Bulg. J. Phys. vol.49 no.2 (2022), pp. 115-135

The Effective Impedances of Infinite Ladder Networks and Dirichlet Problem on Graphs

A. Muranova
Faculty of Mathematics and Computer Science, University of Warmia and Mazury, ul. Sloneczna 54, 10-710 Olsztyn, Poland
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.

doi: https://doi.org/10.55318/bgjp.2022.49.2.115

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