Tuning space mapping design framework exploiting ... - IEEE Xplore

www.ietdl.org Published in IET Microwaves, Antennas & Propagation Received on 18th March 2011 doi: 10.1049/iet-map.2011.0138

ISSN 1751-8725

Tuning space mapping design framework exploiting reduced electromagnetic models S. Koziel1 J.W. Bandler 2 Q.S. Cheng2 1

Engineering Optimization and Modeling Center, School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland 2 Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4K1 E-mail: [email protected]

Abstract: Tuning space mapping (TSM) with embedded tuning elements is a recent development in space mapping technology. The process allows efficient design optimisation of microwave components by substituting sections in an electromagnetic model with corresponding sections of designable equivalent elements. Available parameters of these elements are subsequently tuned and their optimal values are ‘translated’ into relevant changes in the original structure’s design variables. Although the TSM optimisation process typically requires only a few iterations to complete, the simulation of the structure with a number of cocalibrated ports (required for subsequent insertion of the tuning elements) can be substantially longer than that of the original structure. This results in substantial computational overhead of the design process. Here, the authors review a fast TSM algorithm that exploits a reduced structure with significantly fewer co-calibrated ports for creating the tuning model and allows us to obtain dramatic reduction of the computational cost of the optimisation process. In a design framework, the fast TSM as well as other TSM methods are implemented and automated in space mapping framework (SMF) software. Comprehensive verification and comparison with the standard TSM are provided through several examples of microstrip filters.

1

Introduction

Simulation-driven design optimisation and design closure have become an important part of contemporary microwave engineering. Still, they face the fundamental difficulty of high computational cost of electromagnetic (EM) simulation. This cost may be prohibitive, particularly for complex structures. One of the solutions is co-simulation [1 – 3]; however, truly efficient EM-based design optimisation can be realised using surrogate models [4]. Probably the most successful approach of this kind in microwave engineering is space mapping (SM) [5 – 21] as well as various response correction techniques [22 – 26]. For a well-performing SM algorithm with a judiciously selected surrogate model, a satisfactory design is obtained only after a few (typically 3 to 10) full-wave EM simulations of the structure under consideration [5, 6]. Further progress – in terms of reducing the computational cost of the optimisation process – can be obtained using tuning space mapping (TSM): one of the latest and highly specialised developments in space mapping technology [27 – 29]. TSM combines SM with the concept of tuning, which is widely used in microwave engineering [30 – 34]. TSM exploits the so-called tuning model, which is constructed by introducing circuit-theory-based components (e.g. capacitors, coupled-line models) into the CPUintensive structure under consideration (fine model) using, for example, the co-calibrated ports of Sonnet em [35]. IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 10, pp. 1219– 1226 doi: 10.1049/iet-map.2011.0138

Parameters of these auxiliary circuit components are chosen to be tunable. The tuning model is updated and optimised with respect to the tuning parameters. In the calibration process, the optimal values of the tuning parameters are transformed into appropriate modifications of the design variables, which are then assigned to the fine model. TSM with embedded tuning elements (here called embedded TSM, or ETSM, also known as Type 1 embedding) [29] is a variation of TSM where, instead of inserting a tuning element into adjacent ports, an entire section of the structure of interest is replaced by a parameterised tuning element (e.g. a microstrip line model with variable length and width). Unlike the original TSM [27], ETSM is capable of handling cross-sectional parameters such as microstrip line widths and substrate heights and allows calibration without a companion equivalent-circuit calibration model [27]. Automated implementation of the TSM algorithm in space mapping framework (SMF) [36] has been reported in [37]. SMF allows us to solve basic sub-problems of the SM algorithm, that is, the extraction of surrogate model parameters and surrogate model optimisation. It implements elementary SM transforms and contains sockets to several commercial EM and circuit. The prediction capability of the tuning model as a surrogate is usually good because the tuning model explicitly uses an ‘image’ of the fine model (typically, its S-parameter data) [6]. This results in a small number of fine model 1219

