A discrete-time approach to the steady state analysis of distributed nonlinear autonomous circuits

We present a new method for the steady state analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the temporal discretization of the equations that describe the circuit, we obtain a nonlinear algebraic formulation where the unknowns to be determined 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. To illustrate the proposed technique, the time-delayed Chua's circuit is analyzed in its periodic zones.