中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (6): 97-102.

• 研究论文 • 上一篇    下一篇

非线性振荡电路的一种新算法

黄偲   

  1. 中国能源建设集团广东省电力设计研究院网络信息部,广东 广州 510663
  • 收稿日期:2016-04-30 出版日期:2016-11-25 发布日期:2016-11-25
  • 通讯作者: 黄偲(1983年生),男;研究方向:电子通信;Email:lendies@163.com

A new computation method of the nonlinear oscillation circuits

HUANG Cai   

  1. Network & Telecommunication Division, China Energy Construction Group Guangdong Electric Power Design & Research Institute,Guangzhou 510663, China
  • Received:2016-04-30 Online:2016-11-25 Published:2016-11-25

摘要:

提出非线性振荡电路的一种新的计算方法,称之为响应频率迭代法。引进相位角作为自变函数,将非线性振荡电路的波形泛函表示成自变函数的余弦泛函,电路的响应频率即为自变函数对自变量的一阶导数,将电路非线性状态方程的求解归结为响应频率的确定,并用迭代法近似计算之;利用响应频率与相位角的微分关系,计算出反变换即时间与相位角的近似关系式,从而将非线性振荡电路的波形泛函随时间变化而变化的关系表示为以自变函数为参量的参数形式,突破摄动法的激励参数远小于1(即弱非线性)的限制,适用于强、弱非线性电路。具体分析了一类三极管振荡电路,取激励参数为0.8和1,经二次频率迭代,计算结果与数值积分法吻合良好,但摄动法已失效。

关键词: 新算法, 非线性振荡电路, 非线性状态方程, 波形泛函, 响应频率迭代法

Abstract:

A new calculation method of nonlinear oscillation circuit is presented and called as the response frequency alternation method. The phase angle is introduced as the independent functions. The waveform functional of the nonlinear oscillation circuit is shown as the cosine functional of the independent functions. The first derivative of the independent functions about the independent variable is meant by the response frequency of the circuit. The solution of the nonlinear state equation for the circuit is summed the determining of the response frequency for the circuit, and computed it with the alternation method. Using the differential relation of the response frequency between the phase angles, the approximate expression of the inverse transform for the independent variable is computed, and the expression of the variation for the state variable of the nonlinear oscillation circuit following with the time is shown as the parameter form of the independent functions. It is broken through the limit of the excitation parameters much less than 1 (i.e. weakly nonlinear) of the perturbation method and suitable for the strongly and weakly nonlinear circuit. A three-electrode oscillation circuit is discussed specifically with the excitation parameters of the 0.8 and 1, the calculation results are in good agreement with the numerical integral method after two times of iterative frequency, but the perturbation method is invalid.

Key words: new computation method, nonlinear oscillation circuit, nonlinear state equation, waveform functional, response frequency alternation method

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