tuning space mapping: the state of the art

Tuning Space Mapping: The State of the Art

Qingsha S. Cheng,1 John W. Bandler,1 Slawomir Koziel2

1 Simulation Optimization Systems Research Laboratory, Department of Electrical and ComputerEngineering, McMaster University, Hamilton, ON L8S 4K1, Canada

2 School of Science and Engineering, Reykjavik University, 101 Reykjavik, Iceland

Received 31 August 2011; accepted 20 December 2011

ABSTRACT: The electromagnetic (EM)-simulator-based tuning process for rapid microwave

design can combine EM accuracy with circuit-design speed. Our own approach is based on

the intuitive engineering idea of ‘‘space mapping.’’ In this article, we explain the art of

microwave design optimization through ‘‘tuning space mapping’’ procedures. We list various

appropriate types of models (called ‘‘surrogates’’). We demonstrate the implementation

of these surrogates through a simple bandstop filter. We provide application examples

using commercial simulation software. Our purpose is to help microwave engineers

understand the tuning space mapping methodology and to inspire new implementations and

applications. VC 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 00:000–000, 2012.

Keywords: computer-aided design (CAD); engineering optimization and modeling; EM-based

design; tuning space mapping; surrogate models; design tuning

I. INTRODUCTION TO TUNING SPACE MAPPING

The use of accurate and computationally-intensive full-

wave electromagnetic (EM) simulation is now taken for

granted by the microwave industry. Although computers

become ever more powerful, microwave engineers are

faced with still larger design problems, tighter specifica-

tions, and shorter closure time requirements. Thus, EM-

based design remains challenging.

The EM-simulator-based tuning method [1, 2] is a fast

tuning or design approach that combines EM accuracy

with circuit speed. The method allows easy tuning and

instantaneous visualization of the EM-simulated responses

of a structure. The heart of the method is the hybridization

of EM simulation and circuit simulation in one structure

(a tuning model). It is achieved by replacing part of the

EM-simulated structure with equivalent circuit (physics-

based) models or by numerical approximations (predefined

physics-based models are preferable for their minimum

sample data requirements).

Space mapping [3] techniques also target fast but accu-

rate EM-based designs. They exploit surrogates to model

or to iteratively optimize a computationally-intensive EM-

simulated structure (‘‘fine’’ model). The surrogate models

themselves are constructed from a so-called ‘‘coarse’’

model, a less accurate but cheaper to evaluate representa-

tion of the fine model (e.g., an equivalent circuit).

The terms ‘‘tuning’’ and ‘‘space mapping’’ have been

mentioned together [4, 5] in a context where a coarse

model or surrogate is ‘‘tuned’’ within a space mapping

based algorithm. There, only circuit-based surrogates are

tuned. In this article, however, our tuning space mapping

algorithms combine the advantages of the EM-simulator-

based tuning concept with space mapping technology to

bring them to a new level in the realm of engineering

design and modeling. Tuning space mapping algorithms

exploit physics-based tuning models (EM-simulated mod-

els plus tuning components) as surrogates. The surrogates

approximate the full-wave EM simulation responses in an

iterative space mapping updating process, the same way

as do other space mapping approaches.

A tuning space mapping algorithm involves a fine

model (e.g., a full-wave EM simulation), auxiliary fine

models (fine models with tuning ports), a tuning model,

and a calibration scheme that sometimes exploits an extra

calibration (coarse) model. We may induce infinitesimal

tuning gaps (negligible compared with the wavelength)

into the fine model. We add tuning ports into the induced

gap edges or boundary of the fine model to form candi-

date auxiliary fine models. We insert or attach suitable

tuning elements to the tuning ports. Preferably, the tuning

elements are distributed circuit elements with physical

dimensions corresponding to those of the fine model. A

new structure bearing tuning elements is called a tuning

Correspondence to: Q. S. Cheng; e-mail: [email protected]

VC 2012 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20621Published online in Wiley Online Library

(wileyonlinelibrary.com).

