The effective impedances of infinite ladder networks and Dirichlet problem on graphs

Abstract

We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related to the classical differential operators on weighted graphs. As an auxiliary result, we solve a discrete boundary value Dirichlet problem on a finite ladder network.

18 pages, 10 figures

References in corpus (2)

• Power dissipation in fractal Feynman-Sierpinski AC circuits
• On the effective impedance of finite and infinite networks