High-Q Resistance-Capacitance Ladder Phase-Shift Networks

Resistance-capacitance ladder lowpass networks, to obtain a phase shift (φ) of 180° between the input and the output, are examined. It is found that there exists a theoretical maximum value ofQ, defined byω_0/2 |dφ/dω| ω = ω_0whereω_0is 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 aQas 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.