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Stringent performance specifications along with constraints imposed on physical dimensions make the design of contemporary microwave components a truly onerous task. In recent years, the latter demand has been growing in importance with the innovative application of areas such as the Internet of Things coming into play. The need to employ full-wave electromagnetic (EM) simulations for response evaluation, reliable, yet CPU-heavy, only aggravates the issue. This paper proposes a reduced-cost miniaturization algorithm that employs a trust-region search procedure and multi-resolution EM simulations. In our approach, the resolution of the EM model is adjusted throughout the optimization process based on its convergence status starting from the lowest admissible fidelity. As the algorithm converges, the resolution is increased up to the high-fidelity one, used at the final phase to ensure reliability. Four microwave components have been utilized as verification structures: an impedance matching transformer and three branch-line couplers. Significant savings in terms of the number of EM analyses required to conclude the size reduction process of 41, 42, 38 and 50 percent have been obtained (in comparison to a single-fidelity procedure). The footprint area of the designs optimized using the proposed approach are equal to 32, 205, 410 and 132 mm2, in comparison to 52, 275, 525 and 213 mm2 of the initial (and already compact) design. [ABSTRACT FROM AUTHOR]

Geometry parameters of contemporary microwave passives have to be carefully tuned in the final stages of their design process to ensure the best possible performance. For reliability reasons, the tuning has to be carried out at the level of full-wave electromagnetic (EM) simulations. This is because traditional modeling methods are incapable of quantifying certain phenomena that may affect the operation and performance of these devices, such as cross-coupling effects. As a consequence, the designs yielded with the use of equivalent network models may only serve as starting points that need further refinement. Unfortunately, simulation-driven numerical optimization is computationally demanding even in the case of local search procedures. Thus, significant research efforts have been aimed toward identifying effective ways of expediting EM-driven optimization procedures, critical from the point of view of cost of design cycles. Among these, one may list the recently proposed multifidelity optimization frameworks. Another option for accelerating simulation-driven design procedures is sparse sensitivity updating schemes, where costly gradient estimation through finite differentiation (FD) is suppressed for selected variables. This work proposes a novel algorithm that capitalizes on both aforementioned mechanisms to reduce the optimization cost of local gradient-based parameter tuning of compact microwave components. In our approach, multifidelity optimization is further expedited by replacing expensive FD sensitivity updates with the Broyden formula for selected design variables. Verification using two microwave structures, a branch-line coupler and a power divider, demonstrates average savings of around 80% over the basic trust-region (TR) routine, with only minor degradation of the design quality. [ABSTRACT FROM AUTHOR]

Practical microwave design is most often carried out in the nominal sense. Yet, in some cases, performance degradation due to uncertainties may lead to the system failing to meet the prescribed specifications. Reliable uncertainty quantification (UQ) is, therefore, important yet intricate from numerical standpoint, especially when the circuit at hand is to be evaluated using electromagnetic (EM) simulation tools. Tolerance-aware design (e.g., yield improvement) is even more challenging. This article introduces a methodology for low-cost surrogate-based yield optimization of passive microwave components. The novelty of the proposed approach, and, at the same time, its major acceleration factor is to span the metamodel domain with the selected principal vectors, characterized by significant response variability within operating frequency bands of the component under design. This results in a volumewise constriction of the domain (thereby lower cost of the surrogate model setup) without restricting its size along the relevant directions of the parameter space. Consequently, our technique is a one-shot approach for yield optimization that does not require neither domain relocation nor surrogate reconstruction. Our methodology is demonstrated using two microstrip components and favorably compared to benchmark metamodeling techniques in terms of the computational cost of the yield maximization procedure. The average cost is only 130 EM simulations of the respective circuit, versus the average of 800 and over 360 analyses for the benchmark procedures. At the same time, its reliability is verified by means of EM-based Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

In modern electronics, there are many inevitable uncertainties and variations of design parameters that have a profound effect on the performance of a device. These are, among others, induced by manufacturing tolerances, assembling inaccuracies, material diversities, machining errors, etc. This prompts wide interests in enhanced optimization algorithms that take the effect of these uncertainty sources into account and that are able to find robust designs, i.e., designs that are insensitive to the uncertainties early in the design cycle. In this work, a novel machine learning-based optimization framework that accounts for uncertainty of the design parameters is presented. This is achieved by using a modified version of the expected improvement criterion. Moreover, a data-efficient Bayesian Optimization framework is leveraged to limit the number of simulations required to find a robust design solution. Two suitable application examples validate that the robustness is significantly improved compared to standard design methods. [ABSTRACT FROM AUTHOR]

