Mixed-potential volume integral-equation approach for circular spiral inductors

The electromagnetic behavior of circular spiral inductors on layered substrates is analyzed by using the concentric ring approximation. The problem is formulated in terms of mixed-potential volume integral equations. The latter are semianalytically solved within the quasi-one-dimensional approximation. The result is a fast computationally efficient model, which takes into account substrate RF loss, as well as nonuniform current density distribution across inductor windings. The results are in good agreement with experimental data from various inductors on both low- and high-resistivity silicon substrates.