& The Institution of Engineering and Technology 2011

www.ietdl.org evaluations to find a satisfactory solution (typically 1 to 3 iterations are sufficient [28]). However, EM simulation of a structure containing a large number of co-calibrated ports is computationally far more expensive than the simulation of the original structure (without such ports). Depending on the number of design variables, the number of co-calibrated ports may be as large as 30, 50 or more (particularly for ETSM), which may increase the simulation time by one order of magnitude or more. Here, we review the fast embedded TSM (FETSM or fast ETSM) algorithm [38], where the structure for creating the tuning model is simplified by removing all the sections to be replaced by the embedded tuning elements. The reduced structure is much smaller than the original one and contains significantly fewer co-calibrated ports than required by ETSM. We demonstrate that FETSM offers a dramatic reduction of the computational cost of the optimisation process without compromising the design quality when compared with ETSM. We show a design framework that implements the original TSM, ETSM and FETSM. These TSM algorithms are automated in SMF. The effectiveness of the design framework is demonstrated with several examples.

2

TSM with embedded tuning components

In this section, we formulate the microwave design problem and recall the concept and formulation of the TSM algorithm with embedded tuning components. 2.1

Design problem

2.2 TSM with embedded tuning components: tuning model The original TSM technique described in [27] offered exceptional efficiency of the design process with the satisfactory design typically obtained after just one or two iterations. The main drawback of this technique is the somehow-complicated calibration process as well as the difficulty in tuning certain cross-sectional parameters [28]. ETSM [29] effectively alleviates both problems at the expense of a certain reduction in the accuracy of the tuning model, which results in a slightly increased number of iterations necessary to conclude the optimisation process [29]. ETSM involves the tuning model where certain designable sub-sections of the structure of interest are replaced with suitable tuning elements [29]. Preferably they are distributed circuit elements with physical dimensions corresponding to those of the fine model. After a simple alignment procedure, we match the tuning model with the fine model (the original structure without co-calibrated ports). Some of the fine-model couplings are preserved (or represented through S-parameters) in the tuning model. We normally obtain a good surrogate of the fine model. In the next stage, the tuning model is optimised through the design parameters of the embedded tuning elements to satisfy given design specifications. The obtained design parameters become our next fine model iterate. An illustration of the embedded tuning elements concept is shown in Fig. 1a. An example of inserting co-calibrated ports and replacing the coupled-line segment by its circuittheory model is illustrated in Figs. 1b – d.

The goal is to solve the optimisation problem x∗f = arg min U (Rf (x)) x

(1)

where Rf (x) [ R m denotes the response vector of a fine model of the device of interest, for example, |S21| evaluated at m different frequencies. U is a given scalar merit function, for example, a minimax function with upper and lower specifications. Vector xf∗ is the optimal design to be determined. Rf is assumed to be computationally expensive so that direct optimisation is usually prohibitive.

2.3

ETSM: design flow

An iteration of the ETSM algorithm consists of two steps: alignment of the tuning model with the fine model and the optimisation of the tuning model. First, using data at the current design x(i), from the fine model with co-calibrated ports, the current tuning model Rt(i) is built with appropriate tuning elements replacing certain sections of the fine model. The tuning model response generally does not agree with the response of the original fine model at x(i). We therefore

Fig. 1 TSM with embedded tuning elements: concept and illustration a b c d

Conceptual illustration of embedded tuning elements [29] Illustration of TSM with embedded tuning elements: a coupled microstrip line of length L Coupled line with co-calibrated ports inserted Tuning model of the coupled line: the middle section is replaced by a microstrip model (tuning element)

1220 & The Institution of Engineering and Technology 2011

IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 10, pp. 1219–1226 doi: 10.1049/iet-map.2011.0138

www.ietdl.org 3

align these models by the optimisation process (i) p(i) = arg minRf (x(i) ) − R(i) t (x , p) p

(2)

where p represents the parameters of the tuning model used in the alignment process. These parameters might be the ones traditionally used by input, implicit or frequency SM [6]. In the next step, we optimise Rt(i) to meet the design specifications. We obtain the optimal values of the design parameters x(i+1) as (i) x(i+1) = arg min U (R(i) t (x, p )) x

(3)

A flowchart of our ETSM algorithm is shown in Fig. 2.

