A Simple and Accurate Analysis of Conductivity Loss in Millimeter-Wave Helical Slow-Wave Structures

Electromagnetic field analysis of a helix slow-wave structure was carried out and a closed form expression was derived for the inductance per unit length of the transmission-line equivalent circuit of the structure, taking into account the actual helix tape dimensions and surface current on the helix over the actual metallic area of the tape. The expression of the inductance per unit length, thus obtained, was used for estimating the increment in the inductance per unit length caused due to penetration of the magnetic flux into the conducting surfaces following Wheeler’s incremental inductance rule, which was subsequently interpreted for the attenuation constant of the propagating structure. The analysis was computationally simple and accurate, and accrues the accuracy of 3D electromagnetic analysis by allowing the use of dispersion characteristics obtainable from any standard electromagnetic modeling. The approach was benchmarked against measurement for two practical structures, and excellent agreement was observed. The analysis was subsequently applied to demonstrate the effects of conductivity on the attenuation constant of a typical broadband millimeter-wave helical slow-wave structure with respect to helix materials and copper plating on the helix, surface finish of the helix, dielectric loading effect and effect of high temperature operation – a comparative study of various such aspects are covered.