Cascade Synthesis of Lumped and Distributed Networks by Means of the Minkowski Model of Lorentz Space

The Minkowski model of three-dimensional Lorentz space with its submodels of two-dimensional hyperbolic space, namely the Cayley-Klein model, the polar Poincaré model (the Smith Chart), and the rectangular Poincaré model (the Z-plane), can be used both constructively and as a guiding light in the analysis and synthesis of cascaded lumped and distributed two-port networks. The Minkowski model consists of a three-dimensional hyperboloid. Transformations through lossless two-ports correspond to Lorentz transformations which transform points on the hyperboloid into other points on the same surface. The transformations are all rotations. They are of three kinds, elliptic (ex: transmission line), parabolic (ex: series inductor), and hyperbolic (ex: transformer). The transformations lead to the introduction of a new network formalism based on angles (elliptic and hyperbolic) well suited for programming by means of pocket calculators.