Self-resonant frequencies, standing waves, and impedance behavior of air-core helical solenoidal coil

Microwave theory should be used anytime the electrical length of a circuit is comparable with the wavelength of the electromagnetic signal. In this sense, an air-core single-layer solenoid is a critical component, in which this condition is very often attained and lumped element theory is not valid. Besides the electromagnetic analysis of the solenoid helix not be an easy task, for many cases of interest some assumptions and conditions simplify the analysis. In this paper it is shown that the air-core solenoid coil can be treated as a lossless transmission line, or more precisely, as a helical transmission line, and that its impedance behavior and self-resonant frequencies can be found with this theory. Also two new configurations are here presented: a coil with both sides open and a coil with both sides short-circuited. It is shown that, in both configurations, the coils have similar behavior and same resonant frequencies. Simulations and measurements are conducted to validate the presented theory.