Parameter adjustment through numerical optimization has become a commonplace of contemporary microwave engineering. Although circuit theory methods are ubiquitous in the development of microwave components, the initial designs obtained with such tools have to be further tuned to improve the system performance. This is particularly pertinent to miniaturized structures, where the cross-coupling effects cannot be adequately accounted for using equivalent networks. For the sake of reliability, design closure is normally performed using full-wave electromagnetic (EM) simulation models, which entails considerable computational expenses, often impractically excessive. Available mitigation techniques include acceleration of the conventional (e.g., gradient-based) routines using adjoint sensitivities or sparse sensitivity updates, surrogate-assisted and machine learning algorithms, the latter often combined with nature-inspired procedures. Another alternative is the employment of variable-fidelity simulations (e.g., space mapping, co-kriging), which is most often limited to two levels of accuracy (coarse/fine). This work discusses an EM model management approach coupled with trust-region gradient-based routine, which exploits problem-specific knowledge for continuous (multi-level) modification of the discretization density of the microwave structure at hand in the course of the optimization run. The optimization process is launched at the lowest discretization level, thereby allowing for low-cost exploitation of the knowledge about the device under study. Subsequently, based on the convergence indicators, the model fidelity is gradually increased to ensure reliability. The simulation fidelity selection is governed by the algorithm convergence indicators. Computational speedup (i.e., reduction in the number of EM simulations required by the optimization process to converge) is achieved by maintaining low resolution in the initial stages of the optimization run, whereas design quality is secured by eventually switching to the high-fidelity model when close to concluding the process. Numerical verification is carried out using two microstrip circuits, a dual-band power divider and a dual-band branch-line coupler, with the average savings of almost sixty percent when compared to single-fidelity optimization.

Design of contemporary microwave components is-in a large part-based on full-wave electromagnetic (EM) simulation tools. The primary reasons for this include reliability and versatility of EM analysis. In fact, for many microwave structures, notably compact components, EM-driven parameter tuning is virtually imperative because traditional models (analytical or network equivalents) are unable to account for the cross-coupling effects, strongly present in miniaturized layouts. At the same time, the cost of simulation-based design procedures may be significant due to a typically large number of evaluations of the circuit at hand involved. In this paper, a novel approach to expedited design closure of compact microwave passives is presented. The proposed procedure incorporates available designs (e.g., existing from the previous design work on the same structure) in the form of the kriging interpolation models, utilized to yield a reasonable initial design and to accelerate its further refinement. An important component of the framework is an iterative correction procedure that feeds the accumulated discrepancies between the target and the actual design objective values back to the kriging surrogate to produce improved predictions. The efficacy of our methodology is demonstrated using two miniaturized impedance matching transformers with the optimized designs obtained at the cost of a few EM simulations of the respective circuits. The relevance of the iterative correction is corroborated through the comparative studies showing its superiority over rudimentary gradient-based refinement.

Contemporary microwave design heavily relies on full-wave electromagnetic (EM) simulation tools. This is especially the case for miniaturized devices where EM cross-coupling effects cannot be adequately accounted for using equivalent network models. Unfortunately, EM analysis incurs considerable computational expenses, which becomes a bottleneck whenever multiple evaluations are required. Common simulation-based design tasks include parametric optimization and uncertainty quantification. These can be accelerated using fast replacement models, among which the data-driven surrogates are the most popular. Notwithstanding, a construction of approximation models for microwave components is hindered by the dimensionality issues as well as high nonlinearity of system characteristics. A partial alleviation of the mentioned difficulties can be achieved with the recently reported performance-driven modeling methods, including the nested kriging framework. Therein, the computational benefits are obtained by appropriate confinement of the surrogate model domain, spanned by a set of pre-optimized reference designs, and by focusing on the parameter space region that contains high quality designs with respect to the considered performance figures. This paper presents a methodology that incorporates the concept of nested kriging and enhances it by explicit dimensionality reduction based on spectral decomposition of the reference design set. Extensive verification studies conducted for a compact rat-race coupler and a three-section impedance matching transformer demonstrate superiority of the presented approach over both the conventional techniques and the nested kriging in terms of modeling accuracy. Design utility of our surrogates is corroborated through application cases studies.

