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

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. Key words: weighted graphs, analysis on graphs, electrical network, ladder network, Feynman's ladder, effective impedance, Laplace operator. (author)