On the definition of the Generalized Scattering Matrix for a lossless radial line

In this paper the Generalized Scattering Matrix for a radial line (rGSM) is defined. The main problem lies in the fact that, for a radial line, a unique characteristic impedance cannot be defined, since forward waves "see" an enlarging waveguide, while regressive waves a reducing one. Hence, two different impedances are defined and the usual normalization based on $sqrt{Z_0}$, valid for uniform lines, cannot be applied. An equivalent network, representing the transformation between voltages/currents and scattering amplitudes, is introduced. The transformers included in this circuit represent the normalization of electric quantities. The transformer ratios influence the properties of the rGSM, and this will be discussed at length. The rGSM is then applied to the analysis of a linear taper and the results are compared with those obtained with Generalized Telegraphists Equations. Finally, a double linear taper has been realized and the experimental and theoretical results, obtained with rGSM, are compared, showing a very good agreement in a wide band.