A Tunable Wire Loop Inductor based on Bistable Compliant Mechanism

By axially loading of a cylindrical wire we utilize the first order buckling mode to form the shape of a segment of a wire loop inductor. The shape of the deformed wire is expressed in analytical form and provides the basis for a semi-empirical formulation of the loop inductance. Combining several buckling segments and taking advantage of the snap-through behavior of such a segment, the shape of the wire loop in air and hence the loop inductance can be varied mechanically on purpose. The analytical model for the tunable inductance enables a design methodology for bistable compliant inductors. We present two designs of mechanically tuned inductors in the range from 20nH to 50nH. Furthermore the electromagnetic properties of the proposed innovative components are confirmed by method of moments numerical modeling based on quasi-static magnetic fields and by experiment. We finally show that the design process is applicable to regular plane polygonal inductors representing multi-stable compliant stages.