Application of Inductive Topological Transfer Function Generation for a Cascaded Low-Pass Filter

Abstract

This work presents applications of an inductive topological approach in the calculation of the transfer function of a cascading network control system. The method provides a very versatile and effective way of counting all the graphs that contribute and of translating them into their algebraic contribution. The contributing graphs are very simple and reflect the morphology of the original control system signal flow graph. Application of the method and results are presented for an n-cell RC network. We derive an analytical formula relating ω(3 dB) to the filter size (n) and RjCj (j=1,2,…,n). This formula can be used for designing preset frequency range self-loaded LP filters by varying their size. We also derive general expressions for the sensitivities which we use to observe a sensitivity-insensitivity filter transition for various frequency ranges, relaxation times, and, most importantly, filter sizes.