1

model or surrogate. After a simple alignment (also known

as parameter extraction or PE) procedure, we match the

tuning model with the fine model. Some of the fine-model

couplings are preserved (or represented through S-parame-

ters) in the tuning model. We normally obtain a good sur-

rogate of the fine model. In the next stage, the tuning

model is optimized by varying the design parameter val-

ues of the embedded tuning elements to satisfy given

design specifications. The obtained design parameter val-

ues constitute our next fine model iterate.

Figure 1 General tuning space mapping flowchart. [Color figure

can be viewed in the online issue, which is available at wiley

onlinelibrary.com.]

Figure 2 Type 0– tuning space mapping. Tuning ports are

created at the boundary of the fine model: (a) tuning of individual

components and (b) tuning of couplings between components.

[Color figure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

Figure 3 Type 0 and 1 tuning space mapping. Tuning ports

are created inside the fine model. [Color figure can be viewed in

the online issue, which is available at wileyonlinelibrary.com.]

Figure 4 Fast tuning space mapping. The auxiliary fine model

is reduced to allow fast simulation. [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com.]

2 Cheng, Bandler, and Koziel

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 000, No. 000, Month 2012

In this article, we review various tuning space mapping

approaches and categorize them into four main groups:

Type 0� [1, 6, 7], Type 0 [8–10], Type 1 [10–13], and

Type 2 [6, 14, 15].

II. GENERAL TUNING SPACE MAPPING ALGORITHM

We are concerned with the optimization problem

x�f ¼ argminx

U Rf ðxÞ� �

(1)

where Rf [ Rm denotes the response vector of a fine model

of the device of interest, U is a merit function (e.g., a mini-

max function or a norm), x is a vector of design parameters,

and xf* is the optimal solution to be determined.

The iteration of a typical tuning space mapping algo-

rithm consists of several steps: the simulation of the fine

and corresponding auxiliary fine models, the alignment of a

tuning model with the fine model (i.e., the updating of the

tuning model), the optimization of the tuning model, and

the calculation of the corresponding fine model design pa-

rameter values. In the ith iteration, first, based on data from

an auxiliary fine model (for example, a fine model with so-

called cocalibrated ports) at the current design x(i), an initial

tuning model Rt(i) is built on the auxiliary fine model em-

bedded with appropriate tuning elements. The current tun-

ing model is supplied with appropriate (initial) tuning pa-

rameters (parameter values t(i)) determined from microwave

engineering knowledge. We augment this tuning model

with certain other model parameters p (such as input map-

ping parameters and/or preassigned parameters) similar to

those found in the surrogate of the traditional space map-

ping techniques [16]. Our initial tuning model response

may not agree with the response of the original fine model

at x(i). We align these models by:

pðiÞ ¼ argminp

Rf ðxðiÞÞ � RðiÞt ðtðiÞ; pÞ

�� (2)

where Rt [ Rm denotes the response vector of the tuning

model. After p(i) is extracted, we optimize Rt(i) to have it

meet the design specifications w.r.t. the selected tuning pa-

rameters t, giving

Figure 5 Type 2 tuning space mapping. Multiple parts of the

fine models are simulated separately and combined with tuning

elements later in a circuit simulator. [Color figure can be viewed


Figure 6 Simple bandstop microstrip filter: (a) geometry and

(b) coarse model in a circuit simulator [17].

Figure 7 Simple bandstop filter example: (a) Type 0� tuning

model, (b) Type 0 tuning model, and (c) Type 2 tuning model.

Tuning Space Mapping 3

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

tðiÞopt ¼ argmin

tU R

ðiÞt ðt; pðiÞÞ

� �(3)

The new design parameter values x(iþ1) can be calculated

either directly from x(i) þ tðiÞopt � t(i) (when the design pa-

rameters and tuning parameters have the same physical

meaning and units) or by substituting tðiÞopt, t

(i), and x(i) intoa suitable calibration model [9, 10]. Note that the current

initial tuning parameters t(i) are related to how the current

auxiliary fine model and tuning model are setup; their

values may or may not be directly related to the previous

optimal tuning parameter values tði�1Þopt . We show the

flowchart of a general tuning space mapping procedure in

Figure 1.