Electromagnetic (EM)-driven optimization is an important part of microwave design, especially for miniaturized components where the cross-coupling effects in tightly arranged layouts make traditional (e.g., equivalent network) representations grossly inaccurate. Efficient parameter tuning requires reasonably good initial designs, which are difficult to be rendered for newly developed structures or when re-design for different operating conditions or material parameters is required. If global search is needed, due to either the aforementioned issues or multi-modality of the objective function, the computational cost of the EM-driven design increases tremendously. This paper introduces a frequency-related regularization as a way of improving the efficacy of simulation-based design processes. Regularization is realized by enhancing the conventional (e.g., minimax) objective function using a dedicated penalty term that fosters the alignment of the circuit characteristics (e.g., the operating frequency or bandwidth) with the target values specified by the design requirement. This leads to smoothening of the objective function landscape, improves reliability of the optimization process, and reduces its computational cost as compared to the standard formulation. An added benefit is the increased immunity to poor initial designs and multi-modality issues. In particular, regularization can make local search routines sufficient in situations where global optimization would normally be necessary. The presented approach is validated using two miniaturized circuits, a rat-race and a branch line coupler. The numerical results demonstrate its superiority over conventional design problem formulations in terms of reliability of the optimization process.

Full-wave electromagnetic (EM) analysis has been playing a major role in the design of microwave components for the last few decades. In particular, EM tools allow for accurate evaluation of electrical performance of miniaturized structures where strong cross-coupling effects cannot be adequately quantified using equivalent network models. However, EM-based design procedures (parametric optimization, statistical analysis) generate considerable computational expenses. These can be mitigated using fast surrogate models, yet their construction is hindered by the curse of dimensionality but also the utility requirements: a practically useful model needs to cover sufficiently broad ranges of geometry/material parameters as well as operating conditions. The recently proposed constrained modeling methods-both forward and inverse-work around the above issues by setting up the surrogate only in the relevant regions of the parameter space, i.e., containing designs that are of high quality with respect to the assumed performance measures. The model domain is established using pre-optimized sets of reference points. The high cost of generating such designs may significantly diminish the computational savings achieved by operating in confined domains. This article discusses a technique for fast reference design acquisition, involving inverse gradients, and expedited local refinement aided by the response feature technology. The presented approach is validated using a branch-line coupler and miniaturized rat-race coupler. It is also demonstrated to considerably reduce the cost of constructing performance-driven surrogates as well as setting up efficient procedures for fast geometry scaling of microwave components.

Design of contemporary microwave circuits is a challenging task. Typically, it has to take into account several performance requirements and constraints. The design objectives are often conflicting and their simultaneous improvement may not be possible; instead, compromise solutions are to be sought. Representative examples are miniaturized microwave passives where reduction of the circuit size has a detrimental effect on its electrical characteristics. Acquiring information about the best possible design trade‐offs is invaluable for the designer, yet it entails computationally expensive multi‐objective optimization (MO). MO is typically conducted using population‐based metaheuristic algorithms, the cost of which might be extremely high. If the circuit performance is evaluated using full‐wave electromagnetic (EM) analysis, this cost is often prohibitive. A workaround is the employment of fast surrogate models, and a number of surrogate‐assisted frameworks have been proposed in the literature. Unfortunately, a construction of reliable surrogates is hindered in higher dimensional parameter spaces. The recently proposed constrained modeling mitigates this issue to a certain extent by restricting the modeling process to the region containing the Pareto front to be found. This work proposes a novel surrogate‐based MO technique that involves constrained modeling and explicit reduction of the surrogate domain dimensionality. The latter is achieved through the spectral analysis of the extreme Pareto‐optimal design set obtained by local search routines. Our methodology is validated using a 15‐parameter impedance‐matching transformer with the Pareto set identified at the cost of a few hundred EM analyses of the circuit. The numerical experiments also demonstrate a significant reduction of the optimization cost as compared to the state‐of‐the‐art surrogate‐assisted MO methods. [ABSTRACT FROM AUTHOR]

