Search

Breaking through the current power density, efficiency, and cost ceilings is no small feat. With converter designs that reach well beyond 20 kW/L and g99% efficiency, it is no wonder that design optimization has filtered into power electronics to further push these envelopes.

[EN] Space mapping (SM) and aggressive SM (ASM) techniques are widely used in the synthesis and design of microwave filters. Their popularity stems from the inherent simplicity of the procedures and from their effectiveness. The objective of this article is to extend the state of the art of these techniques by discussing how they can also be used very effectively to tune microwave filters. In addition to the theory, the successful tuning of a six-pole inductive waveguide filter is discussed in detail, thereby fully validating the proposed SM techniques., This work was supported by funds from the "La Caixa" Foundation (Code: B004442) and Agencia Estatal de Investigacion (AEI) and Union Europea through Fondo Europeo de Desarrollo Regional-FEDER-"Una manera de hacer Europa" (AEI/FEDER, UE), under Research Project TEC2016-75934-C4-1-R

This paper addresses the problem of expedited surrogate-assisted multi-objective optimization of compact microwave passives. Our methodology adopts the concept of constrained modeling, enhanced by a reduction of the parameter space dimensionality. The latter is realized through the spectral analysis of the supplementary reference design set used to estimate the geometry of the Pareto front. As demonstrated using a 15-parameter impedance transformer, the combination of these mechanisms permits identification of the Pareto set at the cost of just a few hundred of EM circuit simulations. Benchmarking reveals considerable efficiency improvements achieved over the state-of-the-art surrogate-based MO algorithms.

This paper addresses cost-efficient surrogate modeling of miniaturized microwave components. Following the recently proposed performance-driven modeling paradigm, the set of reference designs pre-optimized with respect to the selected operating conditions are employed to determine the model domain and to focus the surrogate build-up process only on the promising regions of the parameter space. Here, the principal component analysis (PCA) is applied to reduce the domain dimensionality. This is achieved by spanning it using a limited number of principal directions which are the most relevant from the point of view of the reference design correlations. The fundamental advantage of the proposed methodology is an improved predictive power of the surrogate and better scalability (as a function of the training data set size), as compared to the previous performance-driven modeling attempts. The procedure is illustrated using a compact impedance matching transformer.

Electromagnetic (EM)-driven parameter tuning plays an ever-increasing role in contemporary microwave design. The primary reason is the growing complexity of circuits and the lack of simpler (analytical, network-equivalent) models capable of accounting for effects such as EM cross-couplings within miniaturized microstrip components. The high CPU cost of EM-based optimization can be alleviated in various ways, one being utilization of already existing designs obtained for various sets of performance specifications. This paper proposes a practical procedure that greatly accelerates parameter tuning by exploiting the information contained in the existing design database. The latter is encoded into an inverse kriging metamodel utilized to yield a good starting point and a forward surrogate providing an initial estimate of a Jacobian matrix of the system response. Our methodology is illustrated using a miniaturized three-section impedance matching transformer with its operating bandwidth edges re-designed from 1.5 GHz to 3.5 GHz (lower end) and 4.5 GHz to 6.5 GHz (upper end).

"Come and look at this," Steve Chen said in 1993. I still see him in the doorway, beckoning me, and I remember where his computer stood and how it was oriented as I leaned toward its screen seconds later for my first glimpse at the results of a novel approach to automated design, a technique that I believe encapsulates the engineer's mysterious "feel" for a problem-an issue that had dogged my 30-year immersion in the art and science of optimization for computer-oriented engineering design.

A recently introduced cognition-driven formulation of space mapping (SM) is an efficient method for equal-ripple optimisation of microwave filters. Feature frequency parameters and ripple height parameters are utilised. The technique requires the assumption that the initial number of feature parameters is correct, and uses an equally divided passband specification as a preliminary target. The present study proposes an enhanced technique which can correct the number of feature frequency parameters, thus it can work well even if the filter response of the initial point has an incorrect number of feature frequency parameters. Additionally, the enhanced technique incorporates filter design knowledge of the Chebyshev filter function into cognition-driven SM. The authors propose to use the feature frequency parameters of the Chebyshev filter function response curve to obtain the target for cognition-driven SM. A new trust region mechanism handles new parameters in the proposed process of correcting the number of feature frequency parameters and guarantees convergence. The technique is suitable for the design of filters with equal-ripple responses. It is illustrated by two microwave filter examples.

Outlines some of the issues we face when preparing for and then delivering a presentation, and we provide hints at the barriers we would like to dismantle on the road to engaging, accessible, and compelling presentations.

