Loudspeaker transducer models with fractional derivatives can accurately approximate the inductive part of the voice coil impedance of a transducer over a wide frequency band, while maintaining the number of fitting parameters to a minimum. Analytical solutions to Maxwell equations in infinite lossy coils can also be interpreted as fractional derivative models. However, they suggest that the fractional order a  cannot be a constant, but rather a function of frequency that takes on values between 1/2 and 1. This paper uses Finite Element (FEM) simulations to bridge the gap between the theoretical first-principles approach and lumped parameter models using fractional derivatives. The study explores the dependence of a on frequency for idealized infinite and finite cores as well as in four real loudspeaker transducers. To better match the measured impedances and frequency-dependent a values we propose to represent the voice coil impedance by a cascade of R-L sections.

Authors: Bezzola, Andri; Brunet, Pascal; Yuan, Shenli
Affiliations: Samsung Research America, Valencia, CA USA; Audio Group - Digital Media Solutions; Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, Stanford, CA, USA(See document for exact affiliation information.)
AES Convention: 143 (October 2017) Paper Number: 9839
Publication Date: October 8, 2017
Subject: Transducers—Part 3

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