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A. Bezzola, P. Brunet, and S. Yuan, "Variable Fractional Order Analysis of Loudspeaker Transducers: Theory, Simulations, Measurements, and Synthesis," Paper 9839, (2017 October.). doi: A. Bezzola, P. Brunet, and S. Yuan, "Variable Fractional Order Analysis of Loudspeaker Transducers: Theory, Simulations, Measurements, and Synthesis," Paper 9839, (2017 October.). doi:
Abstract: 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.

@article{bezzola2017variable,
author={bezzola, andri and brunet, pascal and yuan, shenli},
journal={journal of the audio engineering society},
title={variable fractional order analysis of loudspeaker transducers: theory, simulations, measurements, and synthesis},
year={2017},
volume={},
number={},
pages={},
doi={},
month={october},} @article{bezzola2017variable,
author={bezzola, andri and brunet, pascal and yuan, shenli},
journal={journal of the audio engineering society},
title={variable fractional order analysis of loudspeaker transducers: theory, simulations, measurements, and synthesis},
year={2017},
volume={},
number={},
pages={},
doi={},
month={october},
abstract={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.},}

TY - paper
TI - Variable Fractional Order Analysis of Loudspeaker Transducers: Theory, Simulations, Measurements, and Synthesis
SP - EP -
AU - Bezzola, Andri
AU - Brunet, Pascal
AU - Yuan, Shenli
PY - 2017
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - October 2017 TY - paper
TI - Variable Fractional Order Analysis of Loudspeaker Transducers: Theory, Simulations, Measurements, and Synthesis
SP - EP -
AU - Bezzola, Andri
AU - Brunet, Pascal
AU - Yuan, Shenli
PY - 2017
JO - Journal of the Audio Engineering Society
IS -
VO -
VL -
Y1 - October 2017
AB - 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.