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.

19 pages, 7 figures