Fast ETSM

Although our ETSM algorithm requires very few iterations to yield a satisfactory design, the simulation time of the structure containing co-calibrated ports is substantially longer than that of the original structure (without co-calibrated ports). For medium-scale problems (several design variables), the number of ports is 30, 50 or more, which increases the simulation time by at least one order of magnitude. As a result, the optimisation cost expressed in terms of the number of evaluations of the original structure is quite significant. Moreover, the EM simulation of the structure with co-calibrated ports is normally performed in every iteration of the ETSM algorithm. Here, we describe the FETSM algorithm. The idea is that instead of simulating the entire structure (with co-calibrated ports), we simulate the reduced structure with all the designable sub-sections removed beforehand. An example of such a procedure, corresponding to what is shown in Figs. 1a – c, is explained in Fig. 3. From the tuning model point of view, the reduced structure in Fig. 3b simulates the same fine-model couplings as the one in Fig. 1c in which the middle section is removed later anyway. Thus, the accuracy of the tuning models based on both structures is expected to be similar. As the reduced structure is very simple and the number of co-calibrated ports is halved, its simulation time is expected to be substantially smaller, comparable to the simulation time of the fine model (i.e. the original structure without ports). Moreover, since the reduced structure does not depend on the length parameters, it is usually sufficient to perform its simulation once, at the first iteration of the FETSM algorithm.

4 FETSM and ETSM design framework implementation

Fig. 2 Flowchart of our ETSM algorithm In each iteration, the fine model (original structure) and the fine model with co-calibrated ports are evaluated. The response of the latter is used to set up the tuning model, in particular, the parameter p is adjusted to match the tuning model with the fine model response at the current design x(i) (cf. (2)). The new design, x(i+1), is obtained by optimising the tuning model with respect to the design variables (cf. (3)). Typically, the optimisation process is terminated when the current iteration brings no further design improvement

In this section, we discuss the design framework implementation for ETSM and FETSM. The implementation is based on a more comprehensive design framework that implements the so-called ‘Type 0’ TSM algorithm [37]. It exploits the functionality of our user-friendly SMF system [36] to solve basic sub-problems of the SM algorithm, that is, the extraction of surrogate model parameters and surrogate model optimisation. It implements elementary SM transforms and contains sockets (drivers) to several commercial EM and circuit simulators including Sonnet em [35] and Agilent ADS [39], so that the models implemented with these simulators can be evaluated through SMF. These capabilities can be executed using SMF script commands and are exploited as building blocks to construct the TSM algorithm. Fig. 4 shows the architecture of automated TSM implementation [37]. The actual TSM algorithm is an SMF script that calls necessary procedures and, directly or indirectly, calls model evaluation engines where necessary.

Fig. 3 Fast TSM with embedded tuning element a Coupled microstrip line b Coupled line with co-calibrated ports and middle section removed (reduced structure) c Tuning element inserted in-between co-calibrated ports. The initial parameter values of the tuning element are chosen to coincide with those of the removed section. The number of co-calibrated ports is halved with respect to the ETSM (Fig. 1c) and the structure to be EM-simulated is simpler (no middle section) IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 10, pp. 1219– 1226 doi: 10.1049/iet-map.2011.0138

1221


www.ietdl.org

Fig. 4 Automated ETSM/FETSM: SMF architecture [37]

The fine, auxiliary fine model, tuning and calibration models are linked to the system through model drivers set up using the template project files and other relevant data provided by the user.

