On the notion of effective impedance
arXiv:1905.02047 · doi:10.7153/oam-2020-14-46
Abstract
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two mathematical models of such networks: complex-weighted graphs and graphs with weight from the ordered field of rational functions. The notion of effective impedance in both approaches is defined.
arXiv comment17 pages, 6 figures
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- Networks with complex weights: Green function and power series
- Discrete Laplace and transition operators over non-Archimedean ordered fields