Application of System Identification (SI) to Full--Wave Time Domain Characterization of Microwave and Millimeter Wave Passive Structures

Numerical time–domain methods for electromagnetic field simulations typically provide very broad band frequency–domain characterizations as well as transient response with a single simulation and without in general requiring any pre–processing. However long simulation times and large memory requirements arise for the case of electromagnetic structures characterized by low loss (high quality factor) and high aspect ratios (complex three– dimensional structures), since the first yields long transient responses and the second small time discretization intervals. Passive network impulse responses can be characterized by the singularity expansion method theory, implying that they can be efficiently described by means of exponentially damped oscillating components corresponding to the network natural frequencies. In principle, the entire time behavior of an electromagnetic structure can therefore be predicted from a few time samples by applying high resolution parametric model estimation techniques, based on system identification (SI) methods. These methods allow the determination of the network equivalent model directly from the simulated results. The number of a model’s parameters, also called model order, and the parameters themselves, typically represented by complex natural frequencies or poles, significantly effect this methodology since they are indicators of the complexity and the accuracy of the model respectively. Once correctly identified these parametric analytical descriptions can replace more cumbersome and demanding full–wave numerical models, in network level (SPICE like) simulators, enabling a much faster analysis. Although SI techniques are a quite well known topic in electromagnetic numerical applications, a systematic and effi- cient approach is still missing. The aim of the present work is to develop an improved approach first, by re-examining the theoretical background of the network oriented modelling (NOM) in order to justify the use of a poles series model (Prony model) as the more obvious choice for describing passive electromagnetic structures, and second by reviewing some of the most common and efficient SI techniques for the model order selection and model parameters estimation. The intention is to formulate an algorithm that allows for entire network modelling to be carried out in a completely autonomous and automatic fashion. The methodology is to estimate the model’s parameters from the time–domain responses generated by means of a full–wave analysis, be it the Transmission Line Matrix (TLM) method or the finite difference time–domain (FDTD) method, and by adaptively refining them, fit the model recovered responses, to the numerically simulated ones. This algorithm runs in parallel with a full-wave analysis which is discontinued as soon as the model accuracy becomes satisfactory. In this way a time demanding numerical simulation may be reduced by one order of dimension. Since the model taken in consideration is Prony’s and the parameter estimation procedures are Prony based, the algorithm is called Prony Model based System Identification (PMSI). Once the network responses are available they may be used for identifying the network natural frequencies of the impedance (admittance) Foster representation, enabling the direct implementation of the corresponding lumped element equivalent circuit. Since the Foster representation for the impedance (admittance) is practically a Prony model this operation may be carried out again by means of the PMSI algorithm.