Impedance formulas for planar magnetic structures with spiral windings

It is well established that magnetic components may be reduced in size by operating at high frequency. Miniaturization of magnetic components is ideally suited to microelectronics technologies such as thick films, which lend them to planar geometries. This paper describes new analytical models, which predict inductance- and frequency-dependent eddy-current losses in magnetic substrates. Prototype devices were fabricated by a thick-film process with four layers of conductors on a single ferrite substrate and in a sandwich configuration, consisting of conductors between ferrite slabs. The prototype devices were tested in the frequency range 10 kHz-100 MHz. The measurements confirm the validity of the analytical models. Simulation with finite-element analysis was employed to identify different sources of losses: eddy current losses in ferrite substrates; proximity effect losses in conductors; and dielectric losses