the surrogate to a design
that satisfies the original specification in steps (stages).
The specification tracking technique normally works better
in the first space mapping iteration in which the fine model
and the surrogate are usually misaligned in frequency. The
algorithm disengages the specification tracking step for the
follow-up iterations.
Step 1 The script reads a row in the steps list and
deactivates corresponding components described in that row.
Step 2 The script runs a simulation (optimization).
Step 3 The script updates the optimization variables.
Step 4 The script saves the schematic (the resulting
datasets are saved too).
Step 5 If the algorithm is not completed, the script points
to the next row in the list and goes to Step 1.
The user-defined list of deactivation component rows are
shown as follows:
//list of cortpo(emts to be deactivated in each step
IV. SPACE MAPPING AND SEQUENTIAL OPTIMIZATION
Users can replace the above list with any other combination
of components to implement a different algorithm. The
method we show here is much simpler than designing multiple
schematics and including their names in the batch list file in
[5]. Since all the components in each iteration are placed in
the same schematic, it is easier to make changes to the model
and algorithm. The parameter transfer between steps is easily
maintained through the Update Optimization Values
command after each step. Adding new iteration steps is as
simple as adding a line of code.
We connected Sonnet em and Agilent Momentum as fine
models in our space mapping implementation. To drive
Sonnet em from within the ADS schematic, we need to save
the predicted design parameters in a file on the fly, which can
be done using the write_str( function [Agilent Knowledge
Center Example ID: 299744]. The next step (simulate the
structure using the saved design parameters) is easily achieved
by calling the Sonnet em command line in a var component.
Agilent Momentum can be called using co-simulation in the
schematic view. Design parameters and response data are
easily communicated between layout and schematic design.
step2 = list("component 1", "component 3", ...); st row
d row
step2 = list("component 2", "component 4", ...);
=
..)O1rd
row
step3 list("component 1", "component 2",
steps = list(stepl, step2, step3, ...); //list of deactivation rows
decl loop = 0; Hstarting point of the loop, 0 step 1
decl repeat = 0; //number of times to repeat the loop
The space mapping is implemented in 4 major steps as in
[5]. Instead of four separate schematics we use only one
schematic that combines all the necessary SM algorithm
components. We deactivate appropriate components in the
schematic in each step. The fine model is embedded using cosimulation (Momentum) and an external executable (Sonnet
em) call from the ADS schematic.
A. The Space Mapping Algorithm Steps
Step 1 Multi-stage coarse model optimization. [Deactivate
fine model, PE optimization routine, PE goals.] (Use
specification tracking described in Section III, if necessary.)
Step 2 Fine model simulation. [Deactivate coarse model,
coarse model optimization routine, coarse model goals, PE
optimization routine, PE goals.]
Step 3 Multi-stage parameter extraction. [Deactivate
coarse model optimization routine, coarse model goals.]
Step 4 Multi-stage re-optimization of the surrogate.
[Deactivate fine model, PE optimization routine, PE goal.]
(Use specification tracking, if necessary.)
The steps can be implemented manually. We also designed
an AEL4 script to automate the space mapping algorithm steps.
B. General Purpose Sequential Optimization/Simulation Script
We have designed a general purpose sequential
optimization/simulation program in AEL to facilitate
automatically connecting several simulations or optimizations.
To initialize the script, the user creates the necessary
components for all the optimization/simulation steps in an
ADS schematic. The user creates a list of deactivation
component rows in our AEL script. Each iterative step
corresponds to a component row in which the names of the
components to be deactivated are saved. The rows are linked
to become another list called steps. The user specifies the
loop starting point and the number of loops. The user starts
the sequential optimization/simulation AEL script below.
V. DESIGN EXAMPLES
We show two examples of how this is actually implemented.
Our first example is the open-loop ring resonator bandpass
filter [6] shown in Fig. 2. The design parameters are x =
[L1 L2 L3 L4 S1 S2 g]T mm. Other parameter values are: W=
0.6 mm, W1 = 0.4 mm. The fine model is simulated in Agilent
Momentum. The design specifications are IS21 . -3 dB for
2.8 GHz<. < 3.2 GHz, and S21 < -20 dB for 1.5 GHz<. <
2.5 GHz and 3.5 GHz < c < 4.5 GHz. The coarse model is
implemented in Agilent ADS (Fig. 3). Implicit space
mapping is applied. The preassigned parameters (substrate
height and dielectric constant) of the components with the
same hatch pattern change simultaneously in the parameter
extraction process.
4Application Extension Language, ADS internal C-like script language.
978-1-4244-2743-7/09/$25.00 ©2009 IEEE
36
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2009 IEEE MTT-S International Microwave Workshop Series on
Signal Integrity and High-Speed Interconnects (IMWS2009-R9)
w
for input space mapping are the shifts of the design
parameters, i.e., 3xi, i= 1, ..., 8. We combine the input and
implicit space mapping in one parameter extraction step.
