Realization of a Constant Phase Difference

P E R E N N I A L problem is that of designing a circuit to split a signal into two parts which are the same in amplitude but which differ in phase by a constant amount. A 90-degree phase difference is needed, for example, in the single sideband modulation system due to R. V. L. Hartley. 1 It is well known that it is not possible to obtain exactly equal amplitudes and exactly constant phase differences at all frequencies except in the trivial special case of a 180-degree phase difference. Various methods have been devised, however, for approximating these characteristics over finite frequency ranges. The most obvious method is to use a pair of constant resistance phase shifting sections in parallel at one end and with separate terminations at the other end 2 as indicated in Fig. 1. This paper is devoted to the problem of obtaining approximately constant phase differences under the specific assumption that pairs of constant resistance phase shifting networks are to be used. The paper has been written with two objects in mind. The first is the development of a method for determining the best approximation to a constant phase difference which can be obtained over a prescribed frequency range with a pair of phase shifting networks of a prescribed total complexity. The second object is the description of a straightforward design procedure by means of which the networks can be designed to give this best possible approximation. The problem under consideration is typical of those usually described as problems in network synthesis.