Extraction of causal time-domain network parameters from their band-limited frequency-domain counterparts using rational functions

Network parameters of a lumped element device are usually given in a limited frequency band of interest, or in an operation frequency range. To include them in time-domain simulations, they need to be converted to their causal time-domain correspondences. However, direct conversion with a simple technique such as the Fourier transform often leads to noncausal time-domain network parameters. Even when causal parameters are found, convolutions with them in the time domain are usually too computationally inefficient to carry out for a simulation with a large number of time steps. In this paper, a technique that extracts the causal time-domain parameters using rational function approximations is proposed. It results in time-domain parameters which are not only causal but also of exponential form in time. Consequently, the convolutions with them can be performed in a recursive manner. Numerical examples are provided to verify the effectiveness.