Fast and reliable statistical analysis of compact microwave couplers is addressed. The proposed technique exploits variable-fidelity electromagnetic (EM) simulation models as well as a response feature approach. By establishing a local feature-based surrogate of the structure at hand, as well as a mapping between characteristic points of EM models of various fidelities, yield estimation can be carried out at extremely low cost of a few high-fidelity EM analyses. The methodology has been demonstrated using a CMRC-based miniaturized equal power split rat-race coupler operating at 1 GHz. Reliability of the approach is verified by comparing with direct Monte Carlo analysis and single-fidelity feature-based yield estimation.

The authors introduce a methodology for fast multi-objective design optimisation of miniaturised microwave couplers. The approach exploits the surrogate-based optimisation paradigm with an underlying low-fidelity model constructed from an equivalent circuit of the structure under consideration, corrected through implicit and frequency space mapping. A fast prediction tool obtained this way is subsequently optimised by a multi-objective evolutionary algorithm to identify an initial approximation of the Pareto front, that is, a set of designs representing the best possible trade-offs between conflicting objectives. The correction/optimisation of the surrogate is then iterated by design space confinement and segmentation based on a Pareto set representation obtained thus far in the process. This aims at improving the surrogate model accuracy in the vicinity of the Pareto-optimal solutions. The technique is demonstrated by two design examples of compact rat-race couplers. Experimental validation is also provided.

A simple, reliable, and accurate surrogate modelling technique for microwave structures is presented. A hierarchical surrogate model is constructed using response surface approximations (RSAs) of suitable response features with embedded ‘visible’ knowledge. The authors describe and discuss a novel scanning algorithm for capturing these desired response features. They demonstrate that the dependence of the selected features on the designable parameters is much less non-linear than that of the original responses taken as functions of the design parameters. They illustrate the steps of their algorithm using novel diagrams. They simplify the description of their modelling process by exploiting an operator notation. They discuss relationships between their method and other feature-based approaches such as shape-preserving response prediction (SPRP). They provide a wideband microstrip bandstop filter, a fourth-order ring resonator bandpass filter and a microstrip bandpass filter with open stub inverter examples to demonstrate their approach. Using these examples, they compare their approach with two very different direct RSA methods (kriging and radial basis function) and an SPRP method. The models of all the filter examples are validated using design optimisation.

In this work, methodologies for low-cost and reliable microwave modeling are presented using variable-fidelity response features. The two key components of our approach are: 1) a realization of the modeling process at the level of suitably selected feature points of the responses (e.g., $S$ -parameters versus frequency) of the structure at hand and 2) the exploitation of variable-fidelity EM simulation data, also for the response feature representation. Due to the less nonlinear dependence between the coordinates of the feature points on the geometrical parameters of the structure of interest, the amount of training data can be greatly reduced. Additional cost reduction is obtained by means of generating the majority of the training data at a coarse-discretization EM simulation level and exploiting the correlations between the EM models of various fidelities. We propose two ways of combining the low- and high-fidelity data sets: 1) an external approach, through space mapping (simpler to implement) and 2) an internal approach, using co-kriging (more flexible and potentially offering better accuracy). The operation and performance of our modeling techniques are demonstrated by three microstrip filter examples and a compact rat-race coupler. A comprehensive verification and comparisons with several benchmark techniques, as well as application examples (filter optimization) are also provided.

The paper discusses low-cost multi-objective optimization of compact microwave components using variablefidelity EM simulation models and data-driven surrogates. Our approach builds upon a recently reported method where the initial approximation of the Pareto set is obtained by optimizing the kriging surrogate constructed from sampled data of the coarsediscretization EM model of the structure at hand, with selected designs further refined to obtain the high-fidelity Pareto set. The drawback of the method is a large number of training data samples required to set up the surrogate. Here, considerable savings concerning the training data set size are achieved by Pareto front decomposition based on auxiliary points identified along the front and setting up the kriging models in the corresponding subdomains. The key factor is that the total volume of the sub-domains is considerably smaller than the volume of the original domain. Our considerations are illustrated using a compact rat-race coupler with design optimization cost savings of 29- and 30-percent for two and three sub-domains, respectively.

A simple technique for fast design tuning of compact rat-race couplers is presented. Our approach involves equivalent circuit representation, corrected by nonlinear functions of frequency with coefficients extracted through nonlinear regression. At the same time, the tuning process connects two levels of coupler representation: EM simulation of the entire circuit and re-optimization of the coupler building blocks (slow-wave cells and folded transmission lines) with specifications obtained by appropriate manipulation of the corrected network model. The latter is driven by the necessity of accounting for EM cross-couplings within the coupler that result in performance degradation. Demonstration examples of a miniaturized rat-race coupler indicate that rapid and reliable design closure (at a cost of two or three coupler simulations) can be accomplished even for strong cross-couplings within the structure.

