非线性网络广义频率响应函数统一递推分析法  

An unified recursive analyzed method of generalized frequency response functions of nonlinear network

作　　者：李义府[1] 谢宏[2] 何怡刚[2] 李文华[3] 

机构地区：[1]中南大学信息科学与工程学院,湖南长沙410083 [2]湖南大学电气与信息工程学院,湖南长沙410082 [3]第一军医大学生物医学工程系,广东广州510515

出　　处：《中南大学学报（自然科学版）》2004年第2期268-272,共5页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(59707002);湖南省自然科学基金资助项目(98JJY2038)

摘　　要：假设非线性动态网络解为Volterra级数响应,利用一般的网络分析法,对任一定常非线性动态网络列出其时域的标准动态方程。将该非线性微分方程分解成一个线性动态系统与一组非线性电源,利用线性微分方程求解方法求出线性系统的解,即一阶Volterra级数响应,再考虑系统非线性电源的作用和幂级数递推关系式,导出N阶(N≥2)Volterra响应的递推算式,即可得到非线性网络响应的Volterra级数形式。在此基础上,讨论了Volterra级数时域响应的频域变换,推导出对应的广义频率响应函数,即Volterra级数的频域核的递推算式,并给出了计算实例。Nonlinear dynamic networks are described by nonlinear differential equations which are not yet resolved by unified method. It is supposed that the solution of the equation is a Volterra Series in this paper. By using general network analytic, the standard dynamic equations in time domain for any nonlinear time-invariant dynamic network are given and the nonlinear differential equation can be divided into a linear dynamic subsystem and a group of nonlinear source. The solution of the subsystem which is 1st-order Volterra series response can be gotten by the method of solving linear differential equation. Further more the action of nonlinear source is considered and the recursive relation expression of power series is used, the recursive formulas of Nth (N≥2)order Volterra response is derived. Based on above the frequency transform of Volterra Series and the recursive formulas of corresponding generalized frequency response functions, i.e. transfer function of Volterra Series are derived.

关 键 词：非线性网络 广义频率响应函数 统一递推分析法 VOLTERRA级数 线性微分方程 线性电路 

分 类 号：TM131[电气工程—电工理论与新技术]