Generalizing the Warburg impedance to a Warburg impedance matrix

We seek to generalize and study the well-known Warburg impedance element, which has an impedance proportional to 1/root s (s = j omega is the complex frequency), to a two-port impedance network. For this purpose, we consider an infinite binary tree structure inside which each impedance is treated as a two-port network. We obtain a Warburg impedance matrix, which is both symmetrical and reciprocal, and study its equivalent circuit behavior. Interestingly, the equivalent circuit contains two resistors and a Cole-Davidson type impedance proportional to root 1 + 2/(tau s), where tau is a time constant. Simulation results of the Warburg impedance matrix and its implementation in a resonance circuit are provided and discussed.

Automated summary

The study generalizes the Warburg impedance element to a two-port impedance network using an infinite binary tree structure. The Warburg impedance matrix obtained is symmetrical and reciprocal, with an equivalent circuit behavior containing two resistors and a Cole-Davidson type impedance proportional to root 1 + 2/(tau s). Simulation results and implementation in a resonance circuit are provided and discussed.