A Homotopy Continuation Approach for Testing a Basic Analog Circuit

@article{VzquezLeal2013AHC,
  title={A Homotopy Continuation Approach for Testing a Basic Analog Circuit},
  author={H{\'e}ctor V{\'a}zquez-Leal and Arturo Sarmiento-Reyes and Uriel Filobello-Ni{\~n}o and Yasir Khan and A. Herrera-May and Roberto Casta{\~n}eda-Sheissa and V{\'i}ctor Manuel Jim{\'e}nez-Fern{\'a}ndez and M. Vargas-Dorame and Jesus Sanchez-Orea},
  journal={British Journal of Mathematics \& Computer Science},
  year={2013},
  volume={3},
  pages={226-240}
}
The increase of complexity on integrated circuits has al so raised the demand for new testing methodologies capable to detect functional failures within circuits before they reach the market. Hence, this work proposes to explore the use of homotopy a s a tool for testing a basic analog circuit. The homotopy path is influenced by nonlinearities f rom the equilibrium equation of the circuit; this situation can be used to infer faults by det ecting changes on the homotopy path. The concept was… 

Figures and Tables from this paper

Homotopy-based direct current analysis with formal stop criterion
TLDR
A new double bounded homotopy (DBH) is proposed as a tool to find multiple OP of nonlinear circuits with a reliable mathematical stop criterion based on its property of forming closed trajectories to result in a better performance by the proposed HCM.
PyAMS: A New Software for Modeling Analog Elements and Circuit Simulations
TLDR
The main objective of this software is to simplify the modeling of analog elements and circuits by using the python language to describe design schematics involving libraries, packages, and symbols.
Symbolic Analysis and Reordering of Nonlinear Circuit's Equations in Order to Accelerate Homotopy Simulation
In this work a symbolic study will be performed to establish the nonlinearity degree of nodal equations result of the MNA analysis performed
Improved spherical continuation algorithm with application to the double-bounded homotopy (DBH)
The homotopy continuation methods are useful tools for finding multiple solutions of nonlinear problems. An important issue of this kind of method is the correct implementation of the path-following
Multiple solutions for steady differential equations via hyperspherical path-tracking of homotopy curves
Abstract A multiple solutions finder method for steady Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) is designed combining the classical finite differences

References

SHOWING 1-10 OF 72 REFERENCES
Homotopy method with a formal stop criterion applied to circuit simulation
TLDR
This work shows a new double bounded polynomial homotopy based on aPolynomial formulation with four solution lines separated by a fixed distance, which allows to establish a stop criterion for the simulation in DC.
Fault diagnosis of analog piecewise linear circuits based on homotopy
TLDR
A verification method of diagnosis of analog piecewise linear circuits based on the homotopy approach that gives the possibility of fault localization as well as fault identification.
Artificial parameter homotopy methods for the DC operating point problem
TLDR
The application of globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation is discussed and the theoretical claims of global convergence for such methods are substantiated.
Passivity and no-gain properties establish global convergence of a homotopy method for DC operating points
Finding the DC operating points of transistor circuits is an important task in circuit simulation. The problem is equivalent to solving sets of nonlinear algebraic equations describing transistor
Homotopy techniques for obtaining a DC solution of large-scale MOS circuits
TLDR
A new technique for obtaining a DC operating point of large, hard-to-solve MOS circuits is reported, relying on the provable global convergence of arclength continuation and using a novel method for embedding the continuation parameter into MOS devices.
A fixed-point homotopy method for solving modified nodal equations
Recently, the application of homotopy methods to practical circuit simulation has been remarkably developed, and bipolar analog integrated circuits with more than 10 000 elements are now solved
Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods
  • J. Roychowdhury, R. Melville
  • Mathematics, Computer Science
    IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
  • 2006
TLDR
This paper describes a robust homotopy technique that is effective for solving large metal-oxide-semiconductor (MOS)-based mixed-signal circuits and demonstrates how certain common circuit structures involving turning-point nesting can lead to extreme inefficiency, or failure, of conventional probability-one Homotopy methods.
Constructive homotopy methods for finding all or multiple DC operating points of nonlinear circuits and systems
  • Jaewook Lee, H. Chiang
  • Mathematics, Computer Science
    2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353)
  • 2000
TLDR
A new systematic method to explicitly construct a starting point for each homotopy path is developed and does not require the difficult task of finding a good initial guess and is applicable to general nonlinear circuits and systems.
A novel algorithm that finds multiple operating points of nonlinear circuits automatically
  • L. Goldgeisser, Michael M. Green
  • Mathematics
    ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187)
  • 1998
The use of continuation methods has been shown to be more effective than standard Newton-Raphson-based methods in finding the operating point(s) of circuits with convergence problems. In this paper a
Powering Multiparameter Homotopy-Based Simulation with a Fast Path-Following Technique
TLDR
This work shows how the hypersPhere technique can be adapted and applied to trace a multiparameter homotopy, and presents a path-following technique based on circles (evolved from hypersphere), which is faster, and simpler to be implemented than hyperspheres technique.
...
1
2
3
4
5
...