Effective impedance over ordered fields

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.