S-parameters approximation of coaxial impedance transformer tuning element

The paper investigates possibilities and limitations of polynomial approximation of scattering parameters of a high-power 2.45-GHz coaxial impedance transformer tuning element. The approximation is a basis for a simple and compact mathematical model of the three-stub coaxial tuner, intended for the use in automatic impedance matching devices. The input data are frequency responses of S₁₁ and S₂₁ for various settings of the sliding short. The approximation is a two-dimensional polynomial (in dependence on short position and frequency) of suitably modified S-parameters. Approximation with satisfactory accuracy can be achieved.