III. TYPES OF TUNING MODELS

As the tuning model is based on auxiliary fine models and

appropriate tuning elements, there are many ways to cre-

ate it. We now discuss various types of useful tuning

models of tuning space mapping algorithms.

Our first type is Type 0– tuning, where tuning ports

are added at the boundary of the EM model (fine) as

shown in Figure 2 to form an auxiliary fine model. The

auxiliary fine model is then simulated. The resulting

responses are equipped with tuning ports, where tuning

elements are attached. It is now a tuning model. We can

proceed using the algorithm described in Section II.

Type 0 and 1 tuning methods use internal tuning ports.

The auxiliary fine model is formed by inserting internal

ports into the fine model. The auxiliary fine model is then

Figure 8 Simple bandstop filter example: four different subtypes of Type 1 tuning model (Type 1a, 1b, 1c, and 1d (fast) tuning model).

Type 1a tuning can be used to tune an end section, in which the entire end section can be omitted in the auxiliary (EM) fine model. Type

1b tuning uses a complete fine model with gaps and tuning ports as the auxiliary fine model. Unused tuning ports exist in the tuning

model. In Type 1c tuning, the unused ports and the associated structure in the auxiliary fine model are omitted. In Type 1d tuning, the aux-

iliary fine model is collapsed based on the Type 1c auxiliary fine model.

TABLE I Setup of Simple Stopband Filter Tuning Modelsa

Type Tuning Model

Auxiliary

Fine Model

Momentum

Internal Port(s)

Sonnet em

Internal Port(s)

Sonnet em

Feedline Width

Type 0– Type 0– Type 0– Internal Cocalibrated 1 mm

Type 0 Type 0 Type 0 Single mode Cocalibrated 1 mm

Type 1a (I) Type 1a (unused ports are open) Type 0 Single mode Cocalibrated 1 mm

Type 1a (II) Type 1a Type 1a Single mode Cocalibrated 1 mm

Type 1b (I) Type 1b (unused ports are open) Type 1b Single mode Cocalibrated 1 mm

Type 1b (II) Type 1b (short the unused ports) Type 1b Single mode Cocalibrated 1 mm

Type 1b (III) Type 1b (ground the unused ports) Type 1b Single mode Cocalibrated 1 mm

Type 1c Type 1c Type 1c Single mode Cocalibrated 1 mm

Type 1d Type 1d Type 1d Single mode Cocalibrated 1 mm

Type 2 Type 2 Type 2 (partitioned) Single mode Standard n/a

a Type 1a, 1b, 1c, and 1d are all subtypes of Type 1. Their configurations are shown in Figure 8.



simulated to create multiport responses. We add tuning

elements to the tuning gaps (Type 0 tuning) or replace

fine model sections between the tuning gaps with tuning

elements (Type 1 tuning) to obtain a tuning model as

depicted in Figure 3. The fast tuning space mapping

approach is based on Type 1 tuning but uses a simplified

or reduced auxiliary model (Fig. 4).

Type 2 tuning breaks the fine model into pieces, which

differs from the Type 0–, 0, and 1. Each piece is simu-

lated separately in the EM simulator. The fine model

pieces are connected using tuning elements in a circuit

simulator to form a tuning model. See Figure 5.

We exhibit each type of tuning model using a simple

filter example shown in Figure 6a. We have one design

parameter, the stub length L. The goal is to find L so that

the center frequency of the filter is 5 GHz. The fine model

is simulated in the EM simulator. According to our space

mapping approach, instead of performing direct optimiza-

tion of the fine model, we want to use a fast surrogate

model instead. The traditional space mapping surrogate is

based on a coarse model shown in Figure 6b, which is a

circuit equivalent of the structure in Figure 6a and it is

implemented in a circuit simulator [17]. In tuning space

mapping, the coarse model serves as an initial design and/

or as a calibration model.

