This paper presents a comprehensive approach to engineering design optimization exploiting space mapping (SM). The algorithms employ input SM and a new generalization of implicit SM to minimize the misalignment between the coarse and fine models of the optimized object over a region of interest. Output SM ensures the matching of responses and first-order derivatives between the mapped coarse model and the fine model at the current iteration point in the optimization process. We provide theoretical results that show the importance of the explicit use of sensitivity information to the convergence properties of our family of algorithms. Our algorithm is demonstrated on the optimization of a microstrip bandpass filter, a bandpass filter with double-coupled resonators, and a seven-section impedance transformer. We describe the novel user-oriented software package SMF that implements the new family of SM optimization algorithms

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A Space-Mapping Framework for Engineering Optimization&#8212;Theory and Implementation

Objective functions that appear in engineering practice may come from measurements of physical systems and, more often, from computer simulations. In many cases, optimization of such objectives in a straightforward way, i.e., by applying optimization routines directly to these functions, is impractical. One reason is that simulation-based objective functions are often analytically intractable (discontinuous, non-differentiable, and inherently noisy). Also, sensitivity information is usually unavailable, or too expensive to compute. Another, and in many cases even more important, reason is the high computational cost of measurement/simulations. Simulation times of several hours, days or even weeks per objective function evaluation are not uncommon in contemporary engineering, despite the increase of available computing power. Feasible handling of these unmanageable functions can be accomplished using surrogate models: the optimization of the original objective is replaced by iterative re-optimization and updating of the analytically tractable and computationally cheap surrogate. This chapter briefly describes the basics of surrogate-based optimization, various ways of creating surrogate models, as well as several examples of surrogate-based optimization techniques.

Surrogate-Based Methods

A shape-preserving response prediction methodology for microwave design optimization is introduced. The presented technique allows us to estimate the response of the microwave structure being optimized (fine model) using a computationally cheap representation of the structure (coarse model). The change of the coarse model response is described by the translation vectors corresponding to certain (finite) number of characteristic points of the response. These translation vectors are subsequently used to predict the response change of the fine model. The presented method has very good generalization capability and it is not based on any extractable parameters, which makes it easy to implement. Applications for microwave design optimization are discussed. The robustness of the proposed approach is demonstrated by extensive comparison with space mapping, which is one of the most efficient optimization approaches in microwave engineering so far.

Shape-Preserving Response Prediction for Microwave Design Optimization

A novel super-compact multilayered (ML) composite-right/left-handed (CRLH) transmission line (TL) is proposed. This ML architecture consists of the periodic repetition of pairs of U-shaped parallel plates connected to a ground enclosure by meander lines. The parallel plates provide the left-handed (LH) series capacitance, and the meander lines provide the LH shunt inductance, while the right-handed parasitic series inductance and shunt capacitance are generated by the metallic connections in the direction of propagation and by the voltage gradient from the TL to the ground enclosure, respectively. In contrast to previously reported planar LH or CRLH TLs, the ML TL has its direction of propagation along the vertical direction, perpendicular to the plane of the substrates. This presents the distinct advantage that large electrical length can be achieved over an extremely short TL length and small transverse footprint. The LH-range characteristics of the multilayer CRLH TL are analyzed by the finite-element method and finite-difference time-domain (FDTD) full-wave simulations. In addition, the CRLH equivalent-circuit model is applied to gain simple insight into the behavior of the structure. Finally, the theoretical results are confirmed by experiments using the initial prototype with the very small length (thickness) of 0.016/spl lambda//sub g/ and footprint of 0.06/spl lambda//sub g//spl times/0.08/spl lambda//sub g/ (/spl lambda//sub g/=/spl lambda//sub 0///spl radic//spl epsiv//sub r/=235 mm at the center of the LH band, 0.4 GHz). The proposed miniaturized ML line can find applications in bandpass filters, delay lines, and numerous phase-advance components. As an example of application, a 1-GHz/2-GHz diplexer, composed of two ML CRLH TLs, is demonstrated. The ML CRLH TL proposed here presents a great potential for the development of novel microwave components taking profit of new multilayer technologies such as low-temperature co-fired ceramic technology.

Super-compact multilayered left-handed transmission line and diplexer application

Output space mapping is a technique introduced to enhance the robustness of the space-mapping optimization process in case the space-mapped coarse model cannot provide sufficient matching with the fine model. The technique often works very well; however, in some cases it fails. Especially in the microwave area where the typical model response (e.g., |S 21|) is a highly nonlinear function of the free parameter (e.g., frequency), the output space-mapping correction term may actually increase the mismatch between the surrogate and fine models for points other than the one at which the term was calculated, as in the surrogate model optimization process. In this paper, an adaptive response correction scheme is presented to work in conjunction with space-mapping optimization algorithms. This technique is designed to alleviate the difficulties of the standard output space mapping by adaptive adjustment of the response correction term according to the changes of the space-mapped coarse model response. Examples indicate the robustness of our approach.

