Effects of Dielectric Substrates and Ground Planes on Resonance Frequency of Archimedean Spirals

Superconducting self-resonant spiral structures are of current interest for applications both in metamaterials and as probe coils for nuclear magnetic resonance spectroscopy for high-sensitivity chemical analysis. Accurate spiral models are available in the literature for behavior of a spiral below and up to self-resonance. However, knowledge of the higher modes is also important. We present the relationships between the spiral parameters and the multiple mode frequencies of single-sided spirals on dielectric substrates as modeled by method of moments simulation. In the absence of a ground plane, we find that the mode frequency has linear, although not necessarily harmonic, dependence on the mode number. The effect of a thick substrate can be approximated by an effective dielectric constant. However, when the thickness is less than 20% of the spiral trace width (r outer - r inner ), this approximation is no longer accurate. We have developed a simple empirical formula to predict the higher modes.