Modeling and comparison of different micromachined three-dimensional inductors

3D inductors have been reported using micromachining technology. However, almost all studies focused on the solenoid type inductors. We present a complete way to analyze different 3D inductors. After decomposing the inductor into several current elements, the mutual inductances within them are presented. Although the solenoid type inductor usually has positive mutual inductances, the toroidal-meander type inductor still has a larger density of inductance in some conditions, especially with a thin intermediate layer. Besides, the latter shows better uniformity of current density, less resistance per unit length and higher quality factor.