Accurate models for spiral resonators

Analytically-based circuit models for two types of spiral resonators, a single layer and a double layer spiral, are given. The models are suitable for various spiral and wire cross-sectional shapes. The double layer spiral is composed of two identical spirals of opposite winding in which the inner or outer leads may or may not be connected, such as through a via. For both types, the model can account for the effect of a dielectric slab. The advantage of these models to previous circuit models is shown through their comparison to experimental measurements and numerical simulations.