Application of system identification to time-domain modeling of electromagnetic structures

Time domain techniques as the transmission line matrix (TLM) method, allow to characterize an electromagnetic structure in a wide frequency band with a single simulation. However, in the case of the modeling of low loss electromagnetic structures, the transient response to impulsive excitation will exhibit a long decay time, and to obtain accurate results, simulation times are required which exceed the time discretization interval by several orders of magnitude. The computational time may be reduced considerably by applying system identification (SI) methods. SI approaches, which analyze exciting impulses and corresponding transient responses simultaneously, or spectral analysis (SA) methods can be used to extract transfer admittance and impedance matrices of electromagnetic systems for the subsequent calculation of their corresponding Foster matrix representations [1, 2]. It is well known that input signals which are zero (or sufficiently small) outside some common, sufficiently short, time interval, tend to have essentially the same effect to a macroscopic system [3]. This is a direct consequence of the fact that the spectrum of a sufficiently short transient input signal is broad enough to cover most of the useful spectrum of an electromagnetic device. Under this condition, the determination of the model parameters can be easily performed by means of a system response analysis. From the class of SI methods, Prony's model based techniques [2] are the most popular approaches for the extraction of poles and residues from available transient responses (both simulated or measured). These methods seek to fit a deterministic exponential model to the discrete-time waveforms that constitute the transient response obtained using one of the time-domain methods like TLM or FDTD. In this work, the correspondence between the Pronys model and the equivalent Foster representation of the impedance parameters on the base of the network oriented theory [11] will be shown. An algorithm able to autonomously generate the model once accuracy tolerances and frequency range have been specified, will be presented. This algorithm referred at as Prony's model based System Identification (PMSI) allows adaptive model order estimation by separating the signal subspace from the noise subspace with a SVD based technique [6], while the poles estimation is based on the Pencil Matrix method [7]. The aim of the PMSI algorithm is twofold. in case of time-domain analysis it may be used as impulse response predictor, by yielding a reduction of the overall analysis. Secondly it can be used to extract the Foster's representation directly from the available time domain responses. For both applications numerical results for a one-port passive network are presented and the extension to arbitrary multiport example is discussed.