Frequency Responses Resistance to Variations of Electric Filter Parameters

Abstract

When electric filter designs "on the whole" circuit's parameters are determined as a result of solving the system of equations formed by equating of coefficients at equal powers of the variable in terms of desirable transfer function (TF) and TF filter. The solution of the system of nonlinear equations is the set (or sets) of filter parameters. The transition to practical realization requires bringing the filter parameters to the standard range of nominal values. The frequency responses of the filter are distorted, when the calculated values are replace on the nominal values. Moreover, the nominal value scales themselves have different range of values depending on the selected range. The purpose of the article is to develop evaluation methods of amplitude- and phase-frequency responses resistance of low-pass and high-pass filters to parameter variations during the filters realization. The integral square function of a variable is taken as a measure of deviation of the real frequency response from calculated characteristic. The specific parameter response resistance is defined as the inverse average value of the integral function at the given range of the parameter variations. The inverse sum of average values of the integral function for the specific set of elements serves as integrated evaluation of response resistance to the filters parameter variations. In case there are several solutions of the system of equations, providing filter synthesis, the one should be used that gives closest to the maximum value of integrated evaluation of resistance. The introduced definitions allow to fulfill the successive selection of filter elements in the light of the impact of each element in the total evaluation of the frequency response stability.