RC active synthesis procedure for polynomial filters

The design procedure presented in the paper allows active RC realisation of transfer functions of the general type H/a0+a1+a2x2+¿+anxn where x = p, the complex transform frequency variable, or its reciprocal 1/p. The fundamental idea is to consider the required network as a matrix upon which the desired transfer function imposes certain constraints. The passive-RCnetwork-component values are defined by the matrix elements, which, in turn are derived from the roots of the approximation polynomial. The active devices used in this procedure are nonideal low-gain amplifiers, the precise specifications of which are obtained from the matrix in exactly the same way as the passive component values. Although an understanding of node and mesh matrix analysis is required for the theoretical part of the paper, a working knowledge of the actual synthesis procedures can be obtained from the fifth-order design example which runs parallel with the theory throughout.