A simple, reliable methodology for geometry parameter scaling of compact microstrip couplers is presented. Our approach allows for rapid re-design of the structure with respect to the operating conditions (operating frequency and power split ratio) as well as material parameters of the dielectric substrate (permittivity and thickness). The scaling process involves an inverse surrogate model constructed from a set of optimized reference designs obtained at the level of the equivalent circuit representation of the coupler, as well as an iterative correction procedure for fine tuning of the design. A demonstration example of a compact rat-race coupler indicates that accurate dimension scaling can be achieved at a low cost of up to three EM simulations of the structure, for a wide range of operating conditions (1 GHz to 2 GHz for the operating frequency, −3 dB to 0 dB for power split) and substrate parameters (0.7 mm to 1.5 mm for the thickness, and 2.5 to 3.5 for dielectric permittivity).

[EN] The objective of this paper is to advance the state of the art of aggressive space mapping (ASM) by demonstrating how, for resonant structures, and microwave filters in particular, an ASM-based optimization procedure may converge to the desired target performance in just one step. This behavior is first justifed in physical terms, using the electromagnetic cavity perturbation theory, and is then investigated numerically. Several practical filter design demonstrations are also presented. This paper is concluded with a conceptual definition of Space Alignment in the context of ASM., This work was supported by MINECO (Spanish Government) under R&D Project TEC2016-75934-C4-1-R and R&D Technicians Grant PTA2015-10839-I.

Quantitative microwave holography is a recently developed direct inversion imaging algorithm. This method shows promise in medical imaging due to its low computational cost and ability to quantitatively estimate the tissue permittivity. However, it faces challenges regarding nonphysical permittivity values (i.e., real relative permittivity less than 1, and imaginary relative permittivity greater than 0) in the reconstructed images. Here, we propose an optimization method capable of removing nonphysical values. This approach is demonstrated in a tissue imaging experiment. Additionally, we discuss the impact of phase wrapping on the Rytov's approximation-based version of quantitative microwave holography.

Space mapping is a recognized method for speeding up electromagnetic (EM) optimization. Existing space-mapping approaches belong to the class of surrogate-based optimization methods. This paper proposes a cognition-driven formulation of space mapping that does not require explicit surrogates. The proposed method is applied to EM-based filter optimization. The new technique utilizes two sets of intermediate feature space parameters, including feature frequency parameters and ripple height parameters. The design variables are mapped to the feature frequency parameters, which are further mapped to the ripple height parameters. By formulating the cognition-driven optimization directly in the feature space, our method increases optimization efficiency and the ability to avoid being trapped in local minima. The technique is suitable for design of filters with equal-ripple responses. It is illustrated by two microwave filter examples.

In this paper, we propose a simple, yet reliable methodology to expedite yield estimation and optimization of microwave structures. In our approach, the analysis of the entire response of the structure at hand (e.g., $S$ -parameters as a function of frequency) is replaced by response surface modeling of suitably selected feature points. On the one hand, this is sufficient to determine whether a design satisfies given performance specifications. On the other, by exploiting the almost linear dependence of the feature points on the designable parameters of the structure, reliable yield estimates can be realized at low computational cost. Our methodology is verified using two examples of waveguide filters and one microstrip hairpin filter and compared with conventional Monte Carlo analysis based on repetitive electromagnetic simulations, as well as with statistical analysis exploiting linear response expansions around the nominal design. Finally, we perform yield-driven design optimizations on these filters.

In this paper, a technique for rapid re-design of compact microwave couplers with respect to operating frequency is discussed. Our methodology involves an inverse surrogate model setup using several reference designs optimized (at the level of equivalent circuit representation of the coupler) for a set of operating frequencies within a range of interest. The surrogate establishes the relationship between the operating frequency and geometry parameter values. Upon suitable correction, it can be utilized to re-design the coupler at the EM simulation model level. Further correction — derived from sensitivity analysis of the equivalent network model — is introduced to ensure an equal power split of scaled structure. The overall computational cost of the redesign process, including both correction stages, corresponds to only two EM analyses of the circuit. Our considerations are illustrated using a compact microstrip rat-race coupler scaled for the operating frequency range of 0.5 GHz to 2.5 GHz.

