  Planar spirals offer a highly scalable geometry appropriate for wireless
power transfer via strongly coupled inductive resonators. We numerically derive
a set of geometric scale and material independent coupling terms, and analyze a
simple model to identify design considerations for a variety of different
materials. We use our model to fabricate integrated planar resonators of
handheld sizes, and optimize them to achieve high Q factors, comparable to much
larger systems, and strong coupling over significant distances with
approximately constant efficiency.
