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%.