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Using the method of current images, a simple formula is derived that describes the enhancement effect of a thick magnetic substrate of permeability mu on the inductance of planar inductors. It is shown that a maximum of 100% enhancement of the inductance over the corresponding air-core value can be obtained. This occurs in the limit mu >>1, in which case the inductance becomes independent of mu . Previous and new experimental data as well as a finite-element result are found to be in very good agreement with the theoretical result.>
Roshen et al. (1988) studied this question.
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