Analysis of quality factor of annular core inductors

This paper summarizes and formally presents methods in use during the past 25 years at Bell Telephone Laboratories for the design of high-quality inductors. The quality factor, Q, of annular core inductors can be maximized by adapting core dimensions, winding details, etc., to the specific properties of the magnetic core. Commercial core materials include 2–81 Mo-permalloy powder and carbonyl iron powder. Analysis of the relationships of dimensions and magnetic properties is given first in terms of the bare fundamentals of dc copper resistance and magnetic core losses. The paper then derives expressions for, and considers the effects of, additional losses due to the windings, such as eddy currents in the copper, dielectric losses and the contribution to effective resistance due to parallel distributed capacitance. Finally, a graph is supplied showing the maximum Q and optimum frequency for many commercial sizes of annular cores.