Reliable design optimization of microwave structures using multipoint‐response‐correction space mapping and trust regions

Space mapping (SM) is one of the most efficient simulation‐driven design technologies used in microwave engineering to date. It includes so‐called output SM that ensures exact matching between the EM‐evaluated microwave structure under consideration (fine model) and its surrogate at the current design. The standard, single‐point output SM exploits the fine model data at a single design and is not able to align the models' sensitivity. Here, a multipoint response correction is proposed that generalizes the concept of output SM. By using a design‐variable‐dependent correction term and exploiting all available fine model information, the proposed technique provides exact match between the surrogate and the fine model at several designs. This retains the benefits of output SM but also enhances sensitivity matching between the two models, which results in improved performance of the SM optimization process. The efficiency of the propose approach is demonstrated using several microwave design problems. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Space mapping optimization of waveguide filters using finite element and mode‐matching electromagnetic simulators

For the first time in design optimization of microwave circuits, the aggressive space mapping (SM) optimization technique is applied to automatically align electromagnetic (EM) models based on hybrid mode‐matching/network theory simulations with models based on finite‐element (FEM) simulations. SM optimization of an H‐plane resonator filter with rounded corners illustrates the advantages as well as the challenges of the approach. The parameter extraction phase of SM is given special attention. The impact of selecting responses and error functions on the convergence and uniqueness of parameter extraction is discussed. A statistical approach to parameter extraction involving 𝓁₁ and penalty concepts facilitates a key requirement by SM for uniqueness and consistency. A multipoint parameter extraction approach to sharpening the solution uniqueness and improving the SM convergence is also introduced. Once the mapping is established, the effects of manufacturing tolerances are rapidly estimated with the FEM accuracy. SM has also been successfully applied to optimize waveguide transformers using two hybrid mode‐matching/network theory models: a coarse model using very few modes and a fine model using many modes to represent discontinuities. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 54–70, 1999.     

Response correction techniques for surrogate‐based design optimization of microwave structures

Simulation‐based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high‐computational cost of an accurate EM simulation. In this article, we present a review of EM‐based design optimization techniques exploiting response‐corrected physically based low‐fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high‐fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape‐preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Rapid design and size reduction of microwave couplers using variable‐fidelity EM‐driven optimization

In this article, fast electromagnetic (EM) simulation‐driven design optimization of compact microwave couplers is addressed. The main focus is on explicit reduction of the circuit footprint. Our methodology relies on the penalty function approach, which allows us to minimize the circuit area while ensuring equal power split between the output ports and providing a sufficient bandwidth with respect to the return loss and isolation around the operating frequency. Computational efficiency of the design process is achieved by exploiting variable‐fidelity EM simulations, local response surface approximation models, as well as suitable response correction techniques for design tuning. The technique described in this work is demonstrated using two examples of compact rat‐race couplers. The size‐reduction‐oriented designs are compared with performance‐oriented ones to illustrate available design trade‐offs. Final design solutions of the former case illustrate ～92% of miniaturization for both coupler examples (with corresponding fractional bandwidths of 16%). Alternative design solutions pertaining to the latter case show a lesser size reduction (～90% for both examples), but present a much wider bandwidths (～25% for both couplers). The overall computational cost of the design procedure corresponds to about 20 and 10 high‐fidelity coupler simulations for the first and second design example, respectively. Numerical results are also validated experimentally. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:27–35, 2016.     

EM‐simulation‐driven design optimization of compact microwave structures using multi‐fidelity simulation models and adjoint sensitivities

Reliable design of miniaturized microwave structures requires utilization of full‐wave electromagnetic (EM) simulation models because other types of representations such as analytical or equivalent circuit models are of insufficient accuracy. This is primarily due to considerable cross‐coupling effects in tightly arranged layouts of compact circuits. Unfortunately, high computational cost of accurate EM analysis makes the dimension adjustment process challenging, particularly for traditional methods based on parameter sweeps, but also for conventional numerical optimization techniques. In this article, low‐cost simulation‐driven designs of compact structures were demonstrated using gradient search with adjoint sensitivities as well as multi‐fidelity EM simulation models. The optimization process was arranged sequentially, with the largest steps taken at the level of coarse‐discretization models. Subsequent fine tuning was realized with the models of higher fidelity. Switching between the models was realized by means of adaptively controlled termination conditions. This allowed for considerable reduction of the design cost compared with single‐level optimization. The approach was illustrated using a compact microstrip rat‐race coupler with two cases considered, that is, (i) bandwidth enhancement, and (ii) minimization of the structure size. In both cases, the optimization cost corresponded to a few high‐fidelity EM simulations of the coupler structure. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:442–448, 2016.     

