Turning a loudspeaker into an active Helmholtz resonator: Underlying law, principle and design methodology

This paper is concerned with how to turn a moving-coil loudspeaker into an active Helmholtz resonator (AHR): that is, an active noise control loudspeaker used in conjunction with a microphone and a feedback controller to actively realize the Helmholtz resonator. The natural law of control is studied to justify that the AHR is an effective means for resonant noise control. The principle of duality is then applied to reveal that the AHR can be designed and analyzed in an analogous way to its vibration dual, i.e., the active dynamic absorber. A systematic design methodology is finally established, in consideration of the inherent loudspeaker dynamics. It is theoretically shown that a low, band, and high pass filter of second order are desirable control filters to construct a low-, mid-, and high-band AHR that are, respectively, for uses in the volume displacement, velocity, and acceleration drive frequency range of the loudspeaker used. Experimental work is also presented, in which a high-band AHR was constructed to absorb the broadband resonant noise of a long duct between about 165 Hz and 1.3 kHz, to illustrate the efficacy and to investigate the absorption mechanism of the AHR.