This paper highlights milestones and setbacks in the exciting personal journey from the first special issue of the IEEE Transactions on Microwave Theory and Techniques on Computer-Oriented Microwave Practices, edited by William J. Getsinger, an early visionary in this field, to today's mainstream acceptance of surrogates, surrogate models and space mapping technology in the tuning and design optimization of complex structures to electromagnetic accuracy. Some design automation features and aspirations that had been imagined throughout this period, but have yet to be implemented, need to be seriously revisited, particularly as the focus turns to multiphysics modeling and design. The adoption of physically-based surrogates, space mapping technology, and the refinement of feature-based and cognition-driven approaches take on a new urgency.

A new development of the shape-preserving response prediction (SPRP) technique for microwave design optimisation is presented here. The original SPRP method is enhanced by employing low-cost derivative information obtained through adjoint sensitivities. The authors propose using operator notation to simplify the SPRP surrogate description. The enhancement through sensitivity data is twofold: to ensure first-order consistency between the SPRP surrogate and the high-fidelity electromagnetic (EM) model under optimisation and to speed up the surrogate optimisation process. Fast surrogate optimisation allows us to use coarse-discretisation EM simulations as an underlying low-fidelity model and, therefore, efficiently apply SPRP to cases where reliable circuit models are not available (e.g. design of antenna structures). The proposed approach is demonstrated using a dielectric resonator filter and an ultra-wideband monopole antenna. Comparison with three benchmark techniques, including the original SPRP methods, space mapping with sensitivity and direct optimisation of the high-fidelity model, is also provided.

We present a low-cost modeling methodology for microwave structures exploiting low/high-fidelity electromagnetic (EM) simulations, shape-preserving response prediction (SPRP)/generalized shape-preserving response prediction (GSPRP), and space mapping (SM). Our approach is a two-step process. In step 1, a coarse model is constructed from low-fidelity (coarse discretization) EM simulation data by means of a recently developed SPRP/GSPRP technique. A comparison between the SPRP and GSPRP methods is described. In step 2, the coarse model is enhanced by SM using a fine model (high-fidelity EM simulations). We summarize the substeps in each step of the proposed algorithm and illustrate them graphically. We compare our proposed method with relevant benchmark techniques. Our approach is demonstrated by using two microstrip filter examples. The results and efficiency of our approach are compared with the benchmark techniques, indicating substantial accuracy improvement for comparable training set size. Applications for design optimization are also discussed.

We present, for the first time, an efficient adjoint variable method (AVM) for estimating second-order sensitivities exploiting time-domain transmission-line modeling. For a structure with n designable parameters, the complete Hessian matrix of any desired objective function is estimated using n extra simulations as compared to O(n2) using the traditional finite-difference approaches. Our approach is illustrated through estimating the second-order sensitivities for energy functions and scattering parameter with respect to dimensions and material properties of metallic and dielectric discontinuities. The results achieved using our AVM approach are verified using the expensive finite-difference approaches.

We present a robust space mapping (SM) algorithm exploiting electromagnetic (EM)-based adjoint sensitivities for microwave design optimization. Our approach utilizes low-cost EM-based adjoint sensitivities and trust region methods to improve an SM algorithm at three levels, which are: 1) to build a better overall surrogate while ensuring convergence; 2) to speed up and safeguard the parameter extraction steps; and 3) to speed up and safeguard the surrogate optimization process. We describe the implementation at each level in detail. We review relevant adjoint sensitivity analysis methods. We also review prior SM methods that exploit both sensitivity and adjoint sensitivity. We summarize these methods in four categories. We compare our proposed approach with them. Efficiency, robustness, and versatility of our method are demonstrated by three design examples: an antenna, a planar filter, and a 3-D resonator filter. We compare the results with those obtained by SM without using adjoint sensitivity information and by direct optimization of the high-fidelity EM models.

A handset antenna modeling and design technique using space mapping (SM) is presented. Thin-wire models are exploited as coarse models in the SM algorithms, while the fine models are high-accuracy electromagnetic simulations. The thin-wire models capture the basic physics of handset antennas but are not as accurate as the fine model. On the other hand, they are computationally cheap when analyzed by the method of moments solvers. Detailed guidelines for building thin-wire models are provided. Two SM algorithms are employed: 1) implicit, input and output space mapping and 2) implicit and output space mapping. An internal dual-band patch antenna and an arm-folded planar inverted F antenna are designed through our approach. For comparison, direct optimizations have been performed in each example.

