Research Journal of Applied Sciences, Engineering and Technology 4(6): 670-674, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: December 06, 2011
Accepted: December 26, 2011
Published: March 15, 2012
Application of Implicit Space Mapping in the Design of Hammerhead Filter in
Millimeter-Wave Band
Fuqun Zhong, Bo Zhang, Yong Fan, Minghua Zhao and Guan Gui
School of Electronic Engineering, University of Electronic Science and Technology of China,
Chengdu, 611731, China
Abstract: In this study, we present advances in microwave and millimeter-wave device modeling exploiting
the Space Mapping (SM) technology. New SM-based modeling techniques are used that are easy to implement
entirely in the Agilent ADS framework. The implicit space mapping algorithm is applied to the design of
hammerhead filter in millimeter-wave band. The validity of this method is confirmed by comparison with fullwave EM simulation result and measured data. Based on the proposed method, a filter was designed and
fabricated on a substrate with thickness of 0.254 mm and dielectric constant of 2.2. The experimental results
show good agreement with simulated results. It is proved that the accuracy can be achieved using the implicit
space mapping algorithm, and the design efficiency can be greatly improved.
Key words: Accuracy and high efficiency, hammerhead filter, implicit space mapping algorithm
INTRODUCTION
of reducing CPU demand. Implicit Space Mapping (SM)
technology (Bandler et al., 2004) 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. In the design of microstrip
hammerhead filter, coarse models are realized in Agilent
ADS. We use HFSS as the fine model evaluators. Agilent
ADS schematics organize the ADS optimization engine
and coarse and fine models to perform parameter
extraction and surrogate optimization.
In this study, we adopt the simplified space mapping
implementation in Agilent ADS, all the space mapping
steps are integrated into ADS schematic. The processing
of design for microstrip hammerhead filter was described.
Filters play an important role in the successful
operation of millimeter and submillimeter-wave mixers
and frequency multipliers (Xue et al., 2003; Marsh
et al., 2007; Porterfield, 2007; Maestrini and Ward, 2008;
Zhang et al., 2011; Zhong et al., 2011a,b). Many simple
filters can be designed with direct full-wave
electromagnetic (EM) simulation optimization. However,
occasionally it is necessary to achieve a larger bandwidth
of operation and a greater level of stopband rejection
which often involves the use of more complicated filter
geometries which would spend so much time doing the
direct EM optimization. The relative simplicity and
flexibility of the implicit space mapping algorithm make
it a particalarly attractive tool for design of these more
complex circuits.
The microstrip hammerhead filter has been an
attractive candidate for use in wide stop-band mixer and
frequency multiplier circuits since its introduction many
years ago (MaMaster et al., 1976). Compared with the
traditional low-and-high-impedance microstrip filter, the
microstrip hammerhead filter is characterized by lowinsertion loss, sharp rejection, shorter size and wider stopband. These superior characteristics can be used to
improve the performance of the mixer and multiplier in
microwave and millimeter-wave band. However, complex
structures, too much variables and absence of a simple
and quick method for design have hindered its widespread
use.
Electromagnetic (EM) simulation is accurate, but
CPU intensive; hence, using a full-wave EM simulators
such as Ansoft HFSS, or Agilent Momentum, in the hope
Implicit space mapping algorithm: The formulation of
the implicit space mapping algorithm is presented in
(Bandler et al., 2004; Cheng et al., 2009).
A fine model optimal solution can be expressed as:
x * = arg min U ( R f ( x ))
x
(1)
where, Rf (x) is fine-model response vector, U is typically
a minimax objective function with upper and lower
specifications (Zhu et al., 2007), x is fine-model design
parameters, and x* is the optimal design to be determined.
In order to solve Eq. (1), the following iterative
procedure is used by implicit space mapping:
x k +1 = arg min U ( Rc ( x , p k ))
x
(2)
Corresponding Author: Fuqun Zhong, School of Electronic Engineering, University of Electronic Science and Technology of
China, Chengdu, 611731, China
670
Res. J. Appl. Sci. Eng. Technol., 4(6): 670-674, 2012
where, Rc (x, p) is a response vector of the coarse model
with x and p being the design variables and preassigned
parameters, respectively, Rc (x, pk) is an implicit space
mapping surrogate model with preassigned parameters pk
obtained at iteration k using the parameter extraction
procedure.
p k = arg min R f ( x k ) − Rc ( x k , p)
(3)
p
In which we try to match the surrogate to the fine
model. The initial surrogate model is
Rc (x, p0), where p0 represents the initial preassigned
parameter values. In other words, the surrogate model is
the coarse model with updated values of the preassigned
parameters. From the above derivation of the formulation
of the implicit space mapping algorithm, we can find that
our goal is to obtain the fine model optimal design
without going to direct optimization of the fine model but
instead using the surrogate model; i.e., the coarse model
with updated values of the preassigned parameters.
