Thikness dependence investigation of the mutual inductance link in concentric planar transformers

Abstract

In this paper, we present a new analytic approach for the calculation of the mutual inductance between two concentric planar conductors. From this study, we aim to prove that coil thickness has a minor impact on mutual inductance value. This study will help to determine a simplified adapted expression of the induced voltage output at our electrodynamic microphone ends. This micromachined new sensor exploits the concentric transformer principle which relies on the use of two planar inductors: an outer fixed one and an inner suspended one. If the outer is biased, a mutual inductance link will be generated. This link strongly depends on inductors coil design geometry and the induced output voltage. The present work proves that for long conductors (large number of turns), coil thicknesses above 6μm will have no significant influence on mutual inductance values. This has been proven by an increase of only 0.01% if coil thickness reaches as high as 20 μm. Moreover, for thicknesses under 2μm, mutual inductance value is constant arround 7.2μH. This allows the use of much simpler expressions, with no thickness dependence, to evaluate mutual inductance values.