## Abstract

In this paper, we study the properties of effective impedances of finite electrical networks, considering them as weighted graphs over an ordered field. We prove that a star-mesh transform of finite network does not change its effective impedance. Moreover, we consider two particular examples of infinite ladder networks (Feynman's network or LC-network and CL-network, both with zero at infinity) as networks over the ordered Levi-Cività field R. We show that the sequence of effective impedances of finite LC-networks converges to the limit in the order topology of R, but the sequence of effective impedances of finite CL-networks does not converge in the same topology. We calculate an effective impedance of a finite ladder network as an auxiliary result.

Original language | English |
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Article number | 033502 |

Journal | Journal of Mathematical Physics |

Volume | 62 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2021 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fields of Expertise

- Information, Communication & Computing