Effective Impedance 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.

arXiv comment19 pages, 7 figures

References in corpus (4)

• Power dissipation in fractal Feynman-Sierpinski AC circuits
• Power dissipation in fractal AC circuits
• On the notion of effective impedance
• Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus

Cited by in corpus (6)

• Complex networks with complex weights
• On the effective impedance of finite and infinite networks
• Dynamical processes on metric networks
• Capacity of infinite graphs over non-Archimedean ordered fields
• Recurrence and transience for non-Archimedean and directed graphs
• Discrete Laplace and transition operators over non-Archimedean ordered fields