Tape-helix transmission lines and helical coils have important applications in communication technology, signal measurement, pulse delay, pulse forming and antenna technology. In this paper, a set of fully dispersive propagation theory based on matrix method is firstly introduced to explain the propagation characteristics of travelling electromagnetic waves in multiple stages of helical Blumlein transmission lines with finite lengths. The different stages of helical transmission lines are filled with different propagation dielectrics, and the effects of dispersion and dielectrics on the propagation matrix and S-parameter matrix of the travelling waves are analyzed in detail. Relations of the exciting current waves in the series-connected helical Blumlein transmission lines are studied, and the dispersive transmission coefficients and reflection coefficients of electromagnetic waves at different dielectric ports are also initially analyzed. As an innovation, the proposed fully dispersive propagation theory which was demonstrated by simulation and experiments can substitute the non-propagating tape-helix dispersion theory and the non-dispersive telegraphers' equation to analyze the helical transmission lines.
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