Polynomial Chaos-Based Approach to Yield-Driven EM Optimization

Abstract

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.

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

“…The most critical SBO component is the surrogate model, i.e., an auxiliary model which has to be significantly faster to evaluate than the original (high-fidelity) system representation. Practically utilized surrogates can be divided into two major groups: physicsbased, constructed by appropriate correction of the underlying low-fidelity models (e.g., equivalent networks [19]) and data-driven (also referred to as approximation ones, e.g., kriging [24], neural networks [25], polynomial chaos expansion [26]). Computational efficiency of SBO procedures is a combination of two factors: (i) shifting majority of operations into the surrogate model, and (ii) sparse evaluation of the high-fidelity model (executed for design verification and surrogate model enhancement).…”

Parametric Modeling and Optimization of Electromagnetic and Multiphysics Behaviors of Microwave Components

“…The primary objective of neural network training is to minimize E(w) by adjusting the weighting parameters w. The benefit of the neural network model is more significant when the model is used in design process such as design optimization, Monte Carlo analysis and yield optimization [84]. The more we use the model, the more benefits we have.…”

Advanced Parametric Modeling and Yield Optimization Approaches for Microwave Passive Components

“…Following the suggestion in [25], we set p = q = 1 and the weighting factor α m = 1 in this thesis. These settings lead to an objective function in the following form [50]:…”

“…Step 4) Numerically evaluate the PC coefficients a ij using numerical quadrature based on the sparse grid technique [50].…”

“…A direct application of the objective function U (x 0 ) is feasible if the responses are computed by circuit simulations. When the responses are obtained from EM simulations, it appears to be computationally expensive to apply U (x 0 ) to EM-based yield optimization directly[50]. To address this challenge, we propose in this chapter a parallel SM based yield-driven EM optimization technique incorporating trust region algorithm and PCE.…”