Development of Sensitivity Analysis and Optimization for Microwave Circuits and Antennas in the Frequency Domain

Abstract

<p> This thesis contributes to the development of adjoint variable methods (AVM) and space mapping (SM) technology for computer-aided electromagnetics (EM)-based modeling and design of microwave circuits and antennas.</p> <p> The AVM is known as an efficient approach to design sensitivity analysis for problems of high complexity. We propose a general self-adjoint approach to the sensitivity analysis of network parameters for an Method of Moments (MoM) solver. It requires neither an adjoint problem nor analytical system matrix derivatives. For the first time, we suggest practical and fast sensitivity solutions realized entirely outside the EM solver, which simplifies the implementation. We discuss: (1) features of commercial EM solvers which allow the user to compute network parameters and their sensitivities through a single full-wave simulation; (2) the accuracy of the computed derivatives; (3) the overhead of the sensitivity computation. Our approach is demonstrated by FEKO, which employs an MoM solver.</p> <p> One motivation for sensitivity analysis is gradient-based optimization. The sensitivity evaluation providing the Jacobian is a bottleneck of optimization with full-wave simulators. We propose an approach, which employs the self-adjoint sensitivity analysis of network parameters and Broyden's update for practical EM design optimization. The Broyden's update is carried out at the system matrix level, so that the computational overhead of the Jacobian is negligible while the accuracy is acceptable for optimization. To improve the robustness of the Broyden update in the sensitivity analysis, we propose a switching criterion between the Broyden and the finite-difference estimation of the system matrix derivatives.</p> <p> In the second part, we apply for the first time a space mapping technique to antenna design. We exploit a coarse mesh MoM solver as the coarse model and align it with the fine mesh MoM solution through space mapping. Two SM plans are employed: I. implicit SM and output SM, and II. input SM and output SM. A novel local meshing method is proposed to avoid inconsistencies in the coarse model. The proposed techniques are implemented through the new user-friendly SMF system. In a double annular ring antenna example, the S-parameter is optimized. The finite ground size effect for the MoM is efficiently solved by SM Plan I and the design specification is satisfied after only three iterations. In a patch antenna example, we optimize the impedance through both plans. Comparisons are made. Coarseness in the coarse model and its effect on the SM performance is also discussed.</p>