Accurate performance evaluation of microwave components can be carried out using full‐wave electromagnetic (EM) simulation tools, routinely employed for circuit verification but also in the design process itself. Unfortunately, the computational cost of EM‐driven design may be high. This is especially pertinent to tasks entailing considerable number of simulations (eg, parametric optimization, statistical analysis). A possible way of alleviating these difficulties is utilization of fast replacement models, also referred to as surrogates. Notwithstanding, conventional modeling methods exhibit serious limitations when it comes to handling microwave components. The principal challenges include large number of geometry and material parameters, highly nonlinear characteristics, as well as the necessity of covering wide ranges of operating conditions. The latter is mandatory from the point of view of the surrogate model utility. This article presents a novel modeling approach that incorporates variable‐fidelity EM simulations into the recently reported nested kriging framework. A combination of domain confinement due to nested kriging, and low‐/high‐fidelity EM data blending through cokriging, enables the construction of reliable surrogates at a fraction of cost required by single‐fidelity nested kriging. Our technique is validated using a three‐section miniaturized impedance matching transformer with its surrogate model rendered over wide range of operating frequencies. Comprehensive benchmarking demonstrates superiority of the proposed method over both conventional models and nested kriging. [ABSTRACT FROM AUTHOR]

Full-wave electromagnetic (EM) analysis is a versatile tool for evaluating the performance of high-frequency components. Its potential drawback is its high computational cost, inhibiting the execution of EM-driven tasks requiring massive simulations. The applicability of equivalent network models is limited owing to the topological complexity of compact microstrip components because of EM cross-coupling effects. Development of alternative representations (surrogate models) is therefore necessary. This article proposes a two-level methodology for reliable modelling of compact microstrip components. The keystone is to define the surrogate domain using the first-level model approximating the set of pre-existing reference designs. This limits the volume of the parameter space region that needs to be sampled when constructing the second-level model. The presented approach provides far greater accuracy than conventional methods and is capable of establishing surrogates covering wide ranges of geometric parameters and operating conditions of a particular structure. Applications for parametric optimization are also provided. [ABSTRACT FROM AUTHOR]

Design of microwave components is an inherently multiobjective task. Often, the objectives are at least partially conflicting and the designer has to work out a suitable compromise. In practice, generating the best possible trade‐off designs requires multiobjective optimization, which is a computationally demanding task. If the structure of interest is evaluated through full‐wave electromagnetic (EM) analysis, the employment of widely used population‐based metaheuristics algorithms may become prohibitive in computational terms. This is a common situation for miniaturized components, where considerable cross‐coupling effects make traditional representations (eg, network equivalents) grossly inaccurate. This article presents a framework for accelerated EM‐driven multiobjective design of compact microwave devices. It adopts a recently reported nested kriging methodology to identify the parameter space region containing the Pareto front and to render a fast surrogate, subsequently used to find the first approximation of the Pareto set. The final trade‐off designs are produced in a separate, surrogate‐assisted refinement process. Our approach is demonstrated using a three‐section impedance matching transformer designed for the best matching and the minimum footprint area. The Pareto set is generated at the cost of only a few hundred of high‐fidelity EM simulations of the transformer circuit despite a large number of geometry parameters involved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a novel and compact transmit/receive module (TRM) for enhancing antenna performances to be employed in space applications. The key advancement is the use of a 3-D technology which, to the best of our knowledge, would be for the first time introduced in the space industry for hermetically packaging RF modules. The 3-D module development is based on the highly demanding specifications of space active electronically steerable antennas (AESAs); the TRM consists of two “submodules” electrically connected by an ad hoc interposer. The complete electrical design process, together with a comprehensive discussion on electromagnetic, mechanical, and thermal aspects, is presented, and the achieved module performances such as gain and return losses are detailed. Moreover, several manufactured samples are measured to validate the simulated design, and the excellent results in terms of gain, noise figure, and output power fulfilling the target specs are presented and discussed. The presented data, characterized by a limited variability among the 10 measured samples, make the proposed design and the manufacturing process a good candidate in terms of potential reliability for building the next generation of high-performance space AESA. [ABSTRACT FROM AUTHOR]

Abstract: In this article, fast design closure of microwave components using feature‐based optimization (FBO) and adjoint sensitivities is discussed. FBO is one of the most recent optimization techniques that exploits a particular structure of the system response to “flatten” the functional landscape handled during the optimization process, which leads to reducing its computational complexity. When combined with gradient‐based search involving adjoint sensitivities, the design cost becomes even lower, allowing us to find the optimum design using just a few electromagnetic (EM) simulations of the structure at hand. Here, operation and performance of the algorithm is demonstrated using a waveguide filter and a miniaturized microstrip rat‐race coupler (RRC). Comparative studies indicate considerable savings that can be achieved even compared with adjoint‐based gradient search. In case of RRC, numerical results are supported by experimental validation. [ABSTRACT FROM AUTHOR]