Fig. 4 illustrates the interaction of the SMF system with the models involved in the TSM algorithm. Various stages of the TSM algorithm are realised using separate SMF interfaces launched by appropriate script commands. Our ETSM and

Fig. 5 Third-order Chebyshev filter a b c d

Geometry [40] and the places (the dashed lines) for inserting the tuning ports for ETSM algorithm Tuning model for ETSM algorithm (Agilent ADS) Reduced structure and the places (the dashed lines) for inserting the tuning ports for the FETSM algorithm Tuning model for the FETSM algorithm (Agilent ADS)

1222 & The Institution of Engineering and Technology 2011


www.ietdl.org FETSM algorithm implementations are simpler than that of the Type 0 TSM. They only activate three simulator drivers as denoted by a thick solid line (driver modules are in dashed line).

5

Examples

In this section, a comprehensive verification of the FETSM algorithm is presented. A comparison with the ETSM algorithm is also given. For all considered cases, the performance of both algorithms is essentially the same in terms of the quality of the final design and the number of iterations, however, the cost per iteration and, consequently, the total optimisation time, is substantially smaller for the FETSM algorithm. 5.1

Third-order Chebyshev bandpass filter

Consider the third-order Chebyshev bandpass filter [38, 40] (Fig. 5a). The design parameters are x ¼ [L1 L2 S1 S2]T mm. Other parameters are W1 ¼ W2 ¼ 0.4 mm. The fine model is simulated in Sonnet em [35] with a grid of 0.1 mm × 0.01 mm. The design specifications are |S21| ≥ 23 dB for 1.8 GHz ≤ v ≤ 2.2 GHz, and |S21| ≤ 220 dB for 1.0 GHz ≤ v ≤ 1.6 GHz and 2.4 GHz ≤ v ≤ 3.0 GHz. The evaluation time of the fine model is 27 min. For comparison purposes we consider both the ETSM and the proposed FETSM algorithm. The tuning model for the ETSM algorithm is constructed by inserting tuning ports as in Fig. 5a, loading the resulting S34P data file into the S-parameter component in Agilent ADS [39], and applying the circuit-theory coupled-line components as shown in Fig. 5b (the tuning elements replace the original coupledline sections). The lengths and spacings of the imposed coupled-lines are assigned as tuning parameters. The simulation time of the structure in Fig. 5b with cocalibrated ports is almost 11 h. In the case of the FETSM algorithm, the tuning model is constructed using the S-parameters of the reduced structure shown in Fig. 5c along with appropriate tuning elements, which leads to the circuit shown in Fig. 5d. Note that the reduced structure has a smaller number of co-calibrated ports. Its simulation time is only 38 min, which is 17 times faster than for the structure in Fig. 5a. Fig. 6a shows the fine and tuning model responses at the initial design x(0) ¼ [14.6 15.3 0.56 0.53]T mm. The misalignment between the models is reduced as in (2) using the additive perturbations of the design variables, dL1 , dL2 , dS1 and dS2 , as the parameter p. The tuning model response after performing (2) is also shown in Fig. 6b. Fig. 6b shows the fine model response after two iterations of the FETSM algorithm at x(2) ¼ [14.9 14.7 0.41 0.86]T mm. The optimisation results for ETSM and FETSM are summarised in Table 1. The quality of the final design is quite similar for both algorithms, which indicates that it is indeed sufficient to simulate the reduced structure to maintain the prediction capability of the tuning model. On the other hand, the computational cost is substantially lower for FETSM. 5.2

Fig. 6 Third-order Chebyshev filter optimised using the FETSM algorithm a Responses at the initial design: fine model (solid line), tuning model (dashed line), tuning model after the alignment procedure (2) (dotted line) b Responses at the final design: the fine model (solid line) and the tuning model after the alignment procedure (dashed line)

1.6 GHz and 2.4 GHz ≤ v ≤ 3.5 GHz. The evaluation time of the fine model is 24 min. The structures and the locations of the co-calibrated ports as well as the tuning models for the ETSM and FETSM algorithms are shown in Fig. 7. The simulation times of the structures in Figs. 7b and d are 91 and 10 min, respectively. The difference is smaller than for the previous example because the number of co-calibrated ports is relatively small (24 for original structure and 12 for the reduced one). Fig. 8a shows the fine and tuning model responses at the initial design x(0) ¼ [24.0 24.0 0.2 1.0 1.6]T mm. The misalignment between the models is reduced as in (2) using the additive perturbations of the design variables, dL1 , dL2 , dW1 , dW2 and dS1 , as well as the parameters of the frequency space mapping [6]. The tuning model response after performing (2) is also shown in Fig. 8a. Fig. 8b shows the fine model response after three iterations of the FETSM algorithm at x(3) ¼ [21.4 24.5 0.38 0.30 0.64]T mm. In this case, the reduced structure was evaluated in each iteration Table 1 Algorithm

