Closed-Form Design Formulas for the Equivalent Circuit Characterization of Ferrite Inductors

Miniature inductors, consisting of thin-wire solenoidal or toroidal coils wound on a high-permeability soft ferrite core, find wide application in the filtering of noise or electromagnetic interference at RF. An understanding of the high-frequency parasitic and packaging effects of the inductor, such as stray capacitance, magnetic losses, self-resonance, etc., can be gained from an equivalent circuit characterization of the inductor. In this paper, we present a rigorous experimental method to fully characterize the RF behavior of ferrite inductors. The equivalent circuit parameters of the inductor, namely, series inductance, loss resistance, and stray capacitance, as well as the effective permeability of the core, are extracted in closed form from an accurate measurement of the RF impedance, without recourse to cumbersome optimization procedures usually followed in equivalent circuit extraction from measured data. We derive design equations for the equivalent circuit elements based on the proposed measurement-based model, and rigorously validate the model using inductors wound on commercial toroidal and rod-type Ni-Zn ferrite cores.