Reduced-Cost Microwave Design Closure by Multi-Resolution EM Simulations and Knowledge-Based Model Management

Abstract

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.

An Early History of Optimization Technology for Automated Design of Microwave Circuits

“…Now with Reykjavik University, Iceland, he is surely the most identifiable researcher in our community with respect to all aspects of surrogate methodologies and their applications. Koziel and his team spearheaded innovative electromagnetic simulation-driven and surrogate-based optimization procedures for microwave circuits and antenna design, including variable-fidelity optimization frameworks [209], [210], [211]; surrogate-assisted tuning [191], [212], [213], yield estimation [214], [215], and multi-objective optimization [216], [217], [218], [219], [220]; methodologies for rapid re-design by inverse surrogates [221], [222]; microwave component miniaturization [223], [224]; dimensionally reduced and domain confined surrogates [225], [226], [227]; response feature-based nominal design [228], [229], [230], [231], [232], yield optimization [233], [234], [235], [236], [237], and robust design by tolerance maximization [238], [239], [240].…”

Knowledge-based expedited parameter tuning of microwave passives by means of design requirement management and variable-resolution EM simulations

“…The increase of the model fidelity is continued after reducing D cr ( i ) to zero, i.e., after F cr ( i ) becomes equal to F . This second stage is governed by the procedure discussed in 79 . It is also assumed that the optimization process is concluded if one of the two conditions is met: (i) || x ( i +1) − x ( i ) ||< ε x (convergence in argument), or | U ( x ( i +1) ) − U ( x ( i ) )|< ε U (convergence in the merit function value).…”

“…Therein, ε x and ε U are the termination thresholds, set to ε x = 10 −3 and ε U = 10 −2 , in the numerical experiments of “ Verification case studies ” section. Let us also consider the convergence factor 79 …”

Globalized simulation-driven miniaturization of microwave circuits by means of dimensionality-reduced constrained surrogates

“…Nowadays, parameter tuning is more and more often carried out using rigorous numerical optimization methods, which is recommended due to their ability to handle multiple parameters, objectives and constraints 25 – 27 . Optimization is not only used for the purpose of design closure (final tuning of geometry parameters, often using local algorithms 28 ), but also multi-criterial design 29 , uncertainty quantification (tolerance analysis 30 , design centering 31 ), and global optimization 32 .…”