Improved trust‐region gradient‐search algorithm for accelerated optimization of wideband antenna input characteristics

Full‐wave electromagnetic (EM) simulation models are ubiquitous in carrying out design closure of antenna structures. Yet, EM‐based design is expensive due to a large number of analyses necessary to yield an optimized design. Computational savings can be achieved using, for example, adjoint sensitivities, surrogate‐assisted procedures, design space dimensionality reduction, or similar sophisticated means. In this article, a simple modification of a rudimentary trust‐region‐embedded gradient search with numerical derivatives is proposed for reduced‐cost optimization of input characteristics of wideband antennas. The approach exploits information and history of relative changes of the design (as compared with the trust region size) during algorithm iterations to control the updates of components of the antenna response Jacobian, specifically, to execute them only if necessary. It is demonstrated that the proposed framework may lead to over 50% savings over the reference algorithm with only minor degradation of the design quality, specifically, up to 0.3 dB (or <3%). Numerical results are supported by experimental validation of the optimized antenna designs. The presented algorithm can be utilized as a stand‐alone optimization routine or as a building block of surrogate‐assisted procedures.     

Phase‐spacing optimization of linear microstrip antenna arrays using simulation‐based surrogate superposition models

A technique for simulation‐driven optimization of the phase excitation tapers and spacings for linear arrays of microstrip patch antennas is presented. Our technique exploits two models of the array under optimization: an analytical model which is based on the array factor, as well as an electromagnetic (EM) simulation‐based surrogate model of the entire array. The former is used to provide initial designs which meet the design requirements imposed on the radiation response. The latter is used for tuning of the array radiation response while controlling the array reflection response as well as for validation of the final design. Furthermore, the simulation‐based surrogate model allows for subsequent evaluation of the array responses in the beam scanning operation at negligible computational costs. The simulation‐based surrogate model is constructed with a superposition of simulated radiation and reflection responses of the array under design with only one radiator active at a time. Low computational cost of the surrogate model is ensured by the EM‐simulation data computed with coarse meshes. Reliability of the model is achieved by means of suitable correction carried out with respect to the high‐fidelity array model. The correction is performed iteratively in the optimization process. Performance, numerical efficiency, and accuracy of the technique is demonstrated with radiation pattern synthesis of linear arrays comprising 32 microstrip patch antennas by phase‐spacing optimization. Properties of the optimal designs in the beam scanning operation are then studied using the superposition models and compared to suitably selected reference designs. The proposed technique is versatile as it also can be applied for simulation‐based optimization of antenna arrays comprising other types of individually fed elements. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:536–547, 2015.     

Rapid surrogate‐assisted design optimization of minimum‐size broadband branch‐line couplers with variable topology

This work discusses simulation‐driven design of miniaturized wideband branch‐line couplers with a variable topology. Size reduction is enabled here by replacing uniform transmission lines of the original coupler with slow‐wave structures in the form of cascaded compact cells and meander lines. The primary goal is to determine a number of cells in the cascade and particular cell dimensions for which the minimum size of the coupler as well as its required operating conditions are ensured. To this end, we employ a surrogate‐assisted technique involving a trust‐region gradient search framework. Computational efficiency of the design process stems from estimating the Jacobian of circuit responses at the level of a low‐fidelity model of the cascade. The latter is composed in a circuit simulator from duplicated EM‐evaluated data blocks of a single cell and is well correlated with the corresponding high‐fidelity model. The key advantage of this work is the utilization of a reconfigurable, cheap, and well‐aligned low‐fidelity model. The proposed approach is demonstrated through design of a minimum‐size two‐section branch‐line coupler with quasi‐periodic dumbbell‐shaped cells and meander lines. Excellent circuit performance as well as its small size showcase the reliability and usefulness of the presented method. Experimental verification is also provided.     

