Note on the Analysis and Synthesis of Active RC Filters

Transfer functions with complex poles, as well as zeros, are sometimes implemented by means of arrangements in which feedback is applied to the ground node of a passive network. Formulation of the voltage transfer function of the passive network
T(s) = P(s)/Q(s)
, in terms of admittance products, permits topological organization of the components of the network into subsets of numerator two-trees and denominator two-trees. All numerator two-trees are immune to feedback. Some denominator two-trees are susceptible to feedback, others are not. Identification of susceptible two-trees simplifies the mathematics; it also facilitates determination of alternative designs.