A lot of effort has been devoted in the last decades by technology research to realizing materials with a priori defined electromagnetic (EM) properties. One of the challenges at present is to configure the reflection coefficient (RC) of a structure so that any shape of a fixed microwave response is followed. A method for realizing microwave absorbers made by carbon nanocomposite layers assembly able to mimic a given reflection profile is described and experimentally validated. The multilayer design (layer sequence, material, and thickness) is pursued by means of a customized numerical optimization algorithm, which allows to get the required microwave behavior. The novelty of the research is the possibility of tuning the EM field propagation through the combination of different materials in a specific layered compound, in order to imitate the response of any “real” object (i.e., with known EM properties). For the experimental validation of the process, three multilayered structures were designed and manufactured, and their microwave RC was measured in the frequency range of 2–18 GHz. The comparison with the related targets (an ideal frequency selective pattern and the defined profiles of dry soil and salt water as retrieved from literature survey) highlights the effective simulating capability of the realized structures. The preliminary results suggest to exploit the graded-dielectric properties provided by carbon-based nanocomposites for EM mimicking purposes: this would be an ideal approach to tackle still unsolved issues in EM compatibility, remote sensing, communication, and safety fields, as well as for low-cost and time-saving metrology applications. [ABSTRACT FROM PUBLISHER]

In this paper, a novel methodology for cost-efficient microwave design optimization in the frequency domain is proposed. Our technique, referred to as adaptive response scaling (ARS), has been developed for constructing a fast replacement model (surrogate) of the high-fidelity electromagnetic-simulated model of the microwave structure under design using its equivalent circuit (low-fidelity model). The basic principle of ARS is a nonlinear frequency and amplitude response scaling aimed at accommodating the discrepancies between the low- and high-fidelity models at the reference design and, subsequently, at tracking the low-fidelity model changes that occur during the optimization run. The surrogate model prediction is obtained by applying appropriately composed scaling functions to the high-fidelity model at the reference design. ARS is a parameterless and simple-to-implement method that can be applied to a wide range of microwave structures. The ARS surrogate features excellent generalization capability that translates into improved reliability and reduced design cost. It is demonstrated using an eighth-order microstrip bandpass filter and a miniaturized rat-race coupler. Comparison with several space mapping algorithms is provided. The numerical results are supplemented by measurements of the fabricated optimum designs of the considered structures. [ABSTRACT FROM AUTHOR]

Design optimization of passive microwave components is an intricate process, especially if the primary objective is a reduction of the physical size of the structure. The latter has become an important design consideration for a growing number of modern applications (mobile communications, wearable/implantable devices, internet of things), where miniaturization is imperative due to a limited space allocated for the electronic circuitry. Optimization-based size reduction is a heavily constrained task, with several acceptance thresholds imposed on electrical characteristics of the system. The challenges are pronounced whenever equality constraints are involved (e.g., related to power split ratio requirements), in which case the feasible space is a thin set, thereby difficult to be explored throughout the optimization process. This feature makes conventional methods, such as penalty function approaches or algorithms with explicit constraint handling, of limited reliability. In this paper, we introduce a novel technique for reliable control of equality constraints in simulation-driven size reduction of microwave components. Our methodology involves an intermittent optimization-based correction of equality constraints. This is essentially a knowledge-based decision-making strategy implemented as a supplementary optimization stage, and launched before each iteration of the core algorithm. Constraint violation is reduced without being detrimental to the remaining figures of merit, in particular, the circuit size and inequality constraints. Meanwhile, inequality constraints are handled using a penalty function approach with adaptive adjustment of penalty coefficients. The proposed technique facilitates exploration of the feasible space, and allows for achieving reduced miniaturization rates in comparison to the benchmark methods, while ensuring a reliable control of the design constraints. These advantages have been demonstrated using four microstrip couplers, with consistent results obtained for all considered circuits. [ABSTRACT FROM AUTHOR]

