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仅含两个储能元件的双二阶电路(Biquad Circuits)足以实现各种滤波器[5],本文把它们归纳为L—R—C、C—R—C及L—R—L三类,从降低敏感度S_x~p出发,使用四端口线性电阻网络G的直流参数对其进行了分析、设计。研究结果表明:传递函数H(S)和敏感度S_x~p可用G的7个直流四端口参数准确表示,同时把对H(s)的设计转化成对G的设计,而后者十分容易;当网络的两个等效时间常数相等时,S_x~p取得最小值。文中给出了高通、低通、带通、带阻及全通滤波器的最低敏感度设计公式、步骤,这不但是关于ω、Q的一种最优设计,还免除了广泛寻优的麻烦。此外,这种四端口法还可用于某些四端口“黑箱”的分析之中。
Biquad Circuits, which has only two energy storage elements, is sufficient to implement a wide range of filters [5], which are grouped into three categories: L-R-C, C-R-C and L-R-L , Starting from the reduced sensitivity of S_x ~ p, using the four-port linear resistor network G of the DC parameters were analyzed and designed. The results show that the transfer function H (S) and the sensitivity S_x ~ p can be accurately expressed by the seven DC four-port parameters of G, meanwhile the design of H (s) can be transformed into the design of G, which is very easy. When the two equivalent time constants of the network are equal, S_x ~ p obtains the minimum value. The design formulas and steps of the lowest sensitivity for high-pass, low-pass, band-pass, band-stop and all-pass filters are given in this paper. This is not only an optimal design for ω, Q but also eliminates the need for extensive optimization . In addition, this four-port method can also be used for some four-port “black box” analysis.