一类非线性LC电路的分析与模拟

给出一类非线性LC电路的状态分析和数值模拟：将电容的电荷表示为相位角的简谐函数，电路的响应频率表示为相位角关于时间的变化率；以电路的响应频率为未知函数，对状态方程进行近似求解；算出时间随相位角变化的近似关系式；给出电路的相图、电容的电荷以及电感的磁通链随时间变化关系式及数值模拟，结果与数值积分法吻合良好。

Analysis and Simulation of a Nonlinear LC Circuit

Gives the state analysis and numerical simulations for a nonlinear LC circuit： the capacitor charge is expressed as the harmonic function of the phase angle, the response frequency of the circuit is shown as the rate for the phase angle about the time. With the response frequency as the unknown function, the state equation is solved approximately. The approximate expression for the time varies with the phase angle is computed. And then gives the numerical simulation of the phase portraits for the circuit and the relationship for the charge capacitor and the induc- tance flux chain changes with time. The results are in good agreement with the numerical inte- gral method.