
arXiv: 1907.13239
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.
FOS: Physical sciences, Mathematical Physics (math-ph), Technical applications of optics and electromagnetic theory, Mathematics - Spectral Theory, finite electrical networks, impedance, FOS: Mathematics, Mathematics - Combinatorics, 05C22, 34B45, 05C25, 39A12, 12J15, Non-Archimedean analysis, Combinatorics (math.CO), Spectral Theory (math.SP), Mathematical Physics
FOS: Physical sciences, Mathematical Physics (math-ph), Technical applications of optics and electromagnetic theory, Mathematics - Spectral Theory, finite electrical networks, impedance, FOS: Mathematics, Mathematics - Combinatorics, 05C22, 34B45, 05C25, 39A12, 12J15, Non-Archimedean analysis, Combinatorics (math.CO), Spectral Theory (math.SP), Mathematical Physics
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