Microwave systems design centering exploiting space mapping technology and modified trust region algorithm

System design centering process looks for nominal values of system designable parameters that maximize the probability of satisfying the design specifications (yield function). Statistical design centering implements a statistical analysis method such as Latin hypercube sampling (LHS) for yield function estimation and explicitly optimizes it. In this paper, we introduce a new statistical design centering technique for microwave system design. 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 a derivative-free optimization algorithm that employs quadratic surrogate models to replace the computationally expensive yield function over hyperelliptic trust regions in the optimization process. TR algorithms exhibit global convergence features irrespective the starting point setting. The new design centering approach utilizes the GSM technique to approximate the feasible region in the design parameter space with a sequence of iteratively updated space mapping (SM) surrogates. At each SM iteration, the modified TR algorithm optimizes the yield function for the current SM region approximation to get a better center. Two microwave circuit examples are used to show the effectiveness of the new design centering technique to obtain an optimal design in few SM iterations. In the design process, we employ Sonnet em for the bandstop microstrip filter design and CST Studio Suit for the ultra-wideband (UWB) multiple-input-multiple-output (MIMO) antenna.