Numerical existence proof of five solutions for certain two-transistor circuit equations

Nakaya, Yusuke; Nishi, Tetsuo; Oishi, Shin’ichi; Claus, Martin

doi:10.1007/bf03186538

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Nonlinear effects occur and are applied in different applications (Gu et al , 2021; Peng et al , 2021; Xie et al , 2021). A special attribute of a nonlinear circuit, like a flip-flop, is the possibility of exhibiting multiple DC operating points (Nakaya et al , 2009). To determine all possible DC operating points, a nonlinear algebraic equation has to be solved.…”

Section: Introductionmentioning

confidence: 99%

DC operating points of nonlinear circuits and generalized Carleman linearization

Weber

Mathis²

2023

COMPEL

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Purpose The purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points. Design/methodology/approach A generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals. Findings It is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points. Originality/value A new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits.

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Section: Introductionmentioning

confidence: 99%

DC operating points of nonlinear circuits and generalized Carleman linearization

Weber

Mathis²

2023

COMPEL

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“…But [7] illustrate that some two-transistor have more than three operating points. Later in [8], five operating points of two-transistor circuits are verified based on numerical method. Therefore, simple and efficient verification methods that are guaranteed to find all operating points in even rather simple circuits do not exist.…”

Section: Introductionmentioning

confidence: 99%

Efficient analog verification against Trojan states using divide and contraction method

Chen

2014

2014 IEEE International Symposium on Circuits and Systems (ISCAS)

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Identifying and removing the undesired stable operating point (also called "Trojan state" in analog circuit) is one of the most important problems in circuit design. In this paper, an innovative divide and contraction verification method against Trojan states is proposed. Unlike the traditional methods to find all operating points, it only targets searching the voltage interval containing undesired stable operating point. Based on this, a monotonic divide and contraction algorithm (MDC) is proposed, it could verify the existence of Trojan state in high efficiency. Simulation results show that this method is effective and efficient in identifying Trojan states and verifying the efficacy of Trojan state Elimination (TSE) circuits which is commonly termed start-up circuits.

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Networks, multipoles and multiports

Reibiger

2013

2013 European Conference on Circuit Theory and Design (ECCTD)

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Numerical existence proof of five solutions for certain two-transistor circuit equations

Cited by 3 publications

References 9 publications

DC operating points of nonlinear circuits and generalized Carleman linearization

DC operating points of nonlinear circuits and generalized Carleman linearization

Efficient analog verification against Trojan states using divide and contraction method

Networks, multipoles and multiports

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