Iterative methods for extracting causal time-domain parameters

Recent interest in time-domain modeling techniques has been largely motivated by the demands for simulating broad-band electronic systems and high-speed digital circuits. These techniques normally require strict causality of any parameters to be used with them. However, most of parameters, such as the S-parameters of a transistor, are given only in the frequency domain and over a limited frequency range of interest. Direct applications of regular transformation techniques to these band-limited frequency-domain parameters, such as inverse Fourier transform, often lead to noncausal time-domain correspondents. Therefore, schemes need to be carefully developed for extraction of the time-domain parameters that are causal while retaining the original frequency-domain information within the frequency range of interest. In this paper, two iterative methods are proposed for the causal extraction, and numerical examples are given to validate the effectiveness. The errors of the methods are found to be approximately 1%.

I. Introduction

Recent interest in time-domain modeling methods has been mostly motivated by the demands for simulating broad-band electronic systems and high-speed digital circuits. However, when they are used with black-box types of devices and components, care needs to be taken. For instance, when the finite-difference time-domain (FDTD) method [1] is used, two approaches are normally employed: one is to incorporate the FDTD into the governing voltage–current equations of a device [2], [3] and another is to incorporate the governing voltage–current equations of a device into the FDTD marching equations [4], [5]. In the first approach, the nonlinear circuit model of a device has to be known and solved with the current terms being updated with the field FDTD. In the second approach, however, a nonlinear circuit model is not necessarily needed. Instead, the network parameters of a device, such as the - or -parameters, are used. They are then incorporated or interfaced with the FDTD equations. The implementation of the second approach is relatively simpler, but it has a stringent requirement for the network parameters of the devices: the parameters need to be in the time domain and have to be causal because the FDTD models are causal.