Experimental and analytical periodic motions in a first-order nonlinear circuit system

Abstract

In this paper, the analytical solution of a first-order nonlinear circuit is obtained through the generalized harmonic method. The analytical solutions of periodic motions are firstly expressed by finite Fourier series. Both the stability and bifurcations of the nonlinear system with a sinusoidal power-supply are studied by the eigenvalues of the system matrix. In order to verify the analytical solution, the researchers compared the spectrums and waveforms obtained from the analytical model, the simulation model and the circuit. The comparison of the spectrum shows the generalized harmonic balance method can describe the amplitude and phase of the nonlinear circuit more precisely. The comparison of the waveform indicates the output waveform from the simulation model have a good agreement with the results obtained from the analytical model. In the real circuit system, little errors on the output voltage amplitude and response speed maybe due to the nonlinear elements in the circuit and intrinsic voltage attenuation of the chips.