Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

Yield-driven optimization is important in microwave design due to the uncertainties introduced in the manufacturing process. For the first time, we extend in this paper the use of polynomial chaos (PC) approach from electromagnetic (EM)-based yield estimation to EM-based yield optimization of microwave structures. We first formulate a novel objective function for yield-driven EM optimization. By incorporating the PC coefficients into the formulation, the objective function is analytically related to yield optimization variables, which are the nominal point. We then derive the sensitivity formulas of the PC coefficients with respect to the nominal point, following which we derive the sensitivities of the optimization objective function with respect to yield optimization variables. These sensitivities are then used in gradient-based optimization algorithms to find the optimal yield solution iteratively. The proposed objective function requires fewer EM simulations to provide reliable yield representation than that in the conventional Monte Carlo-based yield optimization approach. As a result, the number of EM simulations required to find the update direction and suitable step size for the change of the nominal point is reduced at each iteration of optimization. This allows the proposed approach to achieve similar yield increase using much fewer EM simulations or greater yield increase using similar number of EM simulations compared to the conventional yield optimization approach. The advantages of our proposed approach are demonstrated by yield-driven EM optimization of three waveguide filter examples.