On the notion of effective impedance. (English) Zbl 1462.05164
Summary: 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 weights from the ordered field of rational functions. The notion of effective impedance in both approaches is defined.
MSC:
| 05C22 | Signed and weighted graphs |
| 05C81 | Random walks on graphs |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 39A12 | Discrete version of topics in analysis |
| 12J15 | Ordered fields |
| 94C05 | Analytic circuit theory |
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