Reduced‐cost microwave filter modeling using a two‐stage Gaussian process regression approach

A technique for the reduced‐cost modeling of microwave filters is presented. Our approach exploits variable‐fidelity electromagnetic (EM) simulations, and Gaussian process regression (GPR) carried out in two stages. In the first stage of the modeling process, a mapping between EM simulation filter models of low and high fidelity is established. The mapping is subsequently used in the second stage, making it possible for the final surrogate model to be constructed from training data obtained using only a fraction of the number of high‐fidelity simulations normally required. As demonstrated using three examples of microstrip filters, the proposed technique allows us to reduce substantially (by up to 80%) the central processing unit (CPU) cost of the filter model setup, as compared to conventional (single‐stage) GPR—the benchmark modeling method in this study. This is achieved without degrading the model generalization capability. The reliability of the two‐stage modeling method is demonstrated through the successful application of the surrogates to surrogate‐based filter design optimization. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:453–462, 2015.     

Efficient multi‐fidelity design optimization of microwave filters using adjoint sensitivity

A simple and robust algorithm for computationally efficient design optimization of microwave filters is presented. Our approach exploits a trust‐region (TR)‐based algorithm that utilizes linear approximation of the filter response obtained using adjoint sensitivity. The algorithm is sequentially executed on a family of electromagnetic (EM)‐simulated models of different fidelities, starting from a coarse‐discretization one, and ending at the original, high‐fidelity filter model to be optimized. Switching between the models is determined using suitably defined convergence criteria. This arrangement allows for substantial cost reduction of the initial stages of the optimization process without compromising the accuracy and resolution of the final design. The performance of our technique is illustrated through the design of a fifth‐order waveguide filter and a coupled iris waveguide filter. We also demonstrate that the multi‐fidelity approach allows for considerable computational savings compared to TR‐based optimization of the high‐fidelity EM model (also utilizing adjoint sensitivity). © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:178–183, 2015.     

Efficient design of SIW filters by using equivalent circuit models and calibrated space‐mapping optimization

This article presents a very efficient technique for the design of filters in substrate‐integrated waveguide (SIW) technology. The proposed design approach is based on the combined use of equivalent circuit models of SIW discontinuities and a “calibrated” space‐mapping optimization technique. The effectiveness of this design technique is demonstrated through some examples. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

Fast simulation‐driven feature‐based design optimization of compact dual‐band microstrip branch‐line coupler

Design of miniaturized microwave components is a challenging task. On one hand, due to considerable electromagnetic (EM) cross‐couplings in highly compressed layouts full‐wave EM analysis is necessary for accurate evaluation of the structure performance. Conversely, high‐fidelity EM simulation is computationally expensive so that automated determination of the structure dimensions may be prohibitive when using conventional numerical optimization routines. In this article, computationally efficient simulation‐driven design of a miniaturized dual‐band microstrip branch‐line coupler is presented. The optimization methodology relies on suitably extracted features of a highly nonlinear response of the coupler structure under design. The design objectives are formulated in terms of the feature point locations, and the optimization is carried out iteratively with the linear model of the features utilized as a fast predictor. The entire process is embedded in the trust‐region framework as convergence safeguard. Owing to only slightly nonlinear dependence of the features on the geometry parameters of the circuit at hand, the optimized design satisfying prescribed performance requirements is obtained at the low computational cost of only 24 high‐fidelity EM simulations of the structure. Experimental validation of the fabricated coupler prototype is also provided. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:13–20, 2016.     

Expedited simulation‐driven design optimization of UWB antennas by means of response features

In this work, a method for fast design optimization of broadband antennas is considered. The approach is based on a feature‐based optimization (FBO) concept where reflection characteristics of the structure at hand are formulated in terms of suitably defined feature points. Redefinition of the design problem allows for reducing the design optimization cost, because the dependence of feature point coordinates on antenna dimensions is less nonlinear than for the original frequency characteristics (here, S‐parameters). This results in faster convergence of the optimization algorithm. The cost of the design process is further reduced using variable‐fidelity electromagnetic (EM) simulation models. In case of UWB antennas, the feature points are defined, among others, as the levels of the reflection characteristic at its local in‐band maxima, as well as location of the frequency point which corresponds to acceptable reflection around the lower corner frequency within the UWB band. Also, the number of characteristic points depends on antenna topology and its dimensions. Performance of FBO‐based design optimization is demonstrated using two examples of planar UWB antennas. Moreover, the computational cost of the approach is compared with conventional optimization driven by a pattern search algorithm. Experimental validation of the numerical results is also provided.     

