Sharpened Forms for Driving Point Impedance Functions at Boundary of Right Half Plane

Abstract

Driving point impedance functions (DPIFs) are frequently used in electrical engineering, and they represent characteristic properties of various types of circuits such as RL, RC, LC and RLC networks. In this paper, boundary analysis of driving point impedance functions are investigated using Schwarz lemma. Assuming that the driving point impedance function, 𝑍(𝑠), is given as 𝑍(𝑠) = 𝐴 2 + 𝑐 𝑝 (𝑠 − 1) 𝑝 + 𝑐 𝑝+1 (𝑠 − 1) 𝑝+1 +. .. and it is analytic in the right half of the s-plane, novel boundaries are obtained for |𝑍 ′ (0)|. Accordingly, it is aimed to obtain novel inequalities which presents higher boundaries for |𝑍′(0)| and derive novel generic driving point impedace functions by performing extremal analysis of these obtained inequalities. It is also aimed to investigate how |𝑍′(𝑠)| can be interpreted when it is considered at the boundary. According to simulation results, frequency characteristics of obtained driving point impedance functions can be used to design of multi-notch filters which are localized at certain frequency values.