We start from the optimal solution of the coarse

model, which is 5.6329 mm. The fine model and auxiliary

fine model are simulated in two EM simulators [18, 19].

The tuning model is constructed using the EM simulation

results and tuning elements in a schematic design [17].

We set up various types and subtypes of tuning models of

the filter as shown in Figures 7 and 8. Table I summarizes

the setup of the tuning models. We can observe (Fig. 9)

that response misalignments between the tuning models

and the fine model vary depending on the tuning types.

The initial center frequency of the filter (fine model) is

4.896 GHz instead of the required 5.000 GHz. We cali-

brate the tuning elements so that the misalignments

between the fine and tuning surrogate models are reduced

(Fig. 10).

The next step is the surrogate model optimization in

which the length of the tuning surrogate model stub is

optimized to obtain the center frequency of 5 GHz. We

can see that almost all the variations of tuning model

have predicted a good result (Fig. 11) in a single iteration

(i.e., two evaluations of the fine model) of the tuning

space mapping algorithm. The responses are clustered at

the neighborhood of the target solution. The design can be

further improved by applying the second iteration of the

algorithm. Herein, we only show the results with an EM

simulator [18] as the fine and auxiliary fine model. With

the other EM simulator [19], similar results are achieved.

Table II summarizes the initial and after-PE matching

errors and the fine model errors and design variable values

after one iteration. Table III shows the number of ports

needed and the simulation metal area for each type.

Readers should not be discouraged by the seemingly

intricate types of tuning model of the synthetic bandstop

microstrip filter example. As an expert approach, building a

tuning model needs expert knowledge. For engineers famil-

iar with a particular device or component, creating a tuning

model based on one of the variations mentioned here

should not be difficult, as demonstrated in Section IV.

Figure 9 Simple bandstop filter example: responses of the tun-

ing models and the fine model [18]. [Color figure can be viewed


Figure 10 Simple bandstop filter example: responses of the

tuning models after PE and the fine model [18]. [Color figure can

be viewed in the online issue, which is available at wileyonline

library.com.]

Figure 11 Simple bandstop filter example: responses of the fine

models after the first iteration [18]. [Color figure can be viewed in




IV. EXAMPLES

We demonstrate in this section various tuning types using

microwave and radio frequency component designs.

A. Type 0� Tuning MethodSwanson and Wenzel [1] tuned a filter in a circuit simula-

tor using multiport S-parameter data and lumped capaci-

tors at the ports. They then optimize the combline filter

rapidly by mapping the ‘‘coarse’’ circuit model to the

‘‘fine’’ finite element method model. This optimization is

shown to converge in a single iteration, with a good start-

ing point. The method can be viewed as a Type 0� tuning

process (tuning elements added at the boundary). In

another Type 0� tuning example [6], a seven-post band-

pass filter is tuned by adding tuning elements (tuning

capacitors and inductors) to each resonator (Fig. 12). The

couplings between the resonators are also tuned by tuning

elements (transmission lines) added between the resona-

tors (Fig. 13). The tuning model is shown in Figure 14.

The after-tuning responses are shown in Figure 15.

B. Type 0 Tuning MethodWe formally introduced the tuning space mapping method

(Type 0 tuning) for microwave design optimization in [9].

We formulate the tuning space mapping concept and show

how it relates to the standard space mapping methodol-

ogy. The tuning model is created using engineering exper-

tise and knowledge of the design problem but also used

the efficiency of space mapping for translating the adjust-

ment of the tuning parameters into relevant updates of the

design variables. We illustrate Type 0 tuning through the

optimization of a high-temperature superconducting (HTS)

filter [9] in Figures 16a and 16b.