An EM‐circuit‐ANN co‐modeling approach for RF module design

A new co‐modeling technique dedicated to RF module design and optimization is described. This approach is based on combined EM, circuit, and artificial neural network simulations. Generic segments are parameterized in geometry, physical properties and frequency by analytical models and are integrated into commercial circuit software. This co‐modeling combines speed and flexibility of circuit simulators and accuracy of EM‐based simulators. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

Fast simulation‐driven antenna design using response‐feature surrogates

In this article, a computationally efficient procedure for electromagnetic (EM)‐simulation‐driven design of antennas is presented. Our methodology is based on local approximation models of the antenna response, established using a set of suitably selected characteristic features rather than the entire response (such as reflection versus frequency). The approximation model is utilized to verify the level of satisfying/violating given performance requirements, and to guide the optimization process towards a better design. By exploiting the fact that the dependence of the response features on the designable parameters of the antenna of interest is simple (close to linear or quadratic), the feature‐based optimization converges faster than conventional optimization of frequency‐based EM‐simulated responses. In order to further speed up the design, coarse‐discretization simulations are utilized to estimate the feature gradients with respect to adjustable parameters of the problem at hand. The optimization algorithm is embedded in the trust‐region framework for safeguarding convergence. The proposed technique is demonstrated using two antenna examples. In both the cases, the optimum design is obtained at the computational cost corresponding to a few high‐fidelity EM antenna simulations. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:394–402, 2015.     

Performance‐driven modeling of compact couplers in restricted domains

Fast surrogate models can play an important role in reducing the cost of Electromagnetic (EM)‐driven design closure of miniaturized microwave components. Unfortunately, construction of such models is challenging due to curse of dimensionality and wide range of geometry parameters that need to be included in order to make it practically useful. In this letter, a novel approach to design‐oriented modeling of compact couplers is presented. Our method allows for building surrogates that cover wide range of operating conditions and/or material parameters, which makes them useful for design purposes. At the same time, careful definition of the model domain permits dramatic (volume‐wise) reduction of the of the design space region that needs to be sampled, thus, keeping the number of training data samples at acceptable levels. The proposed technique is demonstrated using a compact rat‐race coupler modeled for operating frequencies from 1 to 2 GHz and power split of ?6 to 0 dB. Benchmarking and application examples for coupler design optimization as well as experimental validation are also provided.     

Surrogate modeling of impedance matching transformers by means of variable‐fidelity electromagnetic simulations and nested cokriging

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.     

Computational‐budget‐driven automated microwave design optimization using variable‐fidelity electromagnetic simulations

A robust technique for microwave design optimization is presented. It is based on variable‐fidelity electromagnetic (EM) simulations where the approximate optimum of the “coarser” model becomes an initial design for finding the optimum of the “finer” one. The algorithm automatically switches between the models of different fidelity taking into account the computational budget assumed for the design process. Additional mechanisms enhancing the algorithm include: frequency scaling to reduce the misalignment between the models of different fidelity, as well as the local response surface approximation to reduce the number of EM simulations. The presented technique is particularly suitable for problems where simulation‐driven design is the only option, for example, for wideband antennas and dielectric resonator filters. Our method is demonstrated using two filters and one antenna example. In all cases, the optimal design is obtained at a low computational cost corresponding to a few high‐fidelity simulations of the structure. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Parameter optimization of sub-35 nm contact-hole fabrication using particle swarm optimization approach

The major research focus on integrated circuits (ICs) mainly deals with increasing circuit performance and functional complexity of circuit. The lithography process is the most critical step in the fabrication of nanostructure for integrated circuit manufacturing. The most important variable in the lithography process is the line-width or critical dimensions (CDs), which perhaps is one of the most direct impact variables on the device performance and speed. This study presents a hybrid approach combining Taguchi’s robust design, back-propagation neural network modeling technique and particle swarm optimization (PSO) for sub-35 nm contact-hole fabrication in the lithography process. The BP neural network is employed to model the functional relationship between the input parameters and target responses. Particle swarm optimization is adopted to optimize the parameter settings through the well-trained BP model, where each particle is assessed using fitness function. The proposed PSO algorithm applies the velocity updating and position updating formulas to the population composed of many particles such that better particles are generated. Compared with realistic fabricated and measured data, this approach can achieve the optimal parameter settings for minimized CDs or target CDs. Meanwhile, it reduces the CD variation through the design of experiment. The experimental results show that the proposed approach dealing with the process modeling and parameter optimization demonstrates its feasibility and effectiveness for sub-35 nm contact-hole fabrication.