Efficient Analysis of Geometrical Uncertainty in the FDTD Method Using Polynomial Chaos With Application to Microwave Circuits

TLDR

The authors develop a novel FDTD‑based method to analyze 3‑D microwave circuits with uncertain parameters arising from manufacturing variability in physical dimensions and geometry. The method incorporates geometrical variation by parameterizing and distorting the computational lattices, then expands the time‑domain electric and magnetic fields using generalized polynomial chaos basis functions of the uncertain mesh parameters, and is validated on microstrip circuits. The resulting S‑parameters match Monte Carlo statistics over 0–25 GHz and the approach yields a substantial computational speed‑up compared with Monte Carlo simulation.

Abstract

A novel finite-difference time-domain (FDTD)-based method is developed to analyze 3-D microwave circuits with uncertain parameters, such as variability and tolerances in the physical dimensions and geometry introduced by manufacturing processes. The proposed method incorporates geometrical variation into the FDTD algorithm by appropriately parameterizing and distorting the rectilinear and curvilinear computational lattices. Generalized polynomial chaos is used to expand the time-domain electric and magnetic fields in terms of orthogonal polynomial chaos basis functions of the uncertain mesh parameters. The technique is validated by modeling several microstrip circuits with uncertain physical dimensions and geometry. The computed S-parameters are compared against Monte Carlo simulations, and good agreement for the statistics is observed over 0-25 GHz. A considerable computational advantage over the Monte Carlo method is also achieved.