A closed-form integral model of spiral inductor using the Kramers-Kronig relations

In this letter, a closed-form integral model is presented for the rectangular micromachined spiral inductor. The Kramers-Kronig relations provide an elegant theory to describe the inductor behavior without having complicated geometric analysis. Simulation and measurement results validate that the model can provide satisfactory prediction to the inductance of on-chip freely-suspended spiral inductors. Meanwhile, unlike conventional Greenhouse-based formulations, the self-resonant frequency of inductor can be predicted using the integral model.