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A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits
Bonet Dalmau, Jordi; Palà Schönwälder, Pere; Miró Sans, Joan Maria
Universitat Politècnica de Catalunya. Departament d'Enginyeria Minera, Industrial i TIC; Universitat Politècnica de Catalunya. CIRCUIT - Grup de Recerca en Circuits i Sistemes de Comunicació
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.
Peer Reviewed
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació
Telecommunication
Bifurcation
Discrete time systems
Distributed parameter networks
Nonlinear network analysis
Circuit stability
Time-domain analysis
Jacobian matrices
Chua's circuit
Telecomunicació
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Institute of Electrical and Electronics Engineers (IEEE)
         

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