### Abstract

The dc driving-point and transfer characteristics of nonlinear circuits are the multivalued curves that arise from the nature of the circuit. These curves cannot be analyzed by general-purpose circuit simulators. One known method for analyzing these kinds of characteristic curves is the backward differentiation formula (BDF) curve-tracing algorithm proposed by Ushida and Chua. In this method, the circuit equations f(x) = 0, f (·): R^{N+1} → R^{n}, where the input voltage is assumed to be a variable, are analyzed by the predicator-corrector algorithm where the arc-length of the solution curve in n + 1-dimensional space is the parameter. However, it is not clear that this method is practical for large-scale circuits. In this paper, we extend the Ushida-Chua method from a practical method standpoint and demonstrate that the multivalued characteristic curves of large-scale circuits can easily be analyzed using general-purpose circuit simulators. In the proposed method, first, the solution curve in n + 1-dimensional space is projected into m + 1-dimensional space, where m ≤ n and the arc-length of this new curve is used as the parameter. Second, the relationship between the arc-length and the components of the curve is expressed by a function generator circuit, the solution-tracing circuit. Finally, transient analysis is performed using a general-purpose circuit simulator and the solution curve is traced. The effectiveness of this method is verified through several examples, including a bipolar analog IC with 296 nodes.

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

Pages (from-to) | 52-63 |

Number of pages | 12 |

Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 75 |

Issue number | 7 |

Publication status | Published - 1992 Jul |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**DC analysis of nonlinear circuits using solution-tracing circuits.** / Inoue, Yasuaki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - DC analysis of nonlinear circuits using solution-tracing circuits

AU - Inoue, Yasuaki

PY - 1992/7

Y1 - 1992/7

N2 - The dc driving-point and transfer characteristics of nonlinear circuits are the multivalued curves that arise from the nature of the circuit. These curves cannot be analyzed by general-purpose circuit simulators. One known method for analyzing these kinds of characteristic curves is the backward differentiation formula (BDF) curve-tracing algorithm proposed by Ushida and Chua. In this method, the circuit equations f(x) = 0, f (·): RN+1 → Rn, where the input voltage is assumed to be a variable, are analyzed by the predicator-corrector algorithm where the arc-length of the solution curve in n + 1-dimensional space is the parameter. However, it is not clear that this method is practical for large-scale circuits. In this paper, we extend the Ushida-Chua method from a practical method standpoint and demonstrate that the multivalued characteristic curves of large-scale circuits can easily be analyzed using general-purpose circuit simulators. In the proposed method, first, the solution curve in n + 1-dimensional space is projected into m + 1-dimensional space, where m ≤ n and the arc-length of this new curve is used as the parameter. Second, the relationship between the arc-length and the components of the curve is expressed by a function generator circuit, the solution-tracing circuit. Finally, transient analysis is performed using a general-purpose circuit simulator and the solution curve is traced. The effectiveness of this method is verified through several examples, including a bipolar analog IC with 296 nodes.

AB - The dc driving-point and transfer characteristics of nonlinear circuits are the multivalued curves that arise from the nature of the circuit. These curves cannot be analyzed by general-purpose circuit simulators. One known method for analyzing these kinds of characteristic curves is the backward differentiation formula (BDF) curve-tracing algorithm proposed by Ushida and Chua. In this method, the circuit equations f(x) = 0, f (·): RN+1 → Rn, where the input voltage is assumed to be a variable, are analyzed by the predicator-corrector algorithm where the arc-length of the solution curve in n + 1-dimensional space is the parameter. However, it is not clear that this method is practical for large-scale circuits. In this paper, we extend the Ushida-Chua method from a practical method standpoint and demonstrate that the multivalued characteristic curves of large-scale circuits can easily be analyzed using general-purpose circuit simulators. In the proposed method, first, the solution curve in n + 1-dimensional space is projected into m + 1-dimensional space, where m ≤ n and the arc-length of this new curve is used as the parameter. Second, the relationship between the arc-length and the components of the curve is expressed by a function generator circuit, the solution-tracing circuit. Finally, transient analysis is performed using a general-purpose circuit simulator and the solution curve is traced. The effectiveness of this method is verified through several examples, including a bipolar analog IC with 296 nodes.

UR - http://www.scopus.com/inward/record.url?scp=0026889952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026889952&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026889952

VL - 75

SP - 52

EP - 63

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 7

ER -