Validation of a flexible causality treatment for transient analysis of nonlinearly loaded structures

In this paper we study the transient analysis of distributed three dimensional structures loaded by lumped elements. Emphasis is put on the combined electromagnetic (EM)/circuit simulation by making use of band-limited frequency responses. First passive structures are investigated within the spectrum of interest, either by simulation or measurements. Then, causal impulse responses are extracted from the truncated spectrum. For the causality correction, we present a flexible treatment by using exponential functions for the spectrum extrapolation. Finally, the approach is verified by incorporating the causal impulse responses into an EM/circuit simulation. Single and multiple nonlinearly loaded examples are analyzed by means of a time marching procedure based on the causal convolution approach. The results show a good agreement with measurements and the results provided by commercial simulators.