Causal parameter extractions by vector fitting for use in time-domain numerical modeling

In time-domain modeling techniques, such as the finite-difference time-domain method, a lumped parameter electronic device, such as a transistor, is often treated as a black box represented by its time-domain network parameters. The parameters of most electronic devices are, however, often given in the frequency domain and in a limited frequency range. Therefore, they need to be transformed into the corresponding time-domain parameters for inclusion in time-domain modeling. The vector fitting technique is a robust coefficient extraction technique that circumvents the normal ill-conditioning and unbalanced weighting problems occurring in a rational approximation or fitting process. We apply it to obtain frequency domain rational approximation functions of network parameters of a lumped parameter device and then convert them to the corresponding time-domain parameters. As a result, the time-domain parameters are not only causal but also exponential in time. Convolution can then be performed in a recursive fashion without the need to involve a complete past history of the time-domain data. In a long simulation, the CPU time saving factor can be hundreds and thousands of times.