Digital Wave Simulation of Quasi-Static Partial Element Equivalent Circuit Method

The partial element equivalent circuit (PEEC) method is a well-established technique for obtaining a circuit equivalent for an electromagnetic problem. The time domain solution of such models is usually performed using nodal voltages and branch currents, or sometimes charge and currents. The present paper describes a possible alternative approach, which can be obtained expressing and solving the problem in the waves domain. The digital wave theory is used to find an equivalent representation of the PEEC circuit in the wave domain. Through a pertinent continuous to discrete time transformation, the constitutive relations for partial inductances, capacitances, and resistances are translated in an explicit form. The combination of such equations with Kirchhoff laws allows to achieve a semiexplicit resolution scheme. Three different physical configurations are analyzed and their extracted digital wave PEEC models are simulated at growing sizes using the general-purpose digital wave simulator. The results are compared to those obtained by using standard SPICE simulators in both linear and nonlinear cases. When the size of the model is manageable by SPICE, an excellent accuracy and a speed-up factor of up to three orders of magnitude are observed with much lower memory requirements. A comparative analysis of results including the effect of parameters like the simulation time step choice is also presented.