10. Analytical Periodic Motions for a First-Order Nonlinear Circuit System Under Different Excitations

In this chapter, the generalized harmonic method is used to obtain the analytical solutions of first-order nonlinear circuits under different excitations. At first, the direct current, harmonic amplitude and harmonic phase are obtained under different excitation frequencies, with the change of excitation amplitude in finite Fourier series. Then, the stability and bifurcation of the nonlinear system under different excitation forces are studied by the eigenvalues of the system matrix. Further, the spectrums and waveforms are compared with the results obtained from the numerical model, the circuit simulation model and the circuit. The results show that the waveforms and spectrums obtained from numerical model are in agreement well with those of circuit simulation model. However, there exist slight errors in both waveform and spectrum between the two models and the circuit, due to the nonlinear properties of the elements in the circuit and intrinsic voltage parameters of the chips. As a conclusion, the generalized harmonic balance method could accurately describe the output waveforms, amplitude and phase of nonlinear circuits. Moreover, the method can provide theoretical support for precise design of nonlinear circuits.