Numerical optimization has become more important than ever in the design of microwave components and systems, primarily as a consequence of increasing performance demands and growing complexity of the circuits. As the parameter tuning is more and more often executed using full-wave electromagnetic (EM) models, the CPU cost of the overall process tends to be excessive even for local optimization. Some ways of alleviating these issues exist, yet, they are limited either by their accessibility or applicability range. This work presents a novel algorithmic approach to accelerated gradient-based parameter tuning of microwave components with numerical derivatives. In our methodology, computational savings are achieved by exploiting the problem-specific knowledge, specifically, by restricting the gradient updates to an orthonormal basis of essential directions corresponding to the maximum variability of the circuit responses within the frequency bands of interest. The said directions are selected through an automated decision-making process involving the analysis of the circuit response variability. Our approach is demonstrated using two multi-parameter microwave devices. Comprehensive comparison with the benchmark methods, including the standard trust-region algorithm and the three accelerated versions, indicate savings of up to fifty percent associated only with minor reduction of the design quality. • Fast algorithm for microwave design with principal directions is developed. • Sensitivity updates are restricted to directions of maximum response changes. • Principal directions are selected through an automated decision-making process. • Proposed approach is demonstrated to yield significant computational savings. • Efficiency improvements do not compromise optimization process reliability. [ABSTRACT FROM AUTHOR]

To use highly resistive material for Kinetic Inductance Detectors (KID), new designs have to be done, in part due to the impedance match needed between the KID chip and the whole 50 Ω readout circuit. Chips from two new hybrid designs, with an aluminum throughline coupled to titanium nitride microresonators, have been measured and compared to a TiN only chip. In the hybrid chips, parasitic temperature dependent box resonances are absent. The dark KID properties have been measured in a large set of resonators. A surprisingly long lifetime, up to 5.6 ms is observed in a few KIDs. For the other more reproducible devices, the mean electrical Noise Equivalent Power is $5.4 \times 10^{-19}\ \mathrm{W}\sqrt{\mathrm{Hz}}$. [ABSTRACT FROM AUTHOR]

Convergence is a well-known issue for standard space-mapping optimization algorithms. It is heavily dependent on the choice of coarse model, as well as the space-mapping transformations employed in the optimization process. One possible convergence safeguard is the trust region approach where a surrogate model is optimized in a restricted neighborhood of the current iteration point. In this paper, we demonstrate that although formal conditions for applying trust regions are not strictly satisfied for space-mapping surrogate models, the approach improves the overall performance of the space-mapping optimization process. Further improvement can be realized when approximate fine model Jacobian information is exploited in the construction of the space-mapping surrogate. A comprehensive numerical comparison between standard and trust-region-enhanced space mapping is provided using several examples of microwave design problems. [ABSTRACT FROM AUTHOR]

In this article, an optimization procedure is described to align electromagnetic (EM) three-dimensional (3D) models with two-dimensional (2D) models for the design of RF/microwave circuits. The optimization procedure is realized from a modified standard space mapping (SM) approach. The mapping function between the 2D and 3D parameter spaces is directly obtained from a linear iterated prediction method, which reduces the computational cost and also avoids inverse transformations. The linear iterated prediction 2D to 3D SM optimization of evanescent rectangular waveguide bandpass filters with inductive posts for the 2D models and non-inductive posts for the 3D models illustrate the advantages and the challenges of this approach. The proposed method is simple to be implemented, it requires a reduced computational cost and it can be useful for CAD environment with 2D and 3D circuit structure electromagnetic (EM) analysis. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1979–1983, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24459 [ABSTRACT FROM AUTHOR]

The ability to evaluate the effects of fabrication tolerances and other types of uncertainties is a critical part of microwave design process. Improving the immunity of the device to parameter deviations is equally important, especially when the performance specifications are stringent and can barely be met even assuming a perfect manufacturing process. In the case of modern miniaturized microwave components of complex topologies, it is of paramount importance to carry out tolerance-aware design at the highest available accuracy level (i.e., with the use of full-wave electromagnetic (EM) simulations). Although reliable, EM-driven tolerance-aware design is extremely costly if conventional techniques are to be applied (e.g., Monte Carlo simulation). To overcome this setback, this paper proposes a simple and computationally efficient algorithm for robustness enhancement of compact microwave component designs. The objective is to increase the allowed deviations of geometry parameter values (described using the coefficients of an underlying probability distributions, e.g., the variance) so that the prescribed performance specifications are still fulfilled. The presented approach incorporates knowledge-based surrogate models, constructed using the characteristic points (response features) of EM-simulated system outputs, and utilized for low-cost prediction of the fabrication yield. The parameter vector of the microwave circuit of interest is adjusted within the trust-region (TR) framework to identify the maximum levels of deviations still ensuring 100-percent yield. The employment of TR also permits the adaptive control of design relocation and ensures convergence of the optimization process. Numerical verification of the presented methodology is carried out using three miniaturized microstrip circuits, including two equal-split couplers and a wideband filter. The major finding is that incorporating knowledge-based feature surrogates allows for achieving a significant improvement of the acceptable input tolerance levels (nearly two fold on the average) at a remarkably low cost of few dozen EM simulations [ABSTRACT FROM AUTHOR]

