Ladder network characterization and Fibonacci numbers

Abstract

This paper illustrates a new method, proposed by the authors, which allows the direct determination of ladder networks characteristics, from both a numerical and a symbolic point of view, once the number of cells and their circuit elements are known. In particular, using a single treatment for the solution of all the possible ladder networks, the transfer function, node voltages and branch currents, Thevenin's model, input and output impedance, signal-to-noise ratio, transmission, quadrupole and scattering matrices are determined. In the particular case in which the longitudinal and transversal impedances are equal, these electrical characteristics are strictly and surprisingly related to Fibonacci numbers.