Parameter extraction and design optimization are
performed solely on the surrogate model. A prediction of
the next fine model design is also obtained through the
surrogate.
Fig. 1: The structure of microstrip hammerhead filter.
ADS schematic design framework: We implement
implicit space mapping optimization in the ADS
schematic framework in an interactive way to greatly
raise efficiency of microstrip hammerhead filter design.
The space mapping implemented in 5 steps is as fellows:
Step 1: Set up and optimize the coarse model in ADS
schematic
Step 2: Create the parameterized fine model in HFSS,
the structure dimension is same as the value
obtained in Step1
GOAL
Goal
OptimGoal6
Expr="sub_wide"
SimInstanceName="S P1"
Min=
Max=9
Weight=1000
RangeV ar[1]=
RangeMin[1]=
RangeMax[1]=
S-P ARAMETERS
MSub
S_Param
SP1
Start=0 GHz
Stop=9 GHz
Step=1 GHz
Meas
Eqn
MSUB
MSub1
H=1.27 mm
Er=2.2
Mur=1
Cond=5. 8E+7
Hu=3.73 mm
T=90 um
TanD=0. 0009
Var
Eqn
MeasEqn
Meas1
sub_wide=W1+2* W3+2*L2
banch_long=L2-L4
structure=L1-W3-L3
cent er_structure=L5-2*(L3+W3)
V AR
V AR1
GOAL
W1=1.65728 {o}
L4=0.8147 {o}
W2=0.603471 {o}
W3=1.13307 {o}
L3=1.85819 {o}
L1=4.09479 {o}
L5=10.8342 {o}
L2=2.51905 {o}
Rough=0 mil
W=0. 7 mm
L=1 mm
Min=1
Max=
Weight=1/0. 01
RangeVar[1]=
RangeMin[1]=
RangeMax[1]=
MCORN
Corn2
Subst="MSub1"
Subst="MSub1"
W=W3 mm
L=L3 mm
TL3
Subst="MS ub1"
W=W2 mm
L=L2 mm
MLIN
TL2
Subst="MSub1"
MSTEP
Step2
Subst="MS ub1"
W1=W1 mm
W2=0.7 mm
W=W1 mm
L=L1 mm
MLIN
TL9
S ubst="MSub1"
W=W3 mm
L=L3 mm
MLOC
TL26
Subst="MSub1"
W=W3 mm
L=L4mm
L=L4 mm
Subst="MSub1"
W=W3 mm
L=L3 mm
TL29
Subst="MSub1"
W=W2 mm
L=L2 mm
W=W1 mm
L=L5 mm
W1=W1 mm
W2=W2 mm
W3=W1 mm
W4=W2 mm
MLIN
TL11
Subst="MSub1"
W=W3mm
L=L3 mm
MCORN
Corn4
Subst="MSub1"
W=W3 mm
MCORN
Corn12
Subst="MSub1"
W=W3 mm
Fig. 2: The coarse model in ADS
671
MCORN
Corn9
Subst="MSub1"
Subst="MSub1"
W=W3 mm
L=L3 mm
W1=W1 mm
W2=W2 mm
W3=W1 mm
W4=W2 mm
MTE E_ADS
Tee2
Subst="MSub1"
W1=W3mm
W2=W3mm
W3=W2mm
SaveSolns=yes
SaveGoals=yes
SaveOptimVars=no
UpdateDataset=yes
MLIN
MCROSO
Cros2
S ubst="MSub1"
MLOC
TL31
Subst="MSub1"
W=W3 mm
L=L4 mm
UseAllGoal s=yes
SaveCurrentEF=no
SaveNominal=no
SaveAllIterations=no
UseAllOptV ars=yes
MLIN
TL27
MLIN
TL13
S ubst="MSub1"
MLOC
TL12
Subst="MSub1"
W=W3 mm
L=L4 mm
Optim
Optim1
OptimType=Random
MaxIters=10000
DesiredError=0.0
StatusLevel=4
FinalAnalysis="SP1"
NormalizeGoals=no
