DocumentCode :
1315134
Title :
A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits
Author :
Bonet-Dalmau, Jordi ; Pala-Schönwälder, Pere
Author_Institution :
Dept. of Signal Theory & Commun., Univ. Politecnica de Catalunya, Barcelona, Spain
Volume :
47
Issue :
2
fYear :
2000
fDate :
2/1/2000 12:00:00 AM
Firstpage :
231
Lastpage :
236
Abstract :
We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits. An efficient scheme to build the Jacobian matrix with exact partial derivatives with respect to the oscillation period and with respect to the samples of the unknowns is described. Without any modification in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua´s circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations
Keywords :
Chua´s circuit; Jacobian matrices; bifurcation; circuit stability; discrete time systems; distributed parameter networks; nonlinear network analysis; time-domain analysis; Jacobian matrix; autonomous circuits; discrete-time approach; discretization; distributed nonlinear autonomous circuits; exact partial derivatives; generic nonlinear elements; nonlinear algebraic formulation; oscillation period; period-doubling bifurcations; periodic solutions; stability analysis; steady-state analysis; time domain; time-delayed Chua´s circuit; transmission lines; Bifurcation; Circuit stability; Delay; Distributed parameter circuits; Laplace equations; Nonlinear equations; Polynomials; Stability analysis; Steady-state; Transmission line theory;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7122
Type :
jour
DOI :
10.1109/81.828576
Filename :
828576
Link To Document :
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