压控电压源2n阶单位增益巴特沃斯低通滤波器优化设计

Optimal Design of 2nth-Order Voltage-Controlled Voltage Source Unit Gain Butterworth Low-Pass Filter

在分析滤波器误差等值曲线的基础上,提出一个优化设计2n阶压控电压源(VCVS)单位增益巴特沃斯f0Hz低通滤波器的方法:先将2n阶低通分解为n个二阶低通,对第i个低通,若对应多项式的一次项系数为αi,则选取两个电容C1i和C2i,使C2i/C1i为0.25α2i,取两相同电阻R1i和R2i为1/παif0C1i.显然此方法具有方便和低成本的优势.采用Multisim10仿真和实际电路测试可知该方法还具有最稳定的优势.经分析还发现不同位置的C和R的精度对滤波器特性的影响是不同的,可对各元件精度做合理选择,以便在保证质量的前提下降低成本.

Reports a method of design 2nth-order Voltage-controlled Voltage Source（VCVS） low-pass filter,based on analyzing the error isogram by MathCAD,the paper put forward the optimal design plan of 2nth-order VCVS unit-gain Butterworth f0 Hz low-pass filter：firstly,decompose 2nth-order filter into n 2nd-order filters.For the ith one,if monomial coefficient of the polynomial expression is αi,select two capacitances C1i and C2i,making C2i/C1i 0.25α2i,and then calculate value of the two resistances by the same expression 1/παi f0 C1i.Obviously,the design plan has the advantages of convenience,low-cost.And with the aid of Monte Carlo analysis,parameter sweep analysis and real circuit experiment the design plan has also been verified its advantage of stability.In addition,analysises also shows different C,R have different influence on the filter features.