Statistical Analysis of Steady State Response in RF Circuits via Decoupled Generalized Polynomial Chaos

Abstract

One of the major factors in RF circuit design is the ability to predict the performance of these circuits in the presence of uncertainty in the key design parameters. This is referred to as uncertainty quantification in the mathematical literature. Uncertainty about the key design parameters arises mainly from the difficulty of controlling the physical or geometrical features of the underlying design, especially at the nanometer level. With the constant trend to scale down the process feature size, uncertainty quantification becomes crucial in shortening the design time. This thesis presents a new approach to statistically characterize the variability of the Harmonic Balance analysis and its application to Intermodulation distortion analysis in the presence of uncertainty in the design parameters. The new approach is based on the concept of Polynomial Chaos (PC) and Stochastic Galerkin (SG) methods. However, unlike the traditional PC, the proposed approach adopts a new mathematical formulation that decouples the Polynomial Chaos problem into several problems whose sizes are equal to the size of the original Harmonic Balance problem. The proposed algorithm produces significant CPU savings with equivalent accuracy to traditional Monte Carlo and standard PC approaches.