Figure 16a shows the auxiliary fine model constructed

by dividing the five coupled-line polygons in the middle

and inserting the tuning ports at the new cut edges. Figure

16b shows the tuning model implementation in the circuit

simulator [17] where the S22P data file (22 being the num-

ber of ports) of the simulated auxiliary fine model is

loaded. The circuit-theory coupled-line components and ca-

pacitor components are chosen to be the tuning elements

and are inserted into each pair of tuning ports. As all the

tuning elements are embedded in the small gaps in the aux-

iliary fine model, it is called a Type 0 tuning. Figure 17

shows the final response of the HTS filter using a Type 0

tuning space mapping algorithm. In [10], a narrowband 62

GHz interdigitated filter is designed using Type 0 tuning.

Thoma [8] implemented a simple hairpin filter tuning

space mapping design in an EM/circuit simulation suite

[20]. Short line segments are introduced to the EM model

for calibration. We categorize the method as Type 0,

as well.

TABLE II Simple Stopband Filter Tuning Example

Type

Initial Matching

Error

Matching

Error After PE

Fine Model

Objective Function

Value

Design

Variable

Value (mm)

Type 0– 0.632 0.003 1.492 5.529

Type 0 0.041 0.008 0.850 5.530

Type 1a (I) 3.501 0.241 5.063 5.522

Type 1a (II) 2.773 0.040 0.797 5.531

Type 1b (I) 0.282 0.151 3.205 5.526

Type 1b (II) 0.151 0.150 3.205 5.526

Type 1b (III) 0.220 0.169 3.205 5.526

Type 1c 0.173 0.152 3.205 5.526

Type 1d 0.376 0.152 3.665 5.536

Type 2 0.049 0.029 0.797 5.521

TABLE III Simple Stopband Filter Auxiliary Fine ModelComparison

Type Number of Ports Metal Area (mm2)

Type 0– 3 16.64

Type 0 4 16.65

Type 1a (I) 3 16.65

Type 1a (II) 3 13.5

Type 1b (I) 6 16.62

Type 1b (II) 6 16.62

Type 1b (III) 6 16.62

Type 1c 4 13.5

Type 1d 4 13.5

Type 2 4 (3 þ 1) 13.5 (12.5 þ 1)

Figure 12 Seven-post bandpass filter: adding tuning compo-

nents (self-impedance and self-capacitance) to the discrete ports

in each resonator [6] (Reproduced from Ref. [6]). [Color figure

can be viewed in the online issue, which is available at

wileyonlinelibrary.com.]



C. Type 1 Tuning MethodAn implementable microwave design framework is pre-

sented in [11]. In the framework, Type 1 (1b) tuning

space mapping is implemented. We alter an EM model by

replacing a section with suitable tuning elements. The

resulting tuning model is aligned with the original unal-

tered EM model. We then designate the aligned tuning

model as surrogate for design optimization purposes. The

Type 1 tuning space mapping framework is illustrated in

[11] using a simple microstrip line example, an open-loop

ring resonator bandpass filter and a low-

temperature cofired ceramic filter.

In [10], we show that the Type 0 and Type 1 arrange-

ments can be combined. A mixed Type 0 and Type 1b

tuning model of the open-loop ring resonator bandpass

filter is shown in Figure 18. The fine model is simulated

in the EM simulator, while the tuning model is con-

structed and optimized in the microwave circuit simulator

[17]. We divide the microstrip structure and insert cocali-

brated port pairs at the cut edges. Then, we simulate the

auxiliary EM structure with the ports and import the

resulting SNP data file (50 ports) as an SNP S-parameter

component into the circuit simulator. Equivalent circuit

microstrip lines (Type 0) are inserted, and microstrip

coupled-line and gap components (Type 1) replace sec-

tions of the structure in Figure 18. A new tuning model

is now available with tuning parameters [dL1 dL2 dL3 dL4S1 S2 g]

T mm.

As in [11], deviations between the tuning model and

fine model are compensated by calibrating the dielectric

Figure 13 Seven-post bandpass filter: adding tuning components (transmission line) to the discrete ports between the resonators [6]

(Reproduced from Ref. [6]). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 14 Tuning model of the seven-post bandpass filter [6] (Reproduced from Ref. [6]). [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]



constant and substrate height or length offsets of the tun-

ing elements. After compensation, the tuning model or

surrogate is seen as a better representation of the fine

model and is optimized by a circuit simulator [17] with

respect to the design parameters. The new design parame-

ters are then assigned to the fine model. The optimized

tuning model and the corresponding fine model responses

are shown in Figure 19.

