UNIV. NEWS. NORTH-CAUCAS. REG. TECHNICAL SCIENCES SERIES. 2014; 6: 18-26
http://dx.doi.org/10.17213/0321-2653-2014-6-18-26
Parameters of Two-Terminal Series-Parallel Electrical Circuits with N Identical Components
Ivanchenko Alexander Nikolaevich – Candidate of Technical Sciences, professor, department “Software Computer Engineering”, Platov South Russia State Technical University (Novocherkassk Polytechnic Institute). E-mail: ian2008.52@mail.ru
Zasipkin Alexander Sergeevich – Doctor of Technical Sciences, professor, department “Power Plants and Power Systems”, Platov South Russia State Technical University (Novocherkassk Polytechnic Institute). E-mail: aepsnpi@mail.ru
Abstract
The article discusses the two-terminal series-parallel electrical circuits composed of N identical elements (resistors or capacitors). The original algorithm for enumerating (constructing) of all series-parallel circuits containing no more than N elements with the removal of duplicates (circuits with identical electrical parameters) is proposed, and its implementation on an object-oriented language C ++ is executed. The comparison of the received results with similar data from foreign sources is accomplished. Two original approaches to reduction (decreasing) of a set of schemes having practical value were offered. The first is based on the selection from the plurality of circuits with the same resistance to only one, the most effective scheme. The second approach is caused by practical requirement of creation the compact "libraries" of the schemes approximating the set any resistance with the guaranteed relative error. Fragments of "library" for schemes from 4, 5 and 6 elements are presented.
Keywords: two-terminal graph; two-terminal series-parallel network; equivalent networks; essentially series network; essentially parallel network; two-terminal series-parallel electrical circuit; enumeration; combinatorial analysis; recursive algorithm; object-oriented programming; relative error; equivalent resistance; approximation.
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