Simulating circuits with impasse points

Abstract. In this paper circuits with impasse points, i.e. with jumps in their configuration space will be analyzed. These non-regularized circuits exhibit a fold in their configuration space, which can lead to difficulties during the simulation with standard circuit simulators like SPICE. The former developed geometric approach to simulate these circuits without regularization will be extended by a detailed discussion of which coordinate system has to be chosen. Furthermore, two new approaches for a numerically efficient calculation of the hit points will be shown.

[1]  Leon O. Chua,et al.  The effects of parasitic reactances on nonlinear networks , 1971 .

[2]  L. Chua Dynamic nonlinear networks: State-of-the-art , 1980 .

[3]  N. K. Rozov,et al.  Differential Equations with Small Parameters and Relaxation Oscillations , 1980 .

[4]  Leon O. Chua,et al.  Impasse points. Part II: Analytical aspects , 1989 .

[5]  An-Chang Deng,et al.  Impasse points. Part I: Numerical aspects , 1989 .

[6]  S. Reich On a geometrical interpretation of differential-algebraic equations , 1990 .

[7]  L. Watson Globally convergent homotopy algorithms for nonlinear systems of equations , 1990 .

[8]  Peter M. Asbeck,et al.  Analysis of heterojunction bipolar transistor/resonant tunneling diode logic for low-power and high-speed digital applications , 1993 .

[9]  Ljiljana Trajkovic,et al.  Parameter embedding methods for finding dc operating points: formulation and implementation , 1995 .

[10]  Gunther Reissig,et al.  Differential-algebraic equations and impasse points , 1996 .

[11]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[12]  Willy Govaerts,et al.  Cl_matcont: a continuation toolbox in Matlab , 2003, SAC '03.

[13]  Ricardo Riaza,et al.  Differential-Algebraic Systems: Analytical Aspects and Circuit Applications , 2008 .

[14]  W. Mathis,et al.  Geometric dynamics of nonlinear circuits and jump effects , 2011 .

[15]  Wolfgang Mathis,et al.  A numerical approach for nonlinear dynamical circuits with jumps , 2011, 2011 20th European Conference on Circuit Theory and Design (ECCTD).

[16]  R. E. White,et al.  A new homotopy for seeking all real roots of a nonlinear equation , 2011, Comput. Chem. Eng..

[17]  W. Mathis,et al.  Geometrical interpretation of jump phenomena in nonlinear dynamical circuits , 2011, Proceedings of the Joint INDS'11 & ISTET'11.

[18]  W. Mathis,et al.  On the Analysis of Series Connected Resonant Tunneling Diodes , 2012 .

[19]  Tina Thiessen,et al.  Transient solution of fast switching systems without regularization , 2012, 2012 IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS).

[20]  Wolfgang Mathis,et al.  Fast Switching Behavior in Nonlinear Electronic Circuits: A Geometric Approach , 2013, Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering.