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

Ushida, Akio; Yamagami, Yoshihiro; Nishio, Yoshifumi; Kinouchi, I.; Inoue, Y.

doi:10.1109/43.986427

Cited by 63 publications

(46 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[5,7,24], which are potentially capable of finding multiple operating points using the PSP model need some preliminary manipulations or require specific user knowledge. These properties make them difficult to implement.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

See 1 more Smart Citation

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

Tadeusiewicz

Hałgas

2013

Circuits Syst Signal Process

View full text Add to dashboard Cite

This paper is devoted to the analysis of CMOS transistor circuits, fabricated in nanometer technology, having multiple DC operating points. The MOS transistors are characterised by the intricate PSP 103.1.1 model elected by the CMC as a standard. To find the operating points an approach is proposed based on a mathematical concept called a deflation. According to this concept the equations describing the circuit are deformed to avoid the solutions earlier determined and retain the remaining solutions. A new efficient deflation technique is developed and combined with the homotopy method and the discrete circuit equivalent of the Newton-Raphson nodal analysis. An algorithm has been worked out for finding multiple DC operating points of CMOS circuits encountered in practical applications. To illustrate the proposed approach three numerical examples are given.

show abstract

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…Recently several methods have been published which are capable of finding multiple DC operating points but do not guarantee finding all of them [5,7,10,13,15,[21][22][23][24]. They are less time consuming and do not require a high computing power.…”

mentioning

confidence: 99%

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

Tadeusiewicz

Hałgas

2013

Circuits Syst Signal Process

View full text Add to dashboard Cite

show abstract

“…The Newton homotopy has similar properties to the NR method, meaning that every homotopy path in the regular domain crosses at the same solution point. The Newton homotopy [11,18] is described by the following set of nonlinear equations:…”

Section: Newton Homotopymentioning

confidence: 99%

“…The solutions in DC are founded at λ = 1 on the solution curve, changing the start point g(x 0 ) we can trace the another solution curves. If the starting point is selected properly then it possible find all solutions of the system [18].…”

Section: Newton Homotopymentioning

confidence: 99%

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

Torres-Muñoz

Hernandez-Martinez

Vázquez-Leal

2015

Int. J. Appl. Comput. Math

View full text Add to dashboard Cite

The homotopy continuation methods are capable to locate multiple solutions of nonlinear systems of equations. In this paper is presented the path-following technique used to trace the homotopy trajectory. The spherical method is employed resizing the radius of the sphere at each iteration, the above based on the behavior of the radius of curvature. Also the Newton homotopy is applied in conjunction with the proposed methodology for tracing homotopy curve. To prove the usefulness of the proposed method is applied to three examples with different numbers of equations obtaining successful results.

show abstract

“…Many commonly used methods in this area are based on piecewise-linear approximations and computation techniques, e.g. [11,15,19,24,25].…”

mentioning

confidence: 99%

A Very Fast Method for the DC Analysis of Diode–Transistor Circuits

Tadeusiewicz

Kuczyński

2012

Circuits Syst Signal Process

View full text Add to dashboard Cite

The paper offers a universal method for finding a unique or multiple DC operating points of nonlinear circuits. The developed method is based on the theory known as a linear complementarity problem (LCP) and the homotopy concept. It is a combination of Lemke's method for solving LCP and some variant of the homotopy method. To express the problem of finding DC operating points in terms of LCP, an appropriate piecewise-linear approximation of diode characteristic is proposed. Although the method does not guarantee finding all the DC operating points, usually it finds them. The method is very fast and remarkably efficient. Numerical examples, including practical BJT and CMOS circuits having a unique or multiple DC operating points are given.

show abstract

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

Cited by 63 publications

References 44 publications

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

A Very Fast Method for the DC Analysis of Diode–Transistor Circuits

Contact Info

Product

Resources

About