A novel methodology for miniaturization-oriented design of a class of wideband branch-line couplers is proposed. The initial design is chosen from a family of optimized circuits that feature a simplified two-section topology. Compact size of the coupler is attained by using quasi-periodic slow-wave structures instead of conventional lines. Our approach explicitly aims at circuit size reduction by adjusting the number of elements within the recurrent slow-wave structure and its designable parameters to reach the smallest coupler layout possible. This is achieved at a low cost by exploiting a surrogate-based optimization (SBO) process with the underlying model of the recurrent slow-wave structure composed of multiple response surface approximations (RSAs). The SBO scheme incorporates adaptively adjusted design specifications to converge in just two iterations. A rapid fine-tuning procedure is applied to account for T-junction effects omitted during the design process. Our methodology is illustrated through a numerical example supported by experimental verification.

A good compromise between size and electrical performance is an important design consideration for compact microwave structures. Comprehensive information about size/performance trade-offs can be obtained through multi-objective optimization. Due to considerable electromagnetic (EM) cross-couplings in highly compressed layouts, the design process has to be conducted at the level of high-fidelity EM analysis which is computationally prohibitive when using conventional methods (e.g., population-based metaheuristics). Here, we perform multi-objective design of compact structures using a domain patching algorithm. It is a low-cost and deterministic procedure for constructing the path connecting the extreme Pareto-optimal designs (obtained through auxiliary single-objective optimization runs), executed at the level of coarse-discretization EM simulations. The final representation of the Pareto front is then generated from response correction techniques. Our approach is illustrated through a compact impedance matching transformer.

A cognition-driven formulation of space mapping (SM) is effective for equal-ripple optimization of microwave filter. In this paper, we use cognition-driven SM to estimate yield in the design of microwave filters. With mappings from the statistical variable space to feature parameter spaces, we can find the distribution of these intermediate feature parameters with respect to the statistical variables. A correction method is proposed to improve the accuracy of the mappings. Thus, we can determine the yield by checking whether the ripple height parameters and some specific feature frequency parameters satisfy the specifications or not. The number of EM simulations of the proposed yield estimation method is linear with respect to the number of statistical variables. We further propose a yield optimization method using our yield estimation. Our method is verified using a waveguide filter and Monte Carlo analysis.

In this paper, a low-cost procedure for dimension scaling and tuning of microwave filters is proposed. Our approach relies on an inverse model that outputs the filter dimensions for the required center frequency and bandwidth. The model is constructed using several reference designs obtained using surrogate-assisted optimization exploiting a response feature methodology. The initial approximation of the scaled filter design is subsequently corrected using a fast feature-based tuning procedure. The proposed methodology is demonstrated using a fifth-order Chebyshev bandpass filter for the tuning range of 10 GHz to 12 GHz (center frequency) and 6 % to 12 % (relative bandwidth).

After decades of research and development in the computation of electromagnetic (EM) fields, the microwave breakthrough in harnessing commercial field solvers for design optimization appeared in the early 1990s. Almost simultaneously, the commercial implementation of an effective response surface technique was complemented by the discovery of the space mapping concept that promised electromagnetically validated, near optimal solutions at the expense of only a few high-fidelity full-wave simulations. Simplified models, even coarse electromagnetic models, could now be iteratively “mapped” on-the-fly to full-wave models through the 1995 aggressive space mapping algorithm. In this paper, we offer a brief overview of further advances to date, including space mapping, response correction techniques, simulation-based tuning, as well as feature-based modeling and optimization.

We present a versatile technique for constructing fast microwave component models at a low computational cost. Our modeling procedure consists of two stages: (i) kriging interpolation of coarsely discretized electromagnetic simulation data of the device under consideration and (ii) enhancing the kriging model by using space mapping and a limited amount of high-fidelity electromagnetic simulation data. The use of coarse discretization data allows for low-cost model generation, whereas space mapping is a convenient way of ensuring its accuracy. Our approach can be applied to almost any type of microwave device; it can also work with other types of nonsmooth or costly low-fidelity models. The operation and performance of our methodology is demonstrated using a variety of microwave components, including a microstrip filter, a planar ultrawideband antenna, and a microstrip-to-coplanar waveguide transition. Copyright © 2012 John Wiley & Sons, Ltd.

A novel sensitivity-analysis method is proposed to compute the S-parameter Jacobian with respect to metallic shape parameters. The formulation is analytical and is derived from Maxwell's equations directly. It is independent of the field solution method and the respective system matrix. It requires only the field solution on the object surface. The computation is a post-process and its overhead is negligible in comparison with a full-wave simulation. The method provides exact sensitivities. It is validated by the sensitivity analysis of microwave structures where the field solution is provided by commercial solvers based on the finite-element method, the method of moments, and the finite-difference time-domain method.

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. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: 639–651, 2012. © 2012 Wiley Periodicals, Inc.