SetBestValues=yes
Seed=
W=W3mm
MLIN
TL28
MLOC
TL8
Subst="MSub1"
W=W3 mm
Goal
OptimGoal5
Expr="center_structure"
SimInstanceName="SP1"
Min=1
Max=
Weight=1/0.01
RangeVar[1]=
RangeMin[1]=
RangeMax[1]=
MTEE_ADS
Tee5
Subst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MCORN
Corn10
S ubst="MSub1"
W=W3 mm
OPTIM
GOAL
Goal
OptimGoal4
E xpr="structure"
S imInstanceName="SP1"
Min=1
Max=
Weight=1/0.01
RangeVar[1]=
RangeMin[1]=
RangeMax[1]=
MCROSO
Cros1
Subst="MSub1"
MLIN
TL4
Subst="MS ub1"
W=W2 mm
L=L2 mm
MLOC
TL10
S ubst="MSub1"
W=W3 mm
L=L4 mm
MCORN
Corn3
Subst="MSub1"
W=W3 mm
Min=
Max=-25
Weight=1
RangeVar[ 1]="freq"
RangeMin[ 1]=7 GHz
RangeMax[1]=9 GHz
MLIN
L=L4 mm
MLIN
TL1
Subst="MSub1"
Min=
Max=-20
Weight=1/0.09
RangeVar[1]="freq"
RangeMin[1]=0 GHz
RangeMax[1]=3 GHz
MLIN
TL6
Subst="MS ub1"
W=W3 mm
L=L3 mm
MLOC
TL7
Subst="MSub1"
W=W3 mm
Term
Term1
Num=1
Z=50Ohm
Goal
OptimGoal3
Expr="banch_long"
SimInstanceName="SP1"
W=W3 mm
MLIN
TL5
GOAL
GOA L
Goal
OptimGoal 2
Expr="dB(S (2,1))"
SimInstanceName="SP 1"
MTEE_ADS
Tee1
Subst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MCORN
Corn1
Subst="MS ub1"
W=W3 mm
GOAL
Goal
OptimGoal1
E xpr="dB(S(1,1))"
S imInstanceName="SP1"
L=L4 mm
MS TEP
Step12
Subst="MSub1"
W1=W1 mm
W2=0.7 mm
MLIN
TL34
Subst="MSub1"
W=W2 mm
L=L2 mm
MLIN
TL33
Subst="MSub1"
W=W3 mm
L=L3 mm
MLOC
TL25
Subst="MSub1"
W=W3 mm
MLOC
TL30
Subst="MSub1"
W=W3 mm
L=L4 mm
MTEE_A DS
Tee6
Subst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MLIN
TL32
Subst="MSub1"
W=W3 mm
L=L3 mm
MCORN
Corn11
Subst="MSub1"
W=W3 mm
MLIN
TL24
Subst="MSub1"
W=0.7mm
L=1 mm
Term
Term2
Num=2
Z=50 Ohm
Res. J. Appl. Sci. Eng. Technol., 4(6): 670-674, 2012
S-PARAMETERS
MLOC
TL7
Subst="MSub1"
W=W3 mm
L=L4 mm
Term
Term1
Num=1
Z=50 Ohm
MLIN
TL1
Subst="MS ub1"
W=0.7 mm
L=1mm
MLIN
TL5
S ubst="MSub1"
W=W3 mm
L=L3 mm
MCORN
Corn2
Subst="MSub1"
W=W3 mm
MLIN
TL6
Subst="MSub1"
W=W3 mm
L=L3 mm
MCORN
Corn3
Subst="MSub1"
W=W3 mm
MLIN
TL9
Subst="MSub1"
W=W3 mm
L=L3 mm
MLOC
TL12
Subst="MSub1"
W=W3 mm
L=L4 mm
MTEE_ADS
Tee2
Subst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MLIN
TL11
Subst="MSub1"
W=W3 mm
L=L3mm
Term
Term3
Num=3
Z=50 Ohm
VA R
VA R2
E1=2.0213 {o}
H1=0.539067{o}
MCORN
Corn9
S ubst="MSub1"
W=W3 mm
MLIN
TL28
Subst="MS ub1"
W=W3mm
L=L3 mm
MLIN
TL27
Subst="MSub1"
W=W3 mm
L=L3 mm
MLIN
TL29
Subst="MS ub1"
W=W2 mm
L=L2 mm
MLOC
TL25
Subst="MSub1"
W=W3 mm
L=L4 mm