Second-order ring resonator bandpass filter

Our second example is a second-order ring resonator bandpass filter [41] (Fig. 7a). The design parameters are x ¼ [L1 L2 W1 W2 S1]T mm. The fine model is simulated in Sonnet em [35] with a grid of 0.02 mm × 0.04 mm. The design specifications are |S21| ≥ 21dB for 1.85 GHz ≤ v ≤ 2.15 GHz, and |S21| ≤ 220dB for 0.5 GHz ≤ v ≤ IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 10, pp. 1219– 1226 doi: 10.1049/iet-map.2011.0138

ETSM this work (FETSM)

Third-order Chebyshev filter: optimisation results Optimisation results

Optimisation costa

Number of iterations

Specification error, dB

Total time, hours

Equivalent cost (# of Rf evaluations)

2 2

–1.7 –1.7

23.3 1.7

51.0 3.4

a

Excluding the fine model evaluation at the initial design 1223


www.ietdl.org

Fig. 7 Second-order ring resonator bandpass filter a b c d

Geometry [41] and the places (the dashed lines) for inserting the tuning ports for the ETSM algorithm Tuning model for the ETSM algorithm (Agilent ADS) Reduced structure and the places (the dashed lines) for inserting the tuning ports for the FETSM algorithm Tuning model for the FETSM algorithm (Agilent ADS)

of the FETSM algorithm, which is because the width parameters W1 and W2 are used as design variables. As in the previous example, the quality of the final design is similar for both the ETSM and FETSM approaches; however, the computational cost of the optimisation process is much lower for FETSM (Table 2). 5.3

Coupled microstrip bandpass filter

We consider the coupled microstrip bandpass filter [42] (Fig. 9a). The design parameters are x ¼ [L1 L2 L3 L4 S1 S2]T mm. The fine model is simulated in Sonnet em [35] with a grid of 0.1 mm × 0.02 mm (evaluation time 54 min). The design specifications are |S21| ≥ 21 dB for 2.35 GHz ≤ v ≤ 2.45 GHz, and |S21| ≤ 220 dB for 1.5 GHz ≤ v ≤ 2.2 GHz and 2.6 GHz ≤ v ≤ 3.3 GHz. The structures and the locations of the co-calibrated ports used to construct the tuning models for the ETSM and FETSM Table 2

Second-order ring-resonator bandpass filter: optimisation results Algorithm

Fig. 8 Second-order ring resonator bandpass filter optimised using the FETSM algorithm a Responses at the initial design: fine model (solid line), tuning model (dashed line) and tuning model after the alignment procedure (2) (dotted line) b Responses at the final design: the fine model (solid line) and the tuning model after the alignment procedure (dashed line) 1224



Optimisation results

Optimisation costa



Total time [hours]


3 3

– 0.7 – 0.8

5.8 1.7

14.4 4.2

a

Excluding the fine model evaluation at the initial design


www.ietdl.org

Fig. 9 Coupled microstrip bandpass filter a Geometry [42] and the places (the dashed lines) for inserting the tuning ports for the ETSM algorithm b Reduced structure and the places (the dashed lines) for inserting the tuning ports for the FETSM algorithm c Tuning model for the FETSM algorithm (Agilent ADS)

Table 3 Algorithm


Coupled microstrip filter: optimisation results Optimisation results

Optimisation costa



Total time [hours]