7 Output
v
+
*~ ~ ~ ~ ~ ~ ~ ~-
-
S2
1. sL J;
WI~~~~~~~~S
Open-loop Ring filter S-Parameter Simulation
I
Is
Input
Linear Frequency Sweep
S2
t
OT
0w
Surrogate Optimization
OptimType=Mimimax
Maxlt,ers=25
Desire~d"rror0,0
StatusL-evel=4
Fin,alAn,alysis="Non,e"
Nraieol=o
OptVarN2-'SZ''
r3-l"'S'
OptV
OptVarl41--L4`'
OptVaql5j-'L3''
Ota,[
l'1-12`
OptV r7='L'
N-Betalz =ys seIGoals=
yes1ta[]-L1
SaveSolns=yes
SaveCurrentEF=no.
Sa-eGoals=yes
SaveOptimVars=n
UpdateDat.ase=yes
Save
SaveAlNommial=yes
lteations=no
UseAIIOptVars=no.
OptVar[l
Fig 2. Open-loop ring resonator bandpass filter [6] fine model.
MLOC
TL1
W=Wm
L=L1
-L2-L3/2
m
MLIN
MACLIN
SOBND
Bend1
W2-W1 mm
~~~W2=W1
_
MCLINTL3
S=S2 mm
WWmm Clinl
MGAP L=L3
W=W1 mm Gap1
L=L4 mm
W=W1Lmm
Bend3
mm
L-1-3/25mm
S-g mm
l
MLIN
Port
TL7
W=Wmm
L=L1-L2-L3/2
MSOBND
MLINBend7
WWlm
L=L3/2 mm
MACLIN
Wl2=W
=2m
GOL
W=Wl
W=Wl
S=g mm
MSOBND
Bed8
WWlm
,'Ter
.-Num=1
W=Wl mm
MLIN
TL6
W=W1 mm
as3
=
GOAL
Hl=Hl
H_L1l=H_L1
H2-H2
Expr="db(S21)
SimlrstanceName-"SP1".
H_L2=H_L2
H_L4=H_L4
Ohmn
H_S1=H_Sl
Min=-3
Max=
H_S2= H_S2
H_g= H_g
Weight-
Ran,geVa[l ]=''freq'
RargeMin[1]=2.8 GHz!
RargeMax[1]=3.2 GHz:
Z=50 Oh.
N.m=4
~~~Z=50
-77 Li
L=L4 mm
~ Oh.
fine
L1=L1
MLOC
Parameter
L
W-Wmm
PE
OptimType=Ra,d.,,
Fig. 3 Open-loop ring resonator bandpass filter ADS coarse model.
In this example we use one stage surrogate optimization and
two stage parameter-extraction optimization (Random and
Quasi-Newton). The schematic is composed as in Fig. 4. We
list the components to be deactivated.
The first step is the surrogate (coarse model) optimization.
The PE, PEJ and PEGoall and PEGoal2 components in the
Parameter Extraction block are deactivated.
The fine
component is also deactivated.
The second step is fine model simulation. S_Opt and PE,
PEJ are deactivated.
In the third step (the first stage of parameter extraction),
S Opt, SGoall, SGoal2, SGoal3 and PEJ are deactivated.
In the fourth step (the second stage of parameter extraction),
S Opt, SGoall, SGoal2, SGoal3 and PE are deactivated.
After two iterations, we obtained the responses shown in
Fig. 5. The final fine model specification error is -0.392 dB.
We consider a more complicated example, an interdigital
filter design [ 7]. The fine model, shown in Fig. 6, is
implemented in Sonnet em. The substrate height and dielectric
constant are 15 mils and 9.8 respectively. The shielding cover
height is 75 mils. The cell size is set at 1 mil x 1 mil. The
design specifications are IS21 < -30dB for 4.0 GHz
<
c<4.5GHz and for 5.45 GHz <o<6.0GHz and
ISiI < -0.1dB for 4.9 GHz< co < 5.3 GHz.
The initial Agilent ADS coarse model is shown in Fig. 7.
The space mapping approach we adopt is input and implicit
space mapping. In the interdigital filter case, the lengths of
the microstrip lines (X1,X2,X3,X4,X7 and x8) and the gaps (X5
andx6) are defined as design parameters. The implicit space
mapping explores the preassigned parameters in an attempt to
match the details of the surrogate to the fine model. For the
interdigital filter, the preassigned parameter set consists ofcr
(substrate dielectric constant) and capacitors C1 to C6 added
between non-adjacent conductors (cf. Fig. 7). The parameters
Maxlt,rs=25
DesiredError0.0
StatusLevel=4
Fin,alAn,alysis=`None"
NormalzeGoals=no
Se~tBes.tValues=yes
SaveSolns=yes
Sa-eGoals=yes.