MSTEP
S tep12
S ubst="MSub1"
W1=W1 mm
W2=0.7 mm
MCROSO
Cros2
S ubst="MSub1"
W1=W1 mm
W2=W2 mm
W3=W1 mm
W4=W2 mm
MLIN
TL34
Subst="MS ub1"
W=W2mm
L=L2 mm
MLOC
TL31
Subst="MSub1"
W=W3 mm
L=L4 mm
MCORN
Corn4
Subst="MSub1"
W=W3 mm
Var
Eqn
MTE E_ADS
Tee5
Subst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MCORN
Corn10
Subst="MSub1"
W=W3 mm
MLIN
TL13
S ubst="MSub1"
W=W1 mm
L=L5 mm
MLIN
TL4
S ubst="MSub1"
W=W2 mm
L=L2 mm
MLOC
TL10
Subst="MSub1"
W=W3 mm
L=L4 mm
Goal
OptimGoal1
Expr="abs(db(S(2,1))-db(S(4,3)))"
SimInstanceName="SP 1"
Min=
Max=0
Weight=
RangeV ar[1]=
RangeMin[1]=
RangeMax[1]=
MLOC
TL26
S ubst="MSub1"
W=W3mm
L=L4 mm
MCROSO
Cros1
Subst="MSub1"
W1=W1 mm
W2=W2 mm
W3=W1 mm
W4=W2 mm
VAR
VAR1
W1=1.66 {-o}
L4=0.81 {-o}
W2=0.6 {-o}
W3=1.13 {-o}
L3=1.86 {-o}
L1=4.09 {-o}
L5=10.83 {-o}
L2=2.52 {-o}
Var
Eqn
GOAL
Optim
Optim1
OptimType=GradientSaveCurrentEF=no
MaxIters=100
DesiredError=0.0
S tatusLevel=4
FinalAnalysis="S P1"
NormalizeGoals=no
S etB estV alues=yes
S aveS olns=yes
S aveGoals=yes
S aveOptimVars=no
UpdateDataset=yes
S aveNominal=no
S aveA llIterations=no
UseAllOptV ars=yes
UseAllGoals=yes
MLOC
TL8
Subst="MSub1"
W=W3 mm
L=L4 mm
MLIN
TL3
S ubst="MSub1"
W=W2 mm
L=L2 mm
MLIN
TL2
Subst="MSub1"
W=W1 mm
L=L1 mm
MSTEP
S tep2
S ubst="MSub1"
W1=W1 mm
W2=0.7 mm
MSUB
MSub1
H=H1mm
E r=E1
Mur=1
Cond=5.8E+7
Hu=3.73 mm
T=90 um
TanD=0.0009
Rough=0 mil
MTEE_ADS
Tee1
Subst="MS ub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MCORN
Corn1
S ubst="MS ub1"
W=W3 mm
OP TIM
MSub
S_Param
SP1
Start=0 GHz
Stop=9 GHz
Step=1 GHz
MCORN
Corn12
Subst="MS ub1"
W=W3 mm
MLIN
TL33
Subst="MS ub1"
W=W3 mm
L=L3 mm
MLIN
TL24
Subst="MSub1"
W=0.7 mm
L=1mm
Term
Term2
Num=2
Z=50 Ohm
MLOC
TL30
Subst="MSub1"
W=W3mm
L=L4 mm
MTEE_A DS
Tee6
S ubst="MSub1"
W1=W3 mm
W2=W3 mm
W3=W2 mm
MLIN
TL32
Subst="MSub1"
W=W3 mm
L=L3 mm
MCORN
Corn11
S ubst="MSub1"
W=W3 mm
Term
Term4
Num=4
Z=50 Ohm
S2P
SNP 1
File="C:\design_THz\wenzhang\cmrc_SM\cmrc_ori_scale_model_ori.s2p"
1
2
Re f
Fig. 3: Parameter extraction in ADS
Surrogate responses
Fine responses
Surrogate responses
Fine responses
20
0
0
-20
-20
| S21| in dB
| S21| indB
20
-40
-40
-60
-60
-80
-80
-100
-100
0
1
2
3
7
5
6
4
Frequence (GHz)
8
9
0
10
(a)
1
2
3
7
5
6
4
Frequence (GHz)
8
9
10
(b)
Fig. 4: (a) The response of our initial tuning model and fine model,. (b) The response of our tuning model and fine model after the
