非线性 RLC 电路的新解法及数值仿真

摘要

A new solution and its numerical emulation for the nonlinear RLC circuit are given.The state variable of the circuit is expressed as the simple harmonic function of the phase angle.The determination for the first derivative of the phase angle about the time are used to solve the state equations.The relation of the time independent variable with the middle variable of the phase angle is shown as the integral for the reciprocal of the response frequency.The numerical values,including the phase portraits,the time-distance curve,the phase-distance curve,and the time-range curve,and the phase-range curve,and the range-frequency curve,and the phase-frequency curve and the response period,are computed.The re-sults are in good agreement with the numerical integral method.%给出一类非线性 RLC 电路的新解法及数值仿真：电路的状态变量表示为相位角简谐函数；电路状态方程的求解归结为相位角对时间的一阶导数的确定；时间自变量与中间变量相位角的关系由响应频率倒数的积分表示；从而算出电路的相轨线、时程曲线、相程曲线、时幅曲线、相幅曲线、幅频曲线、相频曲线和响应周期，数值仿真显示，结果与数值积分法吻合良好。