A new algorithm for the incorporation of arbitrary linear lumped networks into FDTD simulators

Abstract

The inclusion of lumped elements, both linear and nonlinear, into the finite-difference time-domain (FDTD) algorithm has been recently made possible by the introduction of the lumped-element FDTD method. Such a method, however, cannot efficiently and accurately account for two-terminal networks made of several lumped elements, arbitrarily connected together. This limitation can be removed as proposed in this paper by describing the network in terms of its impedance in the Laplace domain and by using appropriate digital signalprocessing methodologies to fit the resulting description to Yee's algorithm. The resulting difference equations allow an arbitrary two-terminal network to be inserted into one FDTD cell, preserving the full explicit nature of the conventional FDTD scheme and requiring a minimum number of additional storage variables. The new approach has been validated by comparison with the exact solution of a parallel-plate waveguide loaded with lumped networks in the transverse plane.

Application of the Improved Matrix Type FDTD Method for Active Antenna Analysis

“…However, it is straightforward to model this device by the improved matrix type FDTD technique. Besides Equations (9), (10), and (24)-(26), the additional equations required to describe the complex hybrid network are…”

“…Its main limitation is that it cannot account for twoterminal circuit consisting of arbitrary connection of several lumped elements. To improve its application, a recent literature [10] has developed an approach to treat the arbitrary linear lumped network, where the networks are described in terms of its impedance in Laplace domain and then transformed to Z-domain by the bilinear transformation. The time domain port voltage of the linear lumped networks required by Yee's cell can be obtained by using appropriate digital signal processing techniques.…”

“…More recently, Wu et al [11] have proposed another method to incorporate arbitrary high order linear lumped networks into FDTD method. These methods in [10,11] are based on explicit iterative techniques to treat linear lumped network. In order to create an explicit iterative formula, in literature [11] a complex recursion technology has been used.…”

“…In order to create an explicit iterative formula, in literature [11] a complex recursion technology has been used. However, these methods in [10,11] cannot be utilized to analyze linear lumped networks including internal independent sources and active elements. For overcoming the disadvantages in [9][10][11], a matrix method based on Kirchhoff's circuit laws developed in the literature [12] can be used to model linear lumped and active networks, whereas it is very difficult to use this method to deal with the networks in which some elements expressed by high order linear equations are included.…”

The Adi-FDTD Method Including Lumped Networks Using Piecewise Linear Recursive Convolution Technique

“…The so called lumped network finite difference time domain (LN-FDTD) method allows complex microwave circuits to be successfully analyzed; bridging the gap between electromagnetic-field and circuitbased simulators [4]. The key point of researching the LN-FDTD method is to import the current expression of lumped network into the Maxwell's equations.…”