Thévenin equivalents for inhomogeneous ladder networks of generators

Abstract

We find general formulas for Thévenin equivalents (equivalent voltage and equivalent impedance) for inhomogeneous ladder networks of generators defined as a voltage source and an impedance in series. In the projective matrix representation, this is accomplished by adopting a special decomposition of a 3 × 3 transfer matrix which transforms a product of transfer matrices to a product of diagonal matrices up to a prefactor and a postfactor. In particular, we calculate Thévenin equivalents in a closed form for two ladder networks of generators with a periodic transfer matrix of period 1 (tapered ladder network) and period 2.