Optimal design of miniaturized thin-film helical resonators

This paper investigates the optimal miniaturization of a helical resonator, which is in the form of a two turn helix. We theoretically demonstrate that its outmost dimension can be reduced to below 1% of the free space wavelength at resonance. Maximum miniaturization is achieved at an optimal metallic fill ratio of around 0.2 independent of diameter. Simulation and experimental results were used to validate the theoretical model and explore the miniaturization level achievable. The broadside coupled split ring resonators have the same optimal properties, but for identically sized resonator the helical design provides a factor of 2 greater miniaturization.