### Abstract

It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SPICE-oriented Newton homotopy method which can efficiently find out the multiple dc solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

Original language | English |
---|---|

Pages (from-to) | 337-348 |

Number of pages | 12 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 Mar |

Externally published | Yes |

### Fingerprint

### Keywords

- Continuation method
- Multiple dc solutions
- Newton homotopy method
- SPICE-oriented algorithm
- User-friendly simulator

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*,

*21*(3), 337-348. https://doi.org/10.1109/43.986427

**An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method.** / Ushida, Akio; Yamagami, Yoshihiro; Nishio, Yoshifumi; Kinouchi, Ikkei; Inoue, Yasuaki.

Research output: Contribution to journal › Article

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*, vol. 21, no. 3, pp. 337-348. https://doi.org/10.1109/43.986427

}

TY - JOUR

T1 - An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method

AU - Ushida, Akio

AU - Yamagami, Yoshihiro

AU - Nishio, Yoshifumi

AU - Kinouchi, Ikkei

AU - Inoue, Yasuaki

PY - 2002/3

Y1 - 2002/3

N2 - It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SPICE-oriented Newton homotopy method which can efficiently find out the multiple dc solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

AB - It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SPICE-oriented Newton homotopy method which can efficiently find out the multiple dc solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.

KW - Continuation method

KW - Multiple dc solutions

KW - Newton homotopy method

KW - SPICE-oriented algorithm

KW - User-friendly simulator

UR - http://www.scopus.com/inward/record.url?scp=0036494481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036494481&partnerID=8YFLogxK

U2 - 10.1109/43.986427

DO - 10.1109/43.986427

M3 - Article

VL - 21

SP - 337

EP - 348

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 3

ER -