非线性电路的插值迭代计算法

本文提出一种新的迭代计算法──拉格朗日插值迭代计算法。借助于拉格朗日插值公式，先假设一个电流Ｉ０，可算得与假设电流Ｉ０相对应的非线性电阻上的电压Ｕ０，根据欧姆定津算得非线性电阻阻值，再结合节点电压方程，算得节点电压ＵＮ，然后再运用电路中的ＶＣＲ确定电流Ｉ１的数值，并与假设电流Ｉ０进行比较直至其误差在规定范围之内。此方法尤其适用于含有多个非线性电阻元件和受控源电路的分析和设计。计算方法简单，迭代次数少，精度较高。

A New Iterative Method for Nonlinear Circuit Computing

A new iterative method, Lagrangian iterative algorithm, is presented for nonlinear circuitcomputing in the paper.Assuming that a current through a nonlinear resistor is I0, by using Lagrangian interpolation formula the voltage on,h'is resistor U0. can be calculatthe voltage on thais resistor U0. can be callculated, Then by using Ohm'S law, resistance of this nonlinear resistor can also be calculated. Next, with the help of node voltage equation YNUN=IN, node voltage UN can be calculated. Finally, by using VCR in the .circuit, a current I1, is determined and it is compared withthe assumed value I0, to get an error. The process is repeated until the error is within the desired range.The method presented here is particularly suitable for analysing or designing the circuitthat containing several nonlinear resistors and controlled sources. Compared with other methods. the method is simpler, needs less computing time and has higher precision.