The high frequency operation of magnetic components, in applications such as filters, makes them ideal candidates for thick him technology along with resistors and capacitors. This in turn leads to distinct advantages over labor intensive wire wound components: improved reliability, repeatability, accuracy and consequential cost reductions. This paper establishes a new set of formulas for the self and mutual impedances of planar coils on ferromagnetic substrates. A planar coil in air is a special case of the generalized formulas. The formulas are derived directly from Maxwell's equations and therefore serve as a useful yardstick for simpler approximations. The formulas take full account of the current density distribution in the coil cross-section and the eddy current losses in the substrate. Experimental and calculated impedances up to 100 MHz are presented for a four layer device with three turns per layer which is 150 mu m thick and 40 mm(2) in area.