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

The purpose of this paper is to evaluate the displacement of the zeros pk<sub>0</sub> 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 = pk<sub>0</sub>, where m is the multiplicity of pk<sub>0</sub>0, and the proportionality factor equals the coefficient Ak of (p-pk<sup>0</sup>)<sub>-m</sub> in the partial fraction expansion of 1/Z(p).