Quality Factor Optimization of Single-Layer Air Core Toroidal Inductors

The paper proposes a design methodology aimed at maximizing the quality factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(Q_{L})$</tex> of single-layer foil-wire based air-core toroidal inductors having a specified outer radius and a target inductance value at a given operating frequency. The optimal ratio between the inner and outer radius of the toroid is analytically obtained, following which the optimal value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(Q_{L})$</tex> is shown to be proportional to the outer radius of the toroid. A comprehensive design methodology is then proposed for the optimized toroidal inductor. The proposed optimization is experimentally validated using three toroidal inductors, all having the same outer radius but different inner radii. It is demonstrated that the inductor with the optimal design exhibits the highest quality factor.