Analysis of planar sandwich inductors by current images

Inductors with spiral windings sandwiched between top- and bottom-plane thick magnetic plates are investigated theoretically using the method of current images. Expressions are obtained for the inductances, and magnetic fields of these planar structures assuming infinite plane thicknesses. The dependence of the inductance on the permeability and the distances between the spiral windings and the top and bottom plates is studied by numerically evaluating the inductance expressions. It is shown that, except for some limiting cases, the inductance depends only on the net distance between the top and bottom magnetic plates and is independent of the position of the spiral windings within the gap. Furthermore, it is found that, in contrast to open planar structures, the sandwich inductor can yield large values of inductances with the enhancement over air-core values limited only by the permeability of the magnetic plates. Numerical evaluation of the formulas for magnetic fields both inside the magnetic plates and in the gap are used to calculate energy density variation in the device, to estimate lateral dimensions of these sandwich inductors, to discuss construction of multiple devices in a single-sandwich structure, and to discuss calculation of losses in the sandwich inductors