1 1

–0.8 –0.9

18.8 2.4

21.0 2.7

a

Excluding the fine model evaluation at the initial design

algorithms are shown in Figs. 9a and b, respectively. The tuning model for the FETSM algorithm is shown in Fig. 9c. The simulation time of the structure in Fig. 9b, 1.5 h, is much smaller than that for the structure in Fig. 9a (18 h). Fig. 10 shows the fine and tuning model responses at the initial design x(0) ¼ [22.1 5.94 12.6 14.8 0.10 0.16]T mm and after one iteration of the FETSM algorithm at x(1) ¼ [23.0 6.12 10.4 16.9 0.10 0.24]T mm. As before, the additive perturbations of the design variables (here, dL1 to dL4 , dS1 and dS2) are used in the alignment procedure (2). The optimisation results are summarised in Table 3. Again, while the quality of the final design is similar for both the ETSM and FETSM algorithms, the computational cost of the latter is dramatically reduced. Fig. 10 Coupled microstrip filter optimised using the FETSM algorithm a Responses at the initial design: fine model (solid line), tuning model (dashed line) and tuning model after the alignment procedure (2) (dotted line) b Fine model response at the final design (solid line), and the aligned tuning model at the final design (dashed line) IET Microw. Antennas Propag., 2011, Vol. 5, Iss. 10, pp. 1219– 1226 doi: 10.1049/iet-map.2011.0138

6

Conclusion

A fast TSM algorithm is reviewed that permits effective optimisation of microwave structures by combining the concept of tuning and the efficiency of space mapping. Having the tuning model constructed from the simplified 1225


www.ietdl.org structure with a smaller number of co-calibrated ports allows dramatic reduction of the optimisation cost with respect to previously published TSM approaches while maintaining all their attractive features, including straightforward calibration and cross-sectional parameter design. We show a design framework that implements the fast TSM as well as other types of TSM. The robustness of our automated design framework and its computational efficiency are demonstrated through the design of three microstrip filters.

7

Acknowledgments

The authors thank Sonnet Software, Inc., Syracuse, NY, for emTM and Agilent Technologies, Santa Rosa, CA, for making ADS available. This work was supported in part by the Icelandic Centre for Research (RANNIS) Grant 110034021, the Reykjavik University Development Fund under Grant T10006, and the Natural Sciences and Engineering Research Council of Canada under Grants RGPIN7239-06 and STPGP381153-09, and by Bandler Corporation.

