Realization of a Constant Phase Difference

Abstract

This paper bears on the problem of splitting a signal into two parts of like amplitudes but different phases. Constant phase differences are utilized in such circuits as Hartley single sideband modulators. The networks considered here are pairs of constant‐resistance phase‐shifting networks connected in parallel at one end. The first part of the paper shows how to compute the best approximation to a constant phase difference obtainable over a prescribed frequency range with a network of prescribed complexity. The latter part shows how to design networks producing the best approximation.

Realization of Fractional Order Elements

“…Early Multicomponent FOE: In 1950, Darlington developed a method for determination of the best possible approximation and realization of a constant phase difference function, over a desired frequency band, using a pair of phase shifting networks (Darlington 1950). The phase shifters achieve the desired CP and number of all-pass sections determine the CP zone.…”

Broadband analog phase shifter based on multi-stage all-pass networks

“…In contrast, the bandwidth for the phase shift is quite narrow. To improve the bandwidth for phase shift, one may cascade multiple stages of all-pass phase shifters that are designed at different frequencies [3,4,6,7]. Based on this idea, a multi-stage all-pass phase shifter is simulated using the measured S parameters of the single-stage all-pass phase shifter presented in Section 3.…”

“…Although large phase shift can be obtained, the phase shift is however quite narrowband. Cascading multiple stages of all-pass networks has been proposed to provide a constant (equal-ripple) phase shift over a wide frequency range [3,4,6,7]. Nevertheless, the phase error reported in previous work is still large.…”

Complex Filters as as a Cascade of of Buffered Gingell Structures: Design from from Band-Stop Constraints

“…Sidney Darlington's paper explores how to approximate a constant phase difference over a given frequency range and how to design a network capable of producing that approximation [6]. The Hartley single sideband modulator uses this topology.…”

“…The Hartley single sideband modulator uses this topology. The method discussed in [6] outlines the construction of constant resistance phase-shifting networks connected in parallel.…”