S-vOptimVars=n
1-3=L3
OptVar[6]=`H_L2`
OptVar[8]=`H_g`
OptVar[9]=`Er1`
RargeMVat1
OptVar[7]=`H_Ll`
L5=L5
~~~~~6
L6=L
ModelType=MW
iht-
Ra,eVa,
L1=25 4662 Wo
L2-12 6195
OptimType=Quasi-Nevton
25
Maxite,s
Desire)dError=0
StatuLevel=4
0
Fin,alAnalysis="None`
GOAL
N.rnalfizeGoal-.n
SetBes.tValues)=yes
SaveSolns=yes
Sa-eGoals=yes
SaveOpti,,Va-rs=n
Update~Dat-st=yes
Sa-eNomimal=yes
S-vAiteations.=rn
Use~AIIOptVars=rno
OptVar[l1]=`Hl"
S2=0 0932994 o
635{o
H-1=0
H_L2=0
RangeVMin[1]=
RanrgeMax[1]
L=L2--L312
L67=L1-_L2-1-312
Erg=10.2 o
635 M
35 o
H_L2=-0635
H_L4=0
H
63501o
635
H_S10
o
H_S2=0 635 o
H_g=0,635 1.}
Er1=10.2 {o}
Er2=10.2 {ol
ErL1=10 2 {ol
'o}
Er L2=10,2
ErL-4=1012 o
Er Sl=10 2 o
Er S2=I0 2 o
OptVar[J1]="Er
OptVar[12]="Er S1
S2`
OptVar[l13]="Er
OptVar[14]="Er L2"
OptVar[15]="Er Ll"
L4`
OptVar[l16]="Er
Lo
g=0.582939 o
Exp,="imag(S21)-imaag(S43)"
Simlr,stan,c,Na-e=".
Min=-1e-6
OptVar[2]="H2`
UseAIIGoals=yes
OptVar[3]="H_S2" Save~CurrentEF=no
OptVar[4]=`H_Sl`
OptVar[5]=`H_L4"
OptVar[6]="H_L2`
OptVar[7]="H_Ll`
OptVar8=Hg
OptVar[9]="Erl"
OptVar[10]=`Er2`
W0.6
VV=10.4
1-4=3 56046
Sl 261749 {)
S10
HH1=0
opdm
VR6
VAR
G.a
PEGoal2
OptVar[6]="Er_g"
W=W
W1 =Wl
-.
RargeMa
OptVar[l10]=`Er2`
OptVar[1]="Er S2`
~~~~~~~S2-S2
g=9
n
PEGoall
Exp,=r-_m2m
Simlrnsta
c,Name=-I(S43)" 'SP1"~
~ ~
Mir-l1e-6
Max=l1e6
W
UseAIIGoals=yes
OptVar[2]=`lH2`
OptVar3j=`'H_S2` Sav,eCurr,ntEF=no.
OptVar[4]=`H_Sl`
OptVar[5]=`H_L4`
UpdateDataset=yes OptVar12]="Er_S1"
SaveNmial=yes
OptVar1]"E_4
OptVa[4]="Er L2`
S-vA
z
ertions.=rn
UseAIIOptVars=no
OptVa,r[1l5]="Er Ll"
OptVar[l]=`H1"-
L2=L2
Extracticion
~~~~~~~GOAL
Z OPTIM |
L=L2-L3/2
978-1-4244-2743-7/09/$25.00 C2009 IEEE
Z=50
Er2=Er2
Er -L1=Er LI
Er L2=Er L2
Er L4=Er L4
Er Sl=Er S1
Er S2=Er S2
Er g=Er g
g=g
GOAL
Go.1
SGoal3
.--Nm2
E1E1
-L2-1-2
L3=L3
1-4=L4
S1=-S1
S2-S2
Ter.
,'
coase mode_-3
.,Z=50 Oh.
SGoal12
Expr="db(S21 )"
Expr="db(S21 )"
Si, .sta,neName="SP1".
Sim.nstanceName="SPl"
Mi=MsM ax-20
M ax-20
WeightWeightRargeVar[1 ]="fre~q`
R:r,geVa[lI=''f,eq'
RangeMin[1]=15 GI,
Ra,geMi,[l]=3.5 GHz
RangeMax[l]=4.5 GHz
Ran,geMa[l 1=2.5 GHz!
SGoall
hMSOBND
_
Ste~p=0 05 GHz!