first iteration
of the fine model and coarse model is very
small; if
Step 3: Simulate the fine model and import the S
parameter into ADS. Check the stopping criteria
which are that the difference between responses
satisfied, stop. Otherwise, optimize ADS coarse
model to match fine model to perform parameter
extraction
Step 4: Reoptimize the calibrated coarse model design
parameters to predict the next fine model design
Step 5: Update the fine model design and go to Step3
0.254 mm, dielectric constant is er = 2.2, loss tangent is
0.0009, and the metallization is copper. The design
specifications are # S11#< - 15 dB for DC #w#15 GHz, and
# S21##- 25 dB for 35GHz #w# 45GHz.
Because the microstrip hammerhead filter works at
high frequency, we use the scale model with scale factor
of 5 to improve the accuracy of the coarse model in ADS.
In this design, the fine model is simulated in Ansoft
HFSS, the coarse model is constructed and optimized in
Agilent ADS (Fig. 2).
The initial guess is x(0) = [4.09, 2.52, 1.86, 0.81,
10.83, 1.66, 0.6, 1.13]T, the response of our initial tuning
model and fine model is shown in Fig. 4a. One of the
most important steps, parameter extraction, is
implemented entirely in ADS (Fig. 3). We compensate the
deviation between the tuning model and the fine model
Design of microstrip hammerhead filter: Microstrip
hammerhead filter with a rogers 5880 substrate is shown
in Fig. 1. Design parameters are x = [L1, L2, L3, L4, L5,
W1, W2, W3]T mm. Thickness of the substrate is H =
672
Res. J. Appl. Sci. Eng. Technol., 4(6): 670-674, 2012
model and the corresponding fine model are shown in
Fig. 5. Clearly, difference between responses of the fine
model and coarse model is very small. After structure
dimensions of the scale model are divided by the scale
factor of 5, we can get the final microstrip hammerhead
filter satisfying the design specifications, which will be
fabricated in section 5.
Surrogate responses
Fine responses
10
|S21| in dB
0
-10
-20
-30
Filter measurement: The hammerhead filter is fabricated
using current microelectronics technology without any
additional process, and the entire physical configuration
of filter circuit is shown in Fig. 6a, The dimensions of
microstrip hammerhead filter are as follows: L1 = 0.5
mm, L2 = 0.71 mm, L3 = 0.2 mm, L4 = 0.24 mm, L5
=1.53 mm, W1 = 0.18 mm, W2 = 0.1 mm, W3 = 0.1 mm.
The measured S-parameter is shown in Fig. 6b. The LPF
with two hammerhead cells in series has a 25 GHz
stopband from 25 to 50 GHz. This achieves above 100%
(-10 dB) relative bandwidth. As can be seen from Fig.
6b, the insertion loss from DC to 20 GHz is less than 1.1
dB, and the return loss is better than 18 dB in the
passband.
-40
-50
0
1
2
3
7
5
6
4
Frequence (GHz)
8
9
10
Fig. 5: The optimized tuning model and the corresponding fine
model responses.
CONCLUSION
In this study we reviewed the implicit space mapping
concept and adopt the simplified space mapping
implementation in Agilent ADS, all the space mapping
steps are integrated into one ADS schematic. A detailed
and easy-to-follow design optimization procedure was
provided and the Agilent ADS implementation of the
algorithm was described. Implicit SM algorithm greatly
improves the efficiency of the design of complex
structure. It will create favorable conditions for the
widespread use of microstrip hammerhead filter in field of
mixer and frequency multiplier.
(a)
|S21| in dB
0
-20
-40
-60
ACKNOWLEDGMENT
-80
0
10
20
40
Frequence (GHz)
50
This study is supported by the National Natural
Science Foundation of China under Grant No.61001030
and supported by The Fundamental Research Funds for
the Central Universities under Grant No. ZYGX2009J022
60
(b)
Fig. 6: (a) Photograph of hammerhead filter, (b) The
measurement result of hammerhead filter
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