Infinite AC Ladder with a "Twist"

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.