Op-amp relocation: A topological active network synthesis

Methods are presented for generating ideal op-amp circuits by relocating the op-amp in a given realization. Formulas are developed for determining, by inspection, the minimum number of realizations which have identical network equations or which have the same characteristic equation. It is shown that the basic 3-op-amp Mikhael-Bhattacharyya RC active filter has at least 95 other possible 3-op-amp realizations, all with the same transfer function. There are also 767 other possible 3-opamp realizations and 6000 possible 4-op-amp realizations all with the same characteristic equation. Tables of other generated 2- and 3-op-amp active filters are also given. Op-amp relocation is used to reduce the errors in center frequency,
Q
and passband gain, attributed to the nonideal opamp in the Akerberg-Mossberg bandpass filter.