The Role of the Characteristic Load Impedance in Passive Ladder Networks: Again the Presence of the Fibonacci Sequence

R. Lojacono, C. Falconi1, G.Ferri, E. Lo Castro, M.Salmeri, A. Mencattini, M.Santonic, G.Pennazza, A. D Amico

This paper deals with an analysis of the different behaviors existing between ladder networks (LN) terminated and not terminated by the characteristic impedance Z0. The main purpose of this work is to find, in both cases, links with the golden ratio and, as a consequence, with Fibonacci numbers. Results of some simulations related to the determination of impedances, node voltages and branch currents are given in order to underline approximation effects on the node voltages and branch currents related to both the presence and absence of Z0.This study has been firstly applied to R-R ladder networks but it is here extended to consider other kinds of LNs, having other types of single cells such as C-C ; L-L whose characteristic impedances have also been determined. Double resistive LN have also been investigated for which impedances in any cell, currents in any branch and voltages in any node have been determined in the two cases of presence and absence of the characteristic impedance and with different ratio between longitudinal and transversal impedances. This study has another not less relevant aim: find one of the possible platform for the modelization of biosystems like DNA and RNA, because these structures even if much more complex look like a LN