A number of articles and patents dealing with the properties and design of phase splitting networks, particularly in conjunction with single sideband modulators, have been published in the last few years. However, all of them have been restricted either to particular methods of design or to a particular number of design parameters. The present paper gives the results of a general investigation of phase splitting networks, dealing separately with network analysis, network synthesis and performance curve approximation problems. For the most important types of curve approximation, Taylor and Tchebycheff approximations, explicit formulas for any number of design parameters and for any required closeness of approximation are stated. Alternatives to the classical all-pass lattice network are given, and dissipation compensated phase shift networks are developed. In this way, clear and comparatively simple design instructions for simple as well as for difficult specifications for phase splitting networks are obtained. Furthermore, it is believed that some of the theoretical results obtained and methods developed, e.g., the Taylor and Tchebycheff approximations, the method of obtaining dissipation compensation, one of the methods of network synthesis, and the representation of approximating curves as iterated functions of two variables, with fractional index of iteration, are novel and of general theoretical interest.