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., ǀS21ǀ) 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. [ABSTRACT FROM AUTHOR]

The efficiency of space-mapping optimization depends on the quality of the underlying coarse model, which should be sufficiently close to the fine model and cheap to evaluate. In practice, available coarse models are often cheap, but inaccurate (e.g., a circuit equivalent of the microwave structure) or accurate, but too expensive (e.g., a coarse-mesh model). In either case, the space-mapping optimization process exhibits substantial computational overhead due to the excessive fine model evaluations necessary to find a good solution if the coarse model is inaccurate, or due to the cost of the parameter extraction and surrogate optimization sub-problems if the coarse model is too expensive. In this paper, we use an interpolation technique, which allows us to create coarse models that are both accurate and cheap. This overcomes the accuracy/cost dilemma described above, permitting significant reduction of the space-mapping optimization time. Examples verify the performance of our approach. [ABSTRACT FROM AUTHOR]

In this article, the author starts with a quick tutorial about the ports used in EM analysis and how they are calibrated. Then, the paper discussed a new development -perfect internal port calibration. Finally, it concludes with a few examples illustrating the impact that perfect internal port calibration will have on microwave design.The author have also introduced a lot of new concepts in this article: perfectly calibrated box wall ports, perfectly calibrated (cocalibrated) internal ports, floating ground references, global ground references, several new component-based design methodologies, and baseline versus test structure validation. [ABSTRACT FROM PUBLISHER]

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations. [ABSTRACT FROM AUTHOR]

In the paper, a recently reported nested kriging methodology is employed for modeling of miniaturized microwave components. The approach is based on identifying the parameter space region that contains high-quality designs, and, subsequently, rendering the surrogate in this subset. The results obtained for a miniaturized unequal-power-split rat-race coupler and a compact three-section impedance transformer demonstrate reliability of the method even for highly-dimensional parameter spaces, as well as its superiority over conventional modeling methods. [ABSTRACT FROM AUTHOR]

We consider a simple and efficient space mapping (SM)-based interpolation scheme to work in conjunction with SM optimization algorithms. The technique is useful if the fine model (the one that is supposed to be optimized) is available only on a structured grid. It allows us to estimate the response of the fine model at off-grid points and, as a result, increases the effective resolution of the design variable domain search and improves the quality of the fine model solution found by the SM optimization algorithm. The proposed method requires little computational effort. In particular, no additional fine model evaluations are necessary. Several examples that verify the accuracy and robustness of our approach are provided [ABSTRACT FROM PUBLISHER]

A new design technique using the FDTD method and neural networks is applied to a microstrip filter. The total design time is reduced by two means. First, an iterative ARMA signal estimation technique is utilized to reduce the computation time for each FDTD run. Second, the number of FDTD simulations is decreased with the use of the device model provided by a neural network with the ARMA coefficients at the output. The trained network was then incorporated to an optimization procedure for a microstrip filter design. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 219–224, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10422 [ABSTRACT FROM AUTHOR]

Precise tuning of geometry parameters is an important consideration in the design of modern microwave passive components. It is mandatory due to limitations of theoretical design methods unable to quantify certain phenomena that are important for the operation and performance of the devices (e.g., strong cross-coupling effects in miniaturized layouts). Consequently, the initial designs obtained using analytical or equivalent network models require further adjustment. For reliability reasons, it has to be conducted using electromagnetic (EM) simulation tools, which entails considerable computational expenses whenever conventional numerical optimization algorithms are employed. Accelerating EM-driven design procedures is therefore highly desirable. This work discusses a surrogate-based algorithm for fast design closure and dimension scaling of miniaturized microwave passives. Our approach involves a small database of previously obtained designs as well as two metamodels, an inverse one, employed to yield a high-quality initial design, and the forward surrogate that provides predictions of the system sensitivities. The second model is constructed at the level of response features, which enables a more accurate gradient estimation and leads to improved reliability and a faster convergence of the optimization process. The presented technique is validated using two compact microstrip couplers and benchmarked against the state-of-the-art warm-start optimization frameworks. [ABSTRACT FROM AUTHOR]

