Reduced-Cost Gradient-Based optimization of Compact Impedance Matching Transformers in Highly-Dimensional Parameters Spaces

Design of miniaturized microstrip circuits is heavily based on full-wave electromagnetic (EM) simulation tools. This is especially the case for components involving slow-wave compact cells, in which considerable EM cross-coupling effects cannot be adequately accounted for using simpler representations, e.g., equivalent network models. In this paper, a gradient-based procedure with numerical derivatives for accelerated optimization of miniaturized impedance matching transformers in highly-dimensional parameter spaces is proposed. Our approach allows for reducing the number of expensive EM simulations in the course of the optimization process by restricting the use of finite differentiation. This is achieved through a selective execution of a Broyden formula, applied for parameters that satisfy appropriately defined alignment conditions w.r.t. design relocation between the algorithm iterations. Furthermore, to facilitate handling of circuits of various complexities, the acceptance criteria for the mentioned alignment verification are made dependent on the search space dimensionality. The presented methodology is validated using three compact impedance matching transformers. A demonstrated computational speedup is as high as fifty percent as compared to the reference algorithm.