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Space Mapping With Adaptive Response Correction for Microwave Design Optimization

A new concept called the dynamic coarse model is proposed and is applied to the optimization design of low-temperature co-fired ceramic (LTCC) multilayer RF circuits with the aggressive space mapping (ASM) technique. The dynamic coarse model is a combination of an evolutionary equivalent-circuit model and an efficient quasi-static numerical electromagnetic (EM) model-partial-element equivalent-circuit model. Namely, there are two forms of coarse models jointly in use: the coarse schematic model and the coarse EM model. The coarse schematic model evolutionarily incorporates parasitic effects that can be extracted from its accompanying coarse EM model. This process can greatly facilitate the original ASM process by easily determining a "high-quality" optimized coarse model. Two LTCC frequency-selective passive modules, i.e., a bandpass filter and a diplexer, are designed using the proposed scheme and ASM. No nonuniqueness in parameter extraction is encountered. Good convergence performance is achieved for the designs of both modules.

https://www.ee.cuhk.edu.hk/~klwu/pdf/mtt200401.pdf

An effective dynamic coarse model for optimization design of LTCC RF circuits with aggressive space mapping

In this paper, a derived physically expressive circuit model is presented for automatically deriving an equivalent-circuit model of a multilayered embedded RF passive. The scheme is based on the partial-element equivalent-circuit (PEEC) model and a simple circuit transformation. By defining an appropriate cutoff criterion that is related to the highest frequency of interest, most of the internal nodes in the coupling circuit generated by the PEEC model can be approximately absorbed by the remaining frequency-independent LC elements progressively. The model is very simple to implement and has apparent physical meaning. Mathematically, this model progressively recombines the least significant system pole with other less significant poles. The resultant physically expressive circuit model will be very useful in designing multilayer embedded RF circuits. Four examples are given for demonstrating the validity and effectiveness of the scheme.

https://www.ee.cuhk.edu.hk/~klwu/pdf/mtt200605.pdf

A derived physically expressive circuit model for multilayer RF embedded passives

In this article, a system-on-package (SoP) approach for Bluetooth system module applications using low-temperature co-fired ceramic (LTCC) technology is presented. The developed LTCC integrated substrate for our Bluetooth module application is overall 12 × 12 × 1 mm3 in size, with integration of two originally proposed components, a balanced-to-unbalanced bandpass filter and a folded meander-line inverted-F antenna, as well as other passive circuitries. The embedded balanced-to-unbalanced filter, which is derived from the basic center-tapped transformer circuit, works simultaneously as a balun and a bandpass filter, thus leading to a significant amount of size reduction for the overall module. Likewise, comparing to the usual quarter-wavelength inverted-F antennas, our proposed antenna is only one-tenth of a wavelength in length—but no sacrificing of antenna efficiency. Consequently, couplings among different functional blocks of this highly integrated module are crucial to its performance and the resulting effects are discussed. A fully functional prototype is successfully fabricated and tested, demonstrating a promising solution for Bluetooth applications. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.

https://www.ee.cuhk.edu.hk/~klwu/pdf/IJRF200603.pdf

A compact LTCC bluetooth system module with an integrated antenna

In this paper, a system-on-package (SoP) approach for Bluetooth system modules using low temperature co-fired ceramic (LTCC) substrate technology is presented The proposed Bluetooth module is overall 12mm by 12mm in size, with integration of two originally proposed components, a balanced-to-unbalanced filter and an antenna, as well as other passive circuitries The embedded balanced-to-unbalanced filter, which is derived from the basic center-tapped transformer circuit, works simultaneously as a balun and a bandpass filter, thus leads to a significant amount of size reduction for the overall module Likewise, comparing with the usual half-wavelength printed antennas, our proposed antenna is only one-tenth of wavelength in size without sacrificing of efficiency Consequently, couplings among various embedded components of this highly integrated module are crucial to its performance and the resulting effects are discussed A fully functional prototype has been successfully fabricated, showing a promising solution for Bluetooth applications

Development of an integrated LTCC Bluetooth module

The aggressive space mapping (ASM) algorithm is applied to the optimization design of LTCC filters. The partial element equivalent circuit (PEEC) method is utilized as a coarse model. Low-pass and band-pass LTCC filters are designed with HFSS and IE3D adopted as the fine models, respectively. Conductor thickness is taken into account, since it is fairly large with respect to dielectric height. Only a few instances of fine-model simulation are needed. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 24–28, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20034

Jie Wang

Papers

An effective dynamic coarse model for optimization design of LTCC RF circuits with aggressive space mapping

A derived physically expressive circuit model for multilayer RF embedded passives

A compact LTCC bluetooth system module with an integrated antenna

Development of an integrated LTCC Bluetooth module

An efficient design method of LTCC filters with aggressive space mapping technique