Electroacoustic absorbers II: implementation of a digital synthetic admittance for controlling the dynamics of electroacoustic absorbers

This paper discusses the implementation of a synthetic electrical admittance for controlling the dynamics of electroacoustic absorbers. Indeed, different basic control techniques are capable of varying the acoustic impedance of an electroacoustic transducer diaphragm, in view of achieving sound absorption. Among these techniques, one must consider the direct acoustic impedance control, based on acoustic feedbacks (pressure and velocity), and the straightforward shunt loudspeaker approach. Shunting the electric terminals of a loudspeaker with a resistive load will slightly modify the resonance quality factor of the electroacoustic absorber, by merely adding Joule losses, yielding enhanced narrow-band sound absorption. The extension of the resonance bandwidth requires then active circuits, as in acoustic feedback control. Lately, it has been demonstrated that feedback-based principles reveal formal analogies with electrical shunt approaches. Based on this observation, the design of electroacoustic absorbers can be performed through the design of active electric networks shunting the loudspeaker terminals, mimicking the behavior of acoustic feedbacks used in a direct acoustic impedance control. In this paper we present the design of equivalent electrical network in the digital domain (FPGA-based) as well as the practical implementation of this synthetic admittance with an actual electroacoustic transducer, so that the whole device behaves as a broadband sound absorber. Numerical simulations are given to illustrate the dynamic behavior of the transducer once shunted with the designed synthetic admittance. An experimental assessment using a conventional moving-coil loudspeaker in a one-dimensional duct is also presented, thus showing the effectiveness of the synthetic admittance for making it a broadband sound absorber. As a conclusion, general remarks on the overall acoustic performances of such a shunted transducer are discussed, along with practical considerations about stability issues.