Error bounded Padé approximation via bilinear conformal transformation

Since asymptotic waveform evaluation (AWE) was introduced, many interconnect model order reduction methods via Pade approximation have been proposed. Although the stability and precision of model reduction methods have been greatly improved, the following important question has not been answered: "What is the error bound in the time domain?". This problem is mainly caused by the "gap" between the frequency domain and the time domain, i.e., a good approximated transfer function in the frequency domain may not be a good approximation in the time domain. All of the existing methods approximate the transfer function directly in the frequency domain and hence can not provide error bounds in the time domain. In this paper, we present new moment matching methods which can provide guaranteed error bounds in the time domain. Our methods are based on the classic work by Teasdale (1953) which performs Pade approximation in a transformed domain by the bilinear conformal transformation s=(1-z)/(1+z).