Determination of stopband characteristics of asymmetrically loaded helix slow wave structures with Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method

In this paper, a novel reformulated Auxiliary Functions of Generalized Scattering Matrix (AFGSM) method is presented for analyzing stopband characteristics of asymmetrically loaded helix Slow-Wave Structures (SWSs). In this method, the stopband problem of asymmetrically loaded helix SWS is reduced to the determination of zero transitions of J‾_-1 and R‾_-1 auxiliary functions in the vicinity of π-point frequency. Besides, Generalized Scattering Matrix (GSM) representations of a single turn of helix SWS are clearly expressed for different asymmetries which can occur with different ways due to angular offset of the rods, variations of support rod permittivity values and widths, angular offset of metal segments, variations in gap between helix to segment and segment width. In order to show the accuracy of the method, the proposed AFGSM method is verified with open literature. The applicability of the proposed method to analyze asymmetrically loaded helix SWS is quite simple and the method accurately determines Relative Stopband Bandwidths (RSBs) under different asymmetries.