Efficient Gradient-Based Algorithm with Numerical Derivatives for Expedited Optimization of Multi-Parameter Miniaturized Impedance Matching Transformers

Abstract

Full-wave electromagnetic (EM) simulation tools have become ubiquitous in the design of microwave components. In some cases, e.g., miniaturized microstrip components, EM analysis is mandatory due to considera¬ble cross-coupling effects that cannot be accounted for otherwise (e.g., by means of equivalent circuits). These effects are particularly pronounced in the structures in¬volving slow-wave compact cells and their numerical opti¬mization is challenging due to expensive simulations and large number of parameters. In this paper, a novel gradi¬ent-based procedure with numerical derivatives is pro¬posed for expedited optimization of compact microstrip impedance matching transformers. The method restricts the use of finite differentiation which is replaced for se¬lected parameters by a rank-one Broyden updating for¬mula. The usage of the formula is governed by an ac¬ceptance parameter which is made dependent on the pa¬rameter space dimensionality. This facilitates handling circuits of various complexities. The proposed approach is validated using three impedance matching transformer circuits with the number of parameters varying from ten to twenty. A significant speedup of up to 50 percent is demon¬strated with respect to the reference algorithm.