A Spinor Model for Cascading Two-Port Networks in Conformal Geometric Algebra

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port network as a rotation in four dimensional Minkowski space, known as a spinor. This spinor representation is analogous to the scattering transfer matrix in conventional microwave network theory, but has a geometric interpretation. Just as the scattering transfer matrix is parameterized by scattering parameters, so is the spinor model constructed herein. (The direct geometric model of the scattering matrix itself is a different problem not discussed in this paper.) Techniques to translate from two-port scattering matrix data in and out of spinor form are given. Once the translation is laid out, geometric interpretations are proposed for the physical properties of reciprocity, loss, and symmetry and some mathematical groups are identified. Methods to decompose a network into various sub-networks, are given. An example application of interpolating a two-port network is provided, demonstrating an advantage of the spinor model. Since rotations in four dimensional Minkowski space are Lorentz transformations, this model opens up the field of network theory to physicists familiar with relativity, and vice versa. The results of this paper have been numerically tested for consistency using the open-source clifford python package [13].