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.