D. Type 1d Tuning (Fast Tuning) MethodAlthough the tuning space mapping optimization process

typically requires only a few iterations to complete, the

simulation of the structure with a number of cocalibrated

ports (required to insert the tuning elements) is longer

than that of the original structure [13]. In [13], we show a

fast tuning space mapping (Type 1d) algorithm that

exploits a reduced structure (auxiliary fine model) with

fewer cocalibrated ports for creating the tuning model.

This results in reduction of the computational cost of the

optimization process. A third-order Chebyshev filter and a

coupled microstrip bandpass filter are verified and com-

pared with Type 1b tuning space mapping. Note that Type

1d tuning is a compact version of other Type 1 tuning

models.

Consider the third-order Chebyshev bandpass filter

[13] (Fig. 20a). Without the tuning ports, the evaluation

time of the fine model is 27 min. The simulation time

of the auxiliary fine model (with cocalibrated ports) in

Figure 20a is almost 11 h. In the case of the fast tuning

(Type 1d) algorithm, the tuning model is constructed

using the S-parameters of the reduced auxiliary fine model

along with appropriate tuning elements. Note that the

reduced auxiliary fine model (Fig. 20b) has a smaller

number of cocalibrated ports. Its simulation time is only

38 min, which is 17 times faster than for the structure in

Figure 20a.

The optimization results for fast tuning space mapping

(Type 1d) and another Type 1 tuning (Type 1b in this

case) are summarized in Table IV. The quality of the final

design is quite similar for both algorithms, which indi-

cates that it is indeed sufficient to simulate the reduced

Figure 15 Responses of the seven-post bandpass filter after tun-

ing [6] (Reproduced from Ref. [6]). [Color figure can be viewed in


Figure 17 HTS filter [9]: Fine model response (|S21| obtainedwith an EM simulator [19]) at the final design. [Color figure can be

viewed in the online issue, which is available at wileyonline

library.com.]

Figure 16 HTS filter: (a) physical structure [9] in which num-

bered tuning ports (port 3 to 22) and gaps (dashed line) are inserted

to create the auxiliary fine model; (b) tuning model [17]. [Color fig-

ure can be viewed in the online issue, which is available at




auxiliary fine model to maintain the prediction capability

of the tuning model. On the other hand, the computational

cost is lower for fast tuning space mapping.

E. Type 2 Tuning MethodA tuning model can be constructed by simulating the EM

model sections separately and then connecting them with

the tuning components using a ‘‘cosimulation’’ process

[14]. This allows us to implement the tuning space map-

ping algorithm with any EM simulator. Response mis-

alignment between the original structure and the tuning

model is reduced using classical space mapping. In [14],

the Type 2 tuning space mapping algorithm is illustrated

through the design of two microstrip filters simulated in

an EM simulator [21].

Consider the coupled-line bandpass filter [22] shown in

Figure 21a. The fine model is simulated in the EM simu-

lator [21]. A schematic of the cosimulation-based tuning

model is shown in Figure 21b. Subsections marked black

are simulated in [21]. Due to symmetry, only two subsec-

tions need independent evaluation. The tuning model is

handled by the circuit simulator [17] (Fig. 21c).

The alignment procedure uses a vector consisting of

dielectric constants as well as substrate heights of the dis-

tributed circuit components corresponding to the design

variables. Figure 22 shows the fine model response after

the two iteration of the Type 2 algorithm.

