非线性RLC电路的频响特性与稳定性分析

摘要

针对非线性 RLC电路的频响特性和周期解稳定性等问题，建立了电感非线性 RLC串联电路的动力学方程。利用谐波平衡法，导出了电感非线性 RLC 串联电路的频率响应方程，研究了频率响应特性曲线的跳跃和滞后现象及其不产生谐振现象的条件；分析了该电路周期解的稳定性，得出了稳定区和不稳定区的分界线方程；讨论了非线性因素的影响，得出了忽略 RLC 串联电路的电感非线性因素的条件。%A-nonlinear-dynamical-equation-of-the-RLC-series-circuit-with-inductance-nonlinearity-is-established.-The-frequency-response-equation-of-the-RLC-series-circuit-with-inductance-nonlinearity-is-derived,-and-the-jumping-and-hysteresis-of-frequency-response-characteristics-curve-are-studied,-as-well-as-the-condition-under-which-the-resonance-phenomenon-does-not-emerge.-The-stability-of-periodic-solution-of-this-circuit-is-analyzed-by-using-the-method-of-harmonic-balance,-and-the-boundary-equation-of-steady-region-and-instability-region-is-obtained.-The-influence-of-nonlinear-factors-on-the-RLC-series-circuit-is-discussed.-The-condition-of-ignoring-inductance-nonlinear-factors-on-the-RLC-series-circuit-is-acquired.