Chapter 9 MODEL-ORDER REDUCTION IN ELECTROMAGNETICS USING MODEL-BASED PARAMETER ESTIMATION Edmund K. Miller and Tapan K. Sarkar ABSTRACT This chapter outlines and demonstrates the use of model-based parameter estimation (MBPE) in electromagnetics. MBPE can be used to circumvent the requirement of obtaining all samples of desired quantities (e.g., impedance, gain, ReS) from a first-principles model (FPM) or from measured data (MD) by instead using a reduced-order, physically based approximation of the sampled data called a fitting model (FM). One application of a FM is interpolating between (pole-series FMs), and/or extrapolating from (exponential-series FMs), samples of FPM or MD observables to reduce the amount of data that is needed. A second is to use a FM in FPM computations by replacing needed mathematical expressions with simpler analytical approximations to reduce the computational cost of the FPM itself. As an added benefit, the FMs can be more suitable for design and optimization purposes than the usual numerical data that comes from a FPM or MD because the FMs can normally be handled analytically rather than via operations on the numerical samples. Attention here is focused on the use of FMs that are described by exponential and pole series, and how data obtained from various kinds of sampling procedures can be used to quantify such models, i.e., to determine numerical values for their coefficients. 9.1 BACKGROUND AND MOTIVATION Most EM phenomena, whether observed in the time domain (TD) or the frequency domain (FD), or as a function of angle or location, are not of interest at just one or a few discrete times, frequencies, angles, or locations but, instead, require essentially continuous representation over some specified observation interval. Even with increasingly sophisticated instrumentation or computer models, determining EM observables to sufficient resolution as a function of the relevant variable can be expensive as well as potentially error prone. A typical problem now involves determining TD or FD responses over bandwidths that are no longer just a few percent or a few megahertz, but might extend over frequency ranges that are 10:1or more in relative bandwidth or multiple gigahertz bandwidths in absolute terms. Resolving a response that contains many high-O, closely spaced resonances requires slower sweeping rates or long observation times experimentally, or an excessive number of frequency samples or time steps computationally. A computational basis for solving most problems in physics and engineering 371