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
₀
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
₀
, where m is the multiplicity of pk
₀
0, and the proportionality factor equals the coefficient Ak of (p-pk
⁰
)
_-m
in the partial fraction expansion of 1/Z(p).