Application of the recursive convolution technique to modeling lumped circuit elements in FDTD simulations

This paper presents a simple approach for extending the basic Yee FDTD algorithm to allow for modeling combinations of resistors, capacitors and inductors as lumped elements. This approach uses the recursive convolution (RC) technique previously applied in FDTD for simulating pulse propagation in frequency dependent dielectric media. In the application presented, the potential across the lumped load is updated by a recursive evaluation of the convolution of the current with the inverse Fourier transform of the impedance. This approach can be used whenever the impedance can be approximated over the frequency range of interest with functions which have inverse Fourier transforms containing the exponential time dependence required by the RC method. A parallel LCR satisfies this requirement, and any number of parallel LCR circuits in series can be modeled as a lumped load located at a single FDTD cell location. The formulation in this paper also permits a voltage or current source to be included within the lumped element.