Infinite AC Ladder with a "Twist"

TL;DR

This paper investigates the complex impedance behavior of an infinite AC ladder network with a modified topology, revealing how dominant eigenmodes govern electrical propagation in the network.

Contribution

It introduces a novel modification to the infinite AC ladder topology and explains its effects using eigenvector analysis of the transmission matrix.

Findings

Eigenvector analysis explains the impedance behavior

Dominant eigenmodes determine electrical information flow

Modified topology leads to unexpected impedance properties

Abstract

The infinite AC ladder network can exhibit unexpected behavior. Entangling the topology brings even more surprises, found by direct numerical investigation. We consider a simple modification of the ladder topology and explain the numerical result for the complex impedance, using linear algebra. The infinity limit of the network's size corresponds to keeping only the eigenvectors of the transmission matrix with the largest eigenvalues, which can be viewed as the most dominant modes of electrical information that propagate through the network.