Abstract
Electromagnetic waves propagating through the electromagnetic fields of coaxial cables can be analyzed using Fourier series because they propagate at the velocity of light c at any angular frequency. The electromagnetic waves are characterized by steady-state responses and transient responses, which are known in circuit theory. The ztransform used in mathematical physics represents transient responses, which are not a stochastic process used in linear system theory. Electromagnetic waves are expressed by two functions, voltage and current. When the electromagnetic fields of coaxial cables are considered, electromagnetic waves can be converted into a single wave using an ideal transformer. The complex arithmetic expression of the single wave is Scattering matrix (S-matrix). However, S-matrices require that the internal resistance of the power supply and the load resistance be equal, and S-matrices are considered to eliminate the numerical value of the performance characteristics of electromagnetic waves with an angular frequency of nπ + π/2. From the above, we understand that the behavior of electromagnetic waves can be analyzed using “algebraic invariants,” which were studied mainly in the field of pure mathematics in the 19th century.
