Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data

J Michael Frye,Anthony Q Martin

doi:10.1155/2013/563724

Abstract

An efficient procedure is presented to extrapolate a wideband electromagnetic response defined over an arbitrary spatial region using early-time and low-frequency data. The previous procedures presented in the literature are efficient for single-point extrapolation and can readily be applied to spatial regions but are terribly inefficient when a response is desired at many spatial locations. In this work, an optimized algorithm is presented to quickly extrapolate over a large number of spatial locations. The time and frequency behavior of the response is fitted by polynomials and pole terms, and the spatial variation is represented with spatially dependent polynomial coefficients and pole residues. A single set of poles, common to all spatial locations of interest, is shown to sufficiently describe the resonant behavior of response over the entire spatial region. A multisignal formulation of the matrix pencil method is applied to determine poles from early time data. Numerical examples are presented to demonstrate the procedure. Additionally, an automated approach to distinguish physical poles, which correspond to structural resonances, from nonphysical fitting poles is presented. The spatially dependent residues of physical pole terms, referred to here as modal residues, are shown to provide important insight into the resonant behavior of a structure.

Highlights

In [1,2,3,4], electromagnetic responses, such as the driving-point current of an antenna, are simultaneously extrapolated in time and frequency by fitting discrete values of the response evaluated at early time and low-frequency points
It is demonstrated that a single set of poles, shared by each spatial location, is sufficient to describe the resonant behavior of response over the entire spatial region
The spatial region R is specified by z ∈ [0, L] and contains I = 99 spatial locations -spaced along the length of the dipole

Summary

Introduction

In [1,2,3,4], electromagnetic responses, such as the driving-point current of an antenna, are simultaneously extrapolated in time and frequency by fitting discrete values of the response evaluated at early time and low-frequency points. As with the procedures of [1,2,3,4], the reliable application of the approach in this work requires the selection of several polynomial and pole-estimation parameters. To extrapolate a response in a spatial region, one can apply the automated, optimization-based procedure of [2] at each discrete location; this approach is highly inefficient because a separate GA optimization run is required for each location. All necessary parameters are selected using a GA by simultaneously fitting the response, in early time and low frequency, at a small subset of the total number of positions in the spatial region. Coefficients and residues are calculated for each spatial location by fitting the early-time and low-frequency data at each location. The response is accurately extrapolated over the entire spatial region despite selecting parameters based on data at only a few locations. It is shown that the spatial residues of physical pole terms, referred to here as modal residues, correspond to natural modal behavior

Extrapolation of a Spatial Response

Reliable Selection of Parameters

Determining Physical Poles

Results and Discussion

Conclusions