Taylor Series Expansion-Based PEEC Time Domain Solver for Transient Full-Wave Analysis

In this work, a novel time-domain solver for time-domain simulation of partial element equivalent circuit (PEEC) models of electromagnetic systems is presented. The PEEC method is based on the electric field integral equation and the continuity equation. Magnetic and electric field couplings are described separately in terms of partial inductances and coefficients of potential. When the propagation delay is taken into account, they are approximated with the center-to-center assumption. Hence, the enforcement of Kirchhoff current and voltage laws results in a set of delayed differential equations. They are typically solved by using Marching On-in-Time (MOT) schemes which suffer from instabilities. In this work, the Taylor series expansion is used to manage the delays leading to an augmented PEEC time-domain solver. The derivation of the solver is detailed for conductors. Results obtained from the simulations show that the proposed method is accurate and yields good performances.