Displacement of the Zeros of the Impedance Z(p) Due to Incremental Variations in the Network Elements

Abstract

The purpose of this paper is to evaluate the displacement of the zeros pk₀ of the impedance Z(p) due to the variations δz in the impedance of any network element. It is shown that the displacement is approximately proportional to the mth root of (-δz) evaluated at p = pk₀, where m is the multiplicity of pk₀0, and the proportionality factor equals the coefficient Ak of (p-pk⁰)_-m in the partial fraction expansion of 1/Z(p).