The Theorem of Reicht and Network Matrices

Bachelor thesis (2017)

Authors

B.X. van Leeuwen Electrical Engineering, Mathematics and Computer Science

Contributors

J.W. van der Woude (supervisor 1)
Dion Gijswijt (supervisor 2)
J.G. Spandaw (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2017 Bodine van Leeuwen
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Published Date

13-07-2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In 1969, the theorem of Reichert was formulated. Since then, two proofs have been found, both by Z. Jiang and Malcolm C. Smith, one of which in collaboration with Sara Y. Zhang. These proofs are based on the transfer functions of the electrical networks. The aim of this paper is to work toward a proof based on graph theory, linear algebra and differential equations. Whereas a proof has not been found, this paper provides insight on what the theorem of Reichert means, on ways to describe graphs and electrical networks with matrices and on the connection between those matrices. Lastly, we will take a look at Kron reduction: a way to remove resistors from resistive networks by manipulating their descriptive matrices.