Transfer function of multi-stage active filters: a solution based on Pascal's triangle and a general expression

Abstract

A method is proposed to simplify analytical computations of the transfer function for electrical circuit filters, which are made from repetitive identical stages. A method based on the construction of Pascal's triangle is introduced and then a general solution from two initial conditions is provided for the repetitive identical stage. The present analysis is mainly of educational value, but the computing method is also found to be useful in ladder network designs, in applied systems such as transmission line networks and most likely in biological systems involving repetitive units.