Curve fitting of frequency response functions by use of pole-zero models for the loss factor measurement

Abstract

For the loss factor measurement, the half-power-width method and curve fitting method are used. In this paper, two curve fitting methods based on pole-zero models are proposed. The first method is to express the measured and model frequency response functions in decibels and the parameters of the model are changed so that the model response gets close enough to the measured response by the differential iteration method. The second method is to take the distance of the two responses on the complex plane and normalize it to the amplitude of the measured frequency response function. Then, the normalized distance is minimized by the differential iteration method. These two methods have the following features: (1) They can fit the resonance and anti-resonance characteristics simultaneously. (2) They can fit frequency response functions with large loss factors to which the half-power-width method are not applicable. (3) The minimum required numbers of measurement points within the half-power-width for these methods are roughly 1/30 of the number necessary for the half-power-width method.