An upper bound for the number of solutions of a piecewise-linear equation related to two-transistor circuits

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Abstract

This paper discusses the number of solutions for a class of piecewise-linear equations related to two-transistor circuits compised of transistors, linear passive resistors, and DC sources. By using Ebers-Moll model, a transistor is replaced by two nonlinear resistors and two linear current-controlled current sources. We assume in this paper that the nonlinear resistors are ideal diodes. Then a circuit equation for the above circuit is a piecewise-linear equation Ti + Gv = b where each component ik and vk of the vectors i and v respectively are subject to vkik = 0, vk < 0, and ik > 0. We show that the number of solution for the equations is at most 5.

Original languageEnglish
Pages (from-to)99-106
Number of pages8
JournalResearch Reports on Information Science and Electrical Engineering of Kyushu University
Volume6
Issue number1
Publication statusPublished - Mar 2001
Externally publishedYes

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Linear equations
Resistors
Transistors
Networks (circuits)
Diodes

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

Cite this

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abstract = "This paper discusses the number of solutions for a class of piecewise-linear equations related to two-transistor circuits compised of transistors, linear passive resistors, and DC sources. By using Ebers-Moll model, a transistor is replaced by two nonlinear resistors and two linear current-controlled current sources. We assume in this paper that the nonlinear resistors are ideal diodes. Then a circuit equation for the above circuit is a piecewise-linear equation Ti + Gv = b where each component ik and vk of the vectors i and v respectively are subject to vkik = 0, vk < 0, and ik > 0. We show that the number of solution for the equations is at most 5.",
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AB - This paper discusses the number of solutions for a class of piecewise-linear equations related to two-transistor circuits compised of transistors, linear passive resistors, and DC sources. By using Ebers-Moll model, a transistor is replaced by two nonlinear resistors and two linear current-controlled current sources. We assume in this paper that the nonlinear resistors are ideal diodes. Then a circuit equation for the above circuit is a piecewise-linear equation Ti + Gv = b where each component ik and vk of the vectors i and v respectively are subject to vkik = 0, vk < 0, and ik > 0. We show that the number of solution for the equations is at most 5.

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