The quasi-distributed gap technique for planar inductors: design guidelines

The use of low-permeability magnetic materials to form a uniformly distributed gap can facilitate the design of low-AC resistance planar inductors. Alternatively, a quasi-distributed gap, which employs multiple small gaps to approximate a uniformly distributed gap, can effect the same result. Finite-element simulations are used to systematically analyze the design of quasi-distributed gap inductors. It is shown that a good approximation of a distributed gap is realized if the ratio of gap pitch to spacing between gap and conductor is less than four, or if the gap pitch is comparable to a skin depth or smaller. For a practical range of gap lengths, the gap length has little effect, but large gaps can reduce AC resistance. An analytical expression, which closely approximates the AC resistance factor for a wide range of designs, is developed.