Adaptive Stopping Criterion for Fast Time Domain Characterization of Microwave Components

This letter proposes a novel adaptive stopping criterion that facilitates a fast time domain characterization of microwave components. By successively computing a rational macromodel based on time-limited transient responses of the microwave component under study, the proposed stopping criterion limits the number of time steps required to capture the frequency behavior up to a predefined accuracy level. Therefore, it is particularly useful for systems where the transient responses decay slowly.

I. Introduction

In recent years, time domain characterization of complex microwave systems based on e.g. the finite difference time domain (FDTD) technique, the time domain finite element method (TD-FEM), or the time domain method of moments (TD-MoM) has become increasingly important, especially for broadband design and optimization. Compared to their frequency domain counterparts, time domain EM solvers have the advantage that they can capture the overall frequency response in a single simulation run by applying a Fourier transform to the time domain response of the system. Unfortunately, a long record of the time domain samples is often needed to ensure that the transient response on the pulse excitation has decayed sufficiently. Premature termination of the time domain simulation may result in an insufficient frequency resolution, while late termination may lead to an undesired waste of computational resources [1], [2]. To resolve these difficulties, several methods have already been considered in the past, e.g. autoregression [3], [4], generalized-pencil-of-functions [5], neural networks models [6], Prony's method [7] and pole tracking [8]. Many methods often try to extrapolate the transient response, in order to avoid the inaccuracies that arise due to simple zero-padding of the response.