For the sake of comparison, the filter was also optimized

using Matlab’s fminimax routine [23], a pattern search

Figure 18 The open-loop ring resonator bandpass filter realized in the circuit simulator [10] using mixed Type 0 and Type 1 (1b)

embedding. Type 1 tuning elements are in red circles. [Color figure can be viewed in the online issue, which is available at


Figure 19 Responses after two iterations: the tuning model (—)

and the corresponding fine model (*). [Color figure can be viewed


Figure 20 Third-order Chebyshev filter: (a) the geometry [13]

and the places (the dashed lines) for inserting the tuning ports for

the Type 1b algorithm. (b) the reduced structure [13] and the pla-

ces (the dashed lines) for inserting the tuning ports for the fast

tuning space mapping (Type 1d) algorithm.



algorithm [24], as well as a space mapping algorithm

exploiting input, frequency, and output space mapping [25].

The results are shown in Table V.

It can be observed that both space mapping and gradi-

ent-based search fail to find a design satisfying the specifi-

cations. The design obtained using pattern search is slightly

better than that obtained by the technique described here;

however, the design cost is substantially higher.

In another example of Type 2 tuning [6], the author

tunes each resonator of a dual band duplexer for 400 MHz

using a tuning model comprised of connected submodels in

an EM/circuit simulation suite [20]. Tuning elements are

attached to the resonators (Fig. 23). Similarly, another sim-

ulation software vendor demonstrates the technique in

designing filters [26] using its EM [27] and circuit [28]

simulators.

V. DISCUSSION AND RECOMMENDATIONS

As demonstrated through examples, tuning space mapping

permits rapid design improvement with satisfactory

TABLE IV Third-Order Chebyshev Filter: Optimization Results [13]

Algorithm

Optimization Results Optimization Costa

Number of

Iterations

Specification

Error (dB)

Total

Time (h)

Equivalent

Cost (# of Fine Evaluations)

Fast tuning space mapping (Type 1d) 2 �1.7 1.7 3.4

Other Type1 (Type 1b) 2 �1.7 23.3 51.0

a Excluding the fine model evaluation at the initial design.

Figure 21 Cosimulation-based (Type 2) tuning model [14]: (a) a coupled-line bandpass microstrip filter structure [14], (b) its cosimula-

tion tuning model with black sections simulated using an EM solver [21] connecting designable tuning components, (c) circuit simulator

[17] implementation of the tuning model: S-parameters of the EM-simulated sections are stored in S3P and S4P data components SNP1 to

SNP6. Note that all the designable parameters (microstrip lengths, widths, and coupled-line gaps) are associated with the distributed circuit

components, which allows fast optimization of the tuning model. On the other hand, simulating parts of the filter using the EM solver

allows us to maintain good accuracy and predictability of the tuning model.



designs obtained after a few iterations (typically, one to

four). The variants of tuning space mapping mostly differ

in the construction of the tuning model, as well as in the

calibration procedure. The calibration procedure for Type

0 tuning can be quite complex and generally requires an

auxiliary calibration model. On the other hand, Type 0

tuning is probably the most robust technique because the

insertion of the tuning components is realized with mini-

mal or no disturbance to the fine model response. Also,

Type 0 tuning requires a smaller number of tuning ports

Figure 22 Coupled-line bandpass filter: the fine model

response at the final design obtained in two Type 2 iterations.

[Color figure can be viewed in the online issue, which is avail-

able at wileyonlinelibrary.com.]

TABLE V Coupled-Line Bandstop Filter:Cosimulation-Based Tuning (Type 2) VersusOther Optimization Approaches: Design Qualityand Computational Cost Comparison

Algorithm

Best Design

Found (dB)aDesign

Costb

Cosimulation-based

tuning

�1.3 3

Space mapping þ1.5 8

Matlab (fminimax) þ22 208

Pattern search �1.7 155

a Specification error at the final (optimized design).b Number of fine model evaluations.

Figure 23 Tuning model of a dual band duplexer for 400 MHz [6] (Reproduced from Ref. [6]). [Color figure can be viewed in the

online issue, which is available at wileyonlinelibrary.com.]



than does Type 1 tuning, so the simulation time of the

‘‘cut’’ fine model is longer for Type 1 than for Type 0.

