ABSTRACT
Superconducting self-resonant spiral structures are of current interest for applications both in metamaterials and as probe coils for nuclear magnetic resonance (NMR) 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 a linear though not necessarily harmonic dependence on the mode number. The effect of a thick substrate can be approximated by an effective dielectric constant. But when the thickness is less than 20% of the spiral trace width (router - rinner) this approximation is no longer accurate. We have developed a simple empirical formula to predict the higher modes.
ABSTRACT
This work presents an empirical formula to accurately determine the frequencies of the fundamental and higher order resonances of an Archimedean spiral in a uniform dielectric medium in the absence of a ground plane. The formula is based on method-of-moments simulations which have been experimentally validated. This empirical formula is widely applicable to a broad range of spirals from thin-ring to disk-shaped (ratio of inner to outer radii 0 to 1), with 10 or more turns.
