High-Q Resistance-Capacitance Ladder Phase-Shift Networks

Abstract

Resistance-capacitance ladder lowpass networks, to obtain a phase shift ( \phi ) of 180° between the input and the output, are examined. It is found that there exists a theoretical maximum value of Q , defined by \omega_0/2 |d\phi/d\omega| \omega = \omega_0 where \omega_0 is the frequency at which the phase shift is 180°. This theoretical limit can be approached in actual practice, but never reached. It is attempted to synthesize such networks having as high a Q as possible. In addition, the resulting network possesses the property that the open-circuit input impedance and the short-circuit output admittance are simultaneously maximized. A transformation enables one to get the corresponding highpass structure from the lowpass.