ARMA-based time-signature estimator for analyzing resonant structures by the FDTD method

We propose an algorithm for estimation of the optimal "system" parameters o f time sequences (TSs) computed by the finite-difference time-domain (FDTD) method, with the goal of accurate representation of the time-signature usi ng low-order models. The FDTD method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavio r of resonant structures. Therefore, it becomes critical to investigate met hods of reducing the computational time for such objects. Several researche rs have argued that the FDTD-TS can be modeled as the impulse response (IR) of an autoregressive moving average (ARMA) transfer function, However, it is known that determination of ARMA parameters by IR matching is a complex nonlinear optimization problem. Hence, many existing methods in EM literatu re tend to use Prony-based, linear predictor-type spectrum estimation algor ithms, which minimize a linearized "equation error" criterion that approxim ates the true nonlinear model-fitting error criterion. As a result, signifi cantly high model orders are needed by these methods to achieve good corrob oration in the frequency domain, especially when a magnitude spectrum has d eep nulls or notches. In this paper, we propose to use a deterministic ARMA approach, which minimizes the true nonlinear criterion iteratively, and at tains significantly improved IR fit over Prony's method using fewer ARMA mo del parameters. For a given time-sequence of an analyzed circuit, the issue s of model order selection and choice of decimation factor are also address ed systematically. The improved performance of the proposed algorithm is de monstrated with transient simulation and signal analysis of microstrip stru ctures which manifest deep nulls in the frequency domain.