# Effective Impedance over Ordered Fields

## TL;DR

This paper investigates the properties of effective impedance in finite and infinite electrical ladder networks over ordered fields, highlighting convergence behaviors in the Levi-Civita field.

## Contribution

It introduces the analysis of effective impedance in finite and infinite ladder networks over ordered fields, including convergence properties in the Levi-Civita field.

## Key findings

- Finite LC-network impedances converge in Levi-Civita field topology.
- Finite CL-network impedances do not converge in the same topology.
- Study extends impedance analysis to networks over ordered fields.

## Abstract

In this paper, we study properties of effective impedance of finite electrical networks and calculate the effective impedance of a finite ladder network over an ordered field. Moreover, we consider two particular examples of infinite ladder networks (Feynman's network or LC-network and CL-network, both with zero on infinity) as networks over the ordered Levi-Civita field. We show, that effective impedances of finite LC-networks converge to the limit in order topology of Levi-Civita field, but the effective impedances of finite CL-networks do not converge in the same topology.