8

References

1 Rizzoli, V., Costanzo, A., Masotti, D., Spadoni, P.: ‘Circuit-level nonlinear/electromagnetic co-simulation of an entire microwave link’. IEEE MTT-S Int. Microwave Symp. Digest, Long Beach, CA, June 2005, pp. 813– 816 2 Shin, S., Kanamaluru, S.: ‘Diplexer design using EM and circuit simulation techniques’, IEEE Microw. Mag., 2007, 8, (2), pp. 77–82 3 Snyder, R.V.: ‘Practical aspects of microwave filter development’, IEEE Microw. Mag., 2007, 8, (2), pp. 42–54 4 Forrester, A.I.J., Keane, A.J.: ‘Recent advances in surrogate-based optimization’, Progr. Aerosp. Sci., 2009, 45, (1–3), pp. 50– 79 5 Bandler, J.W., Cheng, Q.S., Dakroury, S.A., et al.: ‘Space mapping: the state of the art’, IEEE Trans. Microw. Theory Tech., 2004, 52, (1), pp. 337–361 6 Koziel, S., Bandler, J.W., Madsen, K.: ‘A space mapping framework for engineering optimization: theory and implementation’, IEEE Trans. Microw. Theory Tech., 2006, 54, (10), pp. 3721– 3730 7 Ismail, M.A., Smith, D., Panariello, A., Wang, Y., Yu, M.: ‘EM-based design of large-scale dielectric-resonator filters and multiplexers by space mapping’, IEEE Trans. Microw. Theory Tech., 2004, 52, (1), pp. 386–392 8 Wu, K.-L., Zhao, Y.-J., Wang, J., Cheng, M.K.K.: ‘An effective dynamic coarse model for optimization design of LTCC RF circuits with aggressive space mapping’, IEEE Trans. Microw. Theory Tech., 2004, 52, (1), pp. 393–402 9 Amari, S., LeDrew, C., Menzel, W.: ‘Space-mapping optimization of planar coupled-resonator microwave filters’, IEEE Trans. Microw. Theory Tech., 2006, 54, (5), pp. 2153–2159 10 Rayas-Sańchez, J.E., Gutie´rrez-Ayala, V.: ‘EM-based Monte Carlo analysis and yield prediction of microwave circuits using linear-input neural-output space mapping’, IEEE Trans. Microw. Theory Tech., 2006, 54, (12), pp. 4528–4537 11 Zhang, X.J., Fang, D.G.: ‘Using circuit model from layout-level synthesis as coarse model in space mapping and its application in modelling low-temperature ceramic cofired radio frequency circuits’, IET Microw. Antennas Propag., 2007, 1, (4), pp. 881–886 12 Crevecoeur, G., Dupre, L., Van de Walle, R.: ‘Space mapping optimization of the magnetic circuit of electrical machines including local material degradation’, IEEE Trans. Magn., 2007, 43, (6), pp. 2609– 2611 13 Encica, L., Paulides, J.J.H., Lomonova, E.A., Vandenput, A.J.A.: ‘Aggressive output space-mapping optimization for electromagnetic actuators’, IEEE Trans. Magn., 2008, 44, (6), pp. 1106– 1109 14 Koziel, S., Cheng, Q.S., Bandler, J.W.: ‘Space mapping’, IEEE Microw. Mag., 2008, 9, (6), pp. 105– 122 15 Cao, Y., Simonovich, L., Zhang, Q.J.: ‘A broadband and parametric model of differential via holes using space-mapping neural network’, IEEE Microw. Wirel. Comp. Lett., 2009, 19, (9), pp. 533– 535 16 Tran, T.V., Brisset, S., Brochet, P.: ‘A new efficient method for global multilevel optimization combining branch-and-bound and space mapping’, IEEE Trans. Magn., 2009, 45, (3), pp. 1590–1593

