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Analysis of Linear Time-invariant Networks in the Frequency Domain

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Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 117))

Abstract

It is well-known that linear time-invariant electrical networks represent successful models in nearly all branches of electrical engineering. Therefore networks consisting of linear resistors, capacitors and inductors as well as dependent and independent sources — so-called active RLC networks — are of much interest till now in order to describe linear analog circuits. Studying electrical networks we have to remember the fundamental concept of this class of systems. The main idea is to build systems consisting of relative simple subsystems which are cooperate by means of a connection subsystem. Although this principle is used in many areas of engineering and natural sciences these ‘network concepts’ differ in their mathematical structures and the meaning of its variables. In electrical network theory systems are described by currents and voltages. Therefore we need equations which govern the simple subsystems and the connection subsystem; in this area these simple subsystems are denoted as network elements. First considerations of electrical networks were published by Ohm in 1828 [18]. His studies were continued by Kirchhoff, Helmholtz, Maxwell and others; for a historical overview see Wunsch [29].

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of Wuppertal, D-5600, Wuppertal 1, Fuhlrottstr. 10, Germany

    Wolfgang Mathis

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  1. Wolfgang Mathis
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, C-012, University of California, San Diego, La Jolla, CA, 92093, USA

    R. E. Bank

  2. Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117, Berlin, Germany

    H. Gajewski

  3. Mathematisches Institut der TH München, Postfach 20 24 20, D-80290, München, Germany

    R. Bulirsch

  4. ZTI DES2 Siemens AG, Otto-Hahn-Ring 6, D-81739, München, Germany

    K. Merten

  5. Siemens Corporate Research, Inc., 755 College Road East, Princeton, N. J., 08540, USA

    K. Merten

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© 1994 Springer Basel AG

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Mathis, W. (1994). Analysis of Linear Time-invariant Networks in the Frequency Domain. In: Bank, R.E., Gajewski, H., Bulirsch, R., Merten, K. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. ISNM International Series of Numerical Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8528-7_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8528-7_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9665-8

  • Online ISBN: 978-3-0348-8528-7

  • eBook Packages: Springer Book Archive

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