Statistical Design Centering of Microwave Circuits Using Modified Trust Region Optimization and Space Mapping Surrogates

Abstract

System design centering seeks for nominal values of system parameters which maximize the probability of satisfying the design specifications (yield function). Statistical design centering implements a statistical analysis method like Latin Hypercube sampling (LHS) for yield function estimation, and explicitly optimizes it. In this article, we introduce a new technique for statistical microwave system design centering. The technique combines a modified surrogate-based derivative-free trust region (TR) optimization algorithm, and the generalized space mapping (GSM) technique. The modified TR algorithm is based on quadratic surrogate models with no derivative requirements to replace the computationally expensive yield function over hyper-elliptic trust regions in the optimization process. Any TR algorithm exhibits global convergence features irrespective the starting point setting. The new design centering technique implements the GSM technique, in approximating the feasible region in the design parameter space with a sequence of iteratively updated space mapping (SM) surrogate models. For each SM iteration, the modified TR algorithm is used in optimizing the yield function for the current SM region approximation to get a better center. The proposed design centering technique has been employed to obtain the optimal design center of two microwave circuit examples: ultra-wideband (UWB) multiple-input-multiple-output (MIMO) antenna employing CST and symmetrical bandstop microstrip filter with three open stubs utilizing Sonnet em. Good results are obtained using few space mapping iterations.