VOLTAGE STEP-UP FILTERS NOT USING TRANSFORMERS

A network of resistors and capacitors is to serve as a filter for an arbitrary signal voltage f(t). It consists of twin parts connected in parallel across the input terminals. One part is a low pass ladder filter; the rungs of the ladder are capacitors, and the other branches are resistors. The twin part is connected to the input terminals in the opposite direction. The output signal is the voltage g(t) measured between the end nodes of the ladders. Kirchhoff's current law gives a differential equation relating f and (g - f). If F is the Fourier transform of f, then the transform of the differential equation is an algebraic equation relating the transforms F and (G - F). This equation shows that \G/F\ > 1. Then by Parseval's theorem the norm of f is greater than the norm of g. Thus there is a stepup; the norm of the output always exceeds the norm of the input. Such a filter is here termed an RCformer.