The major benefits of Type 1 tuning are simple cali-

bration and straightforward implementation. Also, Type 1

tuning allows us to tune cross-sectional parameters. The

downside is that a Type 1 tuning model has to be aligned

with the fine model as the insertion of the tuning compo-

nents requires the removal of substantial parts of the origi-

nal structure. For the same reason, the accuracy of the

Type 1 tuning model is not as good as that of the tuning

model in Type 0 tuning, so more iterations are normally

necessary to yield a satisfactory design.

Type 1d tuning (fast tuning) seems to inherit all the

advantages of Type 1 tuning while being computationally

more efficient. One difficulty, however, not observed for

the test problems described in the literature [12, 13], is

that using the reduced structure for complicated circuits

may result in further deterioration of the generalization

capability of the tuning model. This could lead to a larger

number of iterations required by the Type 1d tuning

algorithm.

Type 0� and Type 2 tuning are most found in the tun-

ing processes for waveguide structures. Type 2 tuning

simulates each submodel separately, which allows parallel

processing. However, care has to be taken since the cou-

plings between the submodels are not accounted for.

VI. CONCLUSIONS

We review various types of tuning space mapping proce-

dures and use a simple stopband filter to demonstrate their

differences. We show examples of these types of tuning

space mapping using published examples. Despite the

variations of tuning space mapping, it is generally robust

because misalignments can usually be compensated by

tuning elements. The main considerations for choosing

among the variations are the anticipated difficulties in the

implementations and the simulation cost of the auxiliary

fine model.

ACKNOWLEDGMENTS

This work was supported in part by the Icelandic Centre

for Research (RANNIS) Grant 110034021, and the Natural

Sciences and Engineering Research Council of Canada

under Grants RGPIN7239-11 and STPGP 381153-09, and by

Bandler Corporation. The authors thank Sonnet Software

Inc. for em, and Agilent Technologies, Santa Rosa, CA, for

making ADS available. They also thank F. Hirtenfelder,

CST, Darmstadt, Germany, for providing illustration

examples.

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BIOGRAPHIES

Qingsha S. Cheng was born in

China. He received the B.Eng. and

M.Eng. from Chongqing University,

China, in 1995 and 1998, respec-

tively. He received his Ph.D. from

McMaster University, Canada, in

2004. In 1998, he joined the Depart-

ment of Computer Science and Tech-

nology, Peking University, China. In 1999, he joined the

Department of Electrical and Computer Engineering,

McMaster University. Currently, he is a research engineer

in the Department of Electrical and Computer Engineer-

ing, McMaster University. His research interests are surro-

gate modeling, computer-aided design, modeling of micro-

wave circuits, software design technology, and

methodologies for microwave CAD.

John W. Bandler studied at Imperial

College and received the B.Sc.(Eng.),

Ph.D., and D.Sc.(Eng.) degrees from

the University of London, England,

in 1963, 1967, and 1976, respec-

tively. He joined McMaster Univer-

sity, Canada, in 1969. He is now a

Professor Emeritus. He was President

of Optimization Systems Associates Inc., which he

founded in 1983, until November 20, 1997, the date of

acquisition by Hewlett-Packard Company. He is President

of Bandler Corporation, which he founded in 1997. He is

a Fellow of several societies, including the Royal Society

of Canada. In 2004, he received the IEEE MTT-S Micro-

wave Application Award.

Slawomir Koziel received the M.Sc.

and Ph.D. degrees in electronic engi-

neering from Gdansk University of

Technology, Poland, in 1995 and

2000, respectively. He also received

the M.Sc. degrees in theoretical

physics and in mathematics, in 2000

and 2002, respectively, as well as the

Ph.D. in mathematics in 2003, from the University of

Gdansk, Poland. He is currently a Professor with the

School of Science and Engineering, Reykjavik University,

Iceland. His research interests include CAD and modeling

of microwave circuits, simulation-driven design, surro-

gate-based optimization, space mapping, circuit theory,

analog signal processing, evolutionary computation, and

numerical analysis.



tuning space mapping: the state of the art

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