### 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 i_{k} and v_{k} of the vectors i and v respectively are subject to v_{k}i_{k} = 0, v_{k} < 0, and i_{k} > 0. We show that the number of solution for the equations is at most 5.

Original language | English |
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Pages (from-to) | 99-106 |

Number of pages | 8 |

Journal | Research Reports on Information Science and Electrical Engineering of Kyushu University |

Volume | 6 |

Issue number | 1 |

Publication status | Published - Mar 2001 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

**An upper bound for the number of solutions of a piecewise-linear equation related to two-transistor circuits.** / Jitsumatsu, Yutaka; Nishi, T.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An upper bound for the number of solutions of a piecewise-linear equation related to two-transistor circuits

AU - Jitsumatsu, Yutaka

AU - Nishi, T.

PY - 2001/3

Y1 - 2001/3

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0035269259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035269259&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 99

EP - 106

JO - Research Reports on Information Science and Electrical Engineering of Kyushu University

JF - Research Reports on Information Science and Electrical Engineering of Kyushu University

SN - 1342-3819

IS - 1

ER -