A Spinor Model for Cascading Two-port Scattering Matrices In Conformal
Building on the work in , this paper shows how Conformal
Geometric Algebra (CGA) can be used to model an arbitrary two-port
scattering matrix as a rotation in four dimensional Minkowski space,
known as a spinor. This spinor model plays the role of the
wave-cascading matrix in conventional microwave network theory.
Techniques to translate two-port scattering matrix in and out of spinor
form are given. Once the translation is laid out, geometric
interpretations are given to the physical properties of reciprocity,
loss, and symmetry and some mathe- matical groups are identified.
Methods to decompose a network into various sub-networks, are given. An
example application of interpolating a 2-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.