The performance of space mapping (SM) optimization algorithms depends primarily on the quality of the underlying coarse model. Models available in the microwave area can be cheap but inaccurate or accurate but too expensive. Here, we consider a multicoarse-model technique that allows us to combine the merits of both types of coarse models to substantially reduce the overall computational cost of optimization in comparison to traditional SM. [ABSTRACT FROM PUBLISHER]

Utilization of electromagnetic (EM) simulation tools has become indispensable for reliable evaluation of microwave components. As the cost of an individual analysis may already be considerable, the computational overhead associated with EM-driven tasks that require massive simulations (e.g., optimization) may turn prohibitive. One of mitigation methods is the employment of equivalent network models. Yet, they are incapable of accounting for cross-coupling effects that occur in devices of complex geometries. Another option are fast replacement models (surrogates), especially the data-driven ones: readily available, generic and problem independent. Unfortunately, due to the curse of dimensionality, their applicability is limited to low-dimensional parameter spaces and narrow parameter ranges. From the utility perspective, however, the surrogate has to be valid over broad ranges of parameters and operating conditions. The recently reported performance-modeling techniques (especially nested-kriging) allow for rendering such surrogates even for complex devices. Key concept is to carry out the modeling process within a confined domain, being a subset of the parameter space that encompasses the designs of high-quality regarding the performance figures of choice. The goal of this work is to reduce the cost of reference design acquisition, which adds up to the total cost of constructing the surrogate. Toward this end, gradient-enhanced kriging is incorporated into the performance-driven modeling framework. The predictive power of the surrogates rendered using our approach by far exceeds that of the conventional methods and is comparable to the original nested kriging technique while requiring a significantly smaller number of reference designs (thus, the CPU cost). These features are demonstrated using a three-section transformer and a rat-race coupler. [ABSTRACT FROM AUTHOR]

Electromagnetic (EM) analysis has become ubiquitous in the design of microwave components and systems. One of the reasons is the increasing topological complexity of the circuits. Their reliable evaluation—at least at the design closure stage—can no longer be carried out using analytical or equivalent network representations. This is especially pertinent to miniaturized structures, where considerable EM cross-coupling effects occurring in densely arranged layouts affect the performance in a non-negligible manner. Although mandatory, EM-driven design is normally associated with significant computational expenses. Consequently, expediting the procedures that require massive simulations, such as parametric optimization, is a practical necessity. In this paper, a framework for accelerated parameter tuning is proposed. The keystones of our methodology are a set of pre-existing designs optimized for various design objectives, as well as kriging interpolation surrogates. The latter are constructed to yield—for a given set of performance specifications—a reasonably good starting point and to enable rapid optimization by providing the initial approximation of the Jacobian matrix of the circuit outputs. The proposed approach is validated using two compact impedance matching transformers designed within the objective spaces defined by wide ranges of operating bandwidths. As demonstrated, the average tuning cost corresponds to a few EM simulations of the respective circuit despite large numbers of adjustable parameters. [ABSTRACT FROM AUTHOR]

Redesigning a microwave circuit for various operating conditions is a practically important yet challenging problem. The purpose of this article is development and presentation of a technique for fast geometry scaling of miniaturized microwave couplers with respect to operating frequency. Our approach exploits an inverse surrogate model constructed using several reference designs that are optimized for a set of operating frequencies within a range of interest. For the sake of computational efficiency, the reference designs are obtained for an equivalent network model of the coupler. The surrogate directly predicts the optimum values of geometry parameters of the structure at hand corresponding to a requested operating frequency. By introducing appropriate correction, the model allows for coupler scaling at the EM simulation model level. Because the surrogate does not carry information about the power split ratio of the coupler, an additional analytical corrective procedure is developed to ensure an equal power split of scaled structure. The computational cost of the scaling procedure corresponds to only two EM analyses of the circuit at hand (including both correction steps). The operation and performance of our technique is demonstrated using a compact microstrip rat‐race coupler scaled for the operating frequency range of 0.5‐2.5 GHz. Experimental validation is also provided. [ABSTRACT FROM AUTHOR]