基于MATLAB的模拟电路传递函数的推导与化简

Derivation and simplification of transfer function of analog circuit based on MATLAB

提出了一种采用MATLAB算法来推导与化简电路传递函数的方法,并以一个在单位增益负反馈的条件下的二级CMOS运算放大器的热噪声传递函数为例说明了具体的过程。该方法首先是列出节点的小信号电压方程的线性方程组,然后是利用MATLAB的符号运算方法得到完整的热噪声传递函数,F(s)=N(s)/D(s),接着是对分子N(s)和分母D(s)的s的多项式进行整理。收集所有对同一s^n(n=0,1,2,…)次项有贡献的项,采用两种方法比较这些项的相对大小,保留贡献最大的项,扔掉其他贡献小的项。比较所得到的两个化简的传递函数发现,它们和完整的传递函数在数值上匹配度很好。

A method is proposed to derive and simplify transfer functions of analog circuits by using MATLAB algorithm.The full process is explained through the thermal noise transfer function of a two-stage CMOS amplifier circuit under the unit-gain feedback condition.In this method,a linear equation set for the small signal voltages at different circuit nodes are first listed and solved to obtain the full thermal noise transfer function F(s)=N(s)/D(s)through the MATLAB symbolic operation.Then the numerator polynomial N(s)and the denominator polynomial D(s)are ordered and simplified.All terms contributing to the same s^n(n=0,1,2,…)factor are collected and two methods are used to calculate their relative values.The simplified transfer function is got by only keeping the most important terms and throwing away other ones.Finally,it is found that two simplified transfer functions and the full one have almost the same numerical values.