1226


17 Ouyang, J., Yang, F., Zhou, H., Nie, Z., Zhao, Z.: ‘Conformal antenna optimization with space mapping’, J. Electromagn. Waves Appl., 2010, 24, (2–3), pp. 251 –260 18 Rayas-Sańchez, J.E., Lara-Rojo, F., Martıńez-Guerrero, E.: ‘A linear inverse space mapping (LISM) algorithm to design linear and nonlinear RF and microwave circuits’, IEEE Trans. Microw. Theory Tech., 2005, 53, (3), pp. 960– 968 19 Dorica, M., Giannacopoulos, D.D.: ‘Response surface space mapping for electromagnetic optimization’, IEEE Trans. Magn., 2006, 42, (4), pp. 1123– 1126 20 Pantoja, M.F., Meincke, P., Bretones, A.R.: ‘A hybrid genetic-algorithm space-mapping tool for the optimization of antennas’, IEEE Trans. Antennas Propag., 2007, 55, (3, Part 1), pp. 777– 781 21 Crevecoeur, G., Sergeant, P., Dupre, L., Van de Walle, R.: ‘Two-level response and parameter mapping optimization for magnetic shielding’, IEEE Trans. Magn., 2008, 44, (2), pp. 301–308 22 Echeverria, D., Hemker, P.W.: ‘Space mapping and defect correction’, CMAM Int. Math. J. Comput. Meth. Appl. Math., 2005, 5, (2), pp. 107–136 23 Hemker, P.W., Echeverrıá, D.: ‘A trust-region strategy for manifold mapping optimization’, J. Comput. Phys., 2007, 224, (1), pp. 464 –475 24 Echeverria, D., Lahaye, D., Encica, L., Lomonova, E.A., Hemker, P.W., Vandenput, A.J.A.: ‘Manifold-mapping optimization applied to linear actuator design’, IEEE Trans. Magn., 2006, 42, (4), pp. 1183–1186 25 Koziel, S., Bandler, J.W., Madsen, K.: ‘Space mapping with adaptive response correction for microwave design optimization’, IEEE Trans. Microw. Theory Tech., 2009, 57, (2), pp. 478–486 26 Koziel, S.: ‘Efficient optimization of microwave circuits using shapepreserving response prediction’. IEEE MTT-S Int. Microwave Symp. Digest, Boston, MA, June 2009, pp. 1569–1572 27 Meng, J., Koziel, S., Bandler, J.W., Bakr, M.H., Cheng, Q.S.: ‘Tuning space mapping: a novel technique for engineering design optimization’. IEEE MTT-S Int. Microwave Symp. Digest, Atlanta, GA, June 2008, pp. 991 –994 28 Koziel, S., Meng, J., Bandler, J.W., Bakr, M.H., Cheng, Q.S.: ‘Accelerated microwave design optimization with tuning space mapping’, IEEE Trans. Microw. Theory Tech., 2009, 57, (2), pp. 383–394 29 Cheng, Q.S., Bandler, J.W., Koziel, S.: ‘Space mapping design framework exploiting tuning elements’, IEEE Trans. Microw. Theory Tech., 2010, 58, (1), pp. 136– 144 30 Rautio, J.C.: ‘RF design closure-companion modeling and tuning methods’. IEEE MTT IMS Workshop: Microwave Component Design using Space Mapping Technology, San Francisco, CA, 2006 31 Swanson, D.G., Wenzel, R.J.: ‘Fast analysis and optimization of combline filters using FEM’. IEEE MTT-S IMS Digest, Boston, MA, July 2001, pp. 1159– 1162 32 Rautio, J.C.: ‘EM-component-based design of planar circuits’, IEEE Microw. Mag., 2007, 8, (4), pp. 79–90 33 Swanson, D., Macchiarella, G.: ‘Microwave filter design by synthesis and optimization’, IEEE Microw. Mag., 2007, 8, (2), pp. 55– 69 34 Rautio, J.C.: ‘Perfectly calibrated internal ports in EM analysis of planar circuits’. IEEE MTT-S Int. Microwave Symp. Digest, Atlanta, GA, June 2008, pp. 1373–1376 35 emTM Version 12.54, Sonnet Software, Inc., 100 Elwood Davis Road, North Syracuse, NY 13212, USA, 2009 36 Koziel, S., Bandler, J.W.: ‘SMF: a user-friendly software engine for space-mapping-based engineering design optimization’. Int. Symp. Signals, Systems and Electronics, URSI ISSSE 2007, Montreal, Canada, 2007, pp. 157– 160 37 Koziel, S., Bandler, J.W.: ‘Rapid design optimisation of microwave structures through automated tuning space mapping’, IET Microw. Antennas Propag., 2010, 4, (11), pp. 1892– 1902 38 Koziel, S., Bandler, J.W., Cheng, Q.S.: ‘Design optimization of microwave circuits through fast embedded tuning space mapping’. Proc. 40th European Microwave Conf., Paris, France, October 2010, pp. 1186–1189 39 Agilent ADS, Version 2008, Agilent Technologies, 1400 Fountaingrove Parkway, Santa Rosa, CA 95403-1799, 2008 40 Kuo, J.T., Chen, S.P., Jiang, M.: ‘Parallel-coupled microstrip filters with over-coupled end stages for suppression of spurious responses’, IEEE Microw. Wirel. Comp. Lett., 2003, 13, (10), pp. 440–442 41 Salleh, M.K.M., Pringent, G., Pigaglio, O., Crampagne, R.: ‘Quarterwavelength side-coupled ring resonator for bandpass filters’, IEEE Trans. Microw. Theory Tech., 2008, 56, (1), pp. 156– 162 42 Lee, H.-M., Tsai, C.-M.: ‘Improved coupled-microstrip filter design using effective even-mode and odd-mode characteristic impedances’, IEEE Trans. Microw. Theory Tech., 2005, 53, (9), pp. 2812– 2818