Gc,~a
G.al
mm
|
Stat=1 5 GHz
Stop=4,5 GH2z
=g
MGAPBend6
mm
V\/2=Wl mm
L=L3mm
Port2
TL4
Bend4
Y
mm
CIin4
L=L2-L3/2
W=Wl1m
L=L4 mm
mm
Gap2
TL5
mm
W=Wl
L=L4 mm
MLIN
CIin2
W=W1
I
l
MSOBNJD
Bend5
W=Wl
W
MCLIN
mm
W=Wl mm
W=W mm
Bend2
_W
Nm
CIin3
W-=W1 mm
MLIN
TL2
MSO
S-PARAMETERS
pa-at
S
S Opt
g"
00
Fig. 4. ADS space mapping schematic.
J
-2(
1'{.
-4(
-5(0
__
-4
-6(
0n
1.5
2
2.5
3
frequency
(a)
[GHfz]
3.5
4
4.:
4
4.: .5
-0
-20
-3
-40
.5
--
-50
-70
-60
-7
-83
1.5
2
2.5
I__ 1___
3
frequency
[GHfz]
3.5
(b)
Fig. 5. Fine (-) and surrogate ---)
(
responses: (a) after initial
model optimization; (b) after 3 iterations.
37
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coarse
2009 IEEE MTT-S International Microwave Workshop Series on
Signal Integrity and High-Speed Interconnects (IMWS2009-R9)
We start our design using the optimal design from [7]. A
two-stage (Gradient followed by Quasi-Newton) parameter
extraction process is carried out. We can see that the
specification is not satisfied after the first iteration, but the
parameter extraction using input and implicit SM yields a
good match between the coarse and fine models (Fig. 8). The
surrogate (coarse model) is then optimized to predict a new
fine model design. The specification tracking technique is
deployed in the first iteration of surrogate optimization. In
just three SM iterations, a good fine model solution
(specification error -0.08dB) is obtained (Fig. 9). Our
technique connects the steps or iterations, and repeats the loop
automatically. The step-by-step results are saved after each
step.
Fig. 6. Interdigital filter: fine model structure and dimensions [7]; the
dimensions are in mils.
1
W=W
MLIN
L
TL21
il
Interdigital
x
Fig. 7.
ADS
C,fF
filter: coarse modelTinADS.
CsfF
-20
T-1
2
VI. CONCLUSIONS
MLIN
TL17
C,fF
LE
We present a simple ADS schematic implementation of the
space mapping technique. All the space mapping iteration
steps are implemented in one schematic and can be automated
using the AEL script. This makes the space mapping
technology more accessible to microwave engineers. Model
switching and data exchanges between the steps are facilitated
by the new methodology. A generic sequential ADS program
that facilitates connecting and looping for simulation and
optimization is described. The space mapping algorithm is
verified in this sequential ADS optimization schematic. We
demonstrate our scheme using two examples.
ADS
/T-V2
3W-30
L19
/
-70
,,/
-60
REFERENCES
L2 ,W
[1] J.W. Bandler, Q.S. Cheng, S.A. Dakroury, A.S. Mohamed, M.H.
Bakr, K. Madsen, and J. S0ndergaard, "Space mapping: the state
of the art," IEEE Trans. Microwave Theory Tech., vol. 52, no. 1,
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[2] J.C. Rautio, "A space mapped model of thick, tightly coupled
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[3] A. Kashi, P. Kumar, M. Caron, and V. K. Devabhaktuni, "A
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[4] S. Koziel and J.W. Bandler, "SMF: a user-friendly software
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for
space-mapping-based
engineering design
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Bandler
Corp.,
Dundas,
ON,
Canada,
2006,
0
-7--
4.5
4
5
frequency [GHz]
5.5
6
Fig. 8. Interdigital filter initial design using parameters from [7]: the
IS1 and IS211 responses of the
fine model simulation (-) versus the
coarse model after the first parameter extraction (---).
-0
-20
7
'-
'-
http://www.bandler.com/SMF/.
-30
[5] Q.S. Cheng and J.W. Bandler, "An automated space mapping
framework,"
Frontiers
in
Applied
Computational
Electromagnetics FACE 2006 (Victoria, BC, Canada, June 2006).
[6] S. Koziel and J.W. Bandler, "Space mapping with multiple
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Microwave and Wireless Components Letters, vol. 8, no. 1, pp. 13, Jan. 2008.
[7] J.W. Bandler, R.M. Biernacki, S.H. Chen, and Y.F. Huang,
"Design optimization of interdigital filters using aggressive space
mapping and decomposition," IEEE Trans. Microwave Theory
Tech., vol. 45, no. 5, pp. 761-769, May 1997.
-50~~~~~-60
-80
4
4.5
5
frequency [GHz]
5.5
6
Fig. 9. The interdigital filter IS111 and IS211 responses of the fine
model final simulation (-) versus the surrogate model (---).
978-1-4244-2743-7/09/$25.00 C2009 IEEE
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