Derivative of driving point impedance functions at right half plane

Abstract

The purpose of this paper is to provide a result which concerns with the boundary behaviour of positive real functions. Z(s) = Z(b)+a₁(s - b)+ a₂ (s - b)² +... is an analytic function defined in the right half of the s-plane.
We derive inequalities for the modulus of Z(s) function, |Z'(c)|, by assuming the Z(s) function is also analytic at the boundary point s = c on the imaginary axis, where c = iImb and finally, the sharpness of these inequalities is proved.