Session - Duct Acousticspublished_or_final_versio

Chan, YJ

Huang, L

Zhang, Y

HKU Scholars Hub

Title Low-frequency noise absorption by a shunted loudspeakerAuthor(s) Zhang, Y; Chan, YJ; Huang, LCitationThe 20th International Congress on Sound and Vibration(ICSV20), Bangkok, Thailand, 7-11 July 2013. In ConferenceProceedings, 2014, v. 1, p. 729-736, paper no. 637Issued Date 2014URL http://hdl.handle.net/10722/191670Rights Creative Commons: Attribution 3.0 Hong Kong License      ICSV20, Bangkok, Thailand, 7-11 July 2013  1 LOW-FREQUENCY NOISE ABSORPTION BY A SHUNT-ED LOUDSPEAKER Yumin Zhang, Yum-Ji Chan and Lixi Huang Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong E-mail: yumin@connect.hku.hk Low-frequency noise is annoying and hard to deal with. By connecting certain shunt circuit to a moving-coil loudspeaker, we demonstrate improved low-frequency absorption of normal incident sound. The loudspeaker is installed in a cavity of 5cm in depth. Negative impedance converter is used to construct a hybrid RLC-parallel and RLC-series shunt circuit.  The low-frequency reactance of the shunted loudspeaker system is reduced in magnitude together with a modified system damping. The proposed device is measured in a well calibrated impedance tube, and good noise absorption performance is achieved in the frequency range of 100Hz to 400Hz as predicted. 1. Introduction Low-frequency noise are very annoying 1 and difficult to control using readily available passive devices. New passive approaches such as metamaterials have been developed 2, 3. A single-layer metamaterial can handle low-frequency noise in a narrow band effectively. Recently, broadband absorption in the low-frequency region by lining metematerials layers was also reported 4. However, constrained by back cavity stiffness, the effective frequency band is not located in the sufficient low range. Another approach of passive method is to introduce external load to tune the impedance of devices to match that of air 5, 6. The use of an electro-magnetic-mechanical absorber, which is a moving-coil loudspeaker in this case, belongs to the latter category. Loudspeaker is used as a sample absorber in this work, and its reactance is reduced by a shunt circuit connected to the system. Such an approach is able to improve broadband impedance match-ing between the loudspeaker in cavity enclosure and air at low frequencies, thus improving sound absorption in that region. Both simulation and experimental results are presented.   Shunt circuits were first introduced into electromechanical vibrator by Hagood and von Flotow 7 who applied it in vibration control of piezoelectric ceramic. After that, researchers employed vari-ous types of circuits aiming to control the impedance of different electromechanical devices. Shunt circuit was hence introduced to tune the acoustic characteristics of piezoelectric panels in 2002 8; and afterward 9, 10, 11. Recently, studies are concentrated on exploring the possibility of adding shunt circuit to loudspeakers. A moving-coil loudspeaker was used by Fleming et al. 12 to suppress the duct acoustic modes by constructing a side-branch Helmholtz resonator. Pietrzko’s series of work on the use of negative impedance converter (NIC) is also reported with both simulation and experi-ments 13, 14. Meynial et al. 15 first adopted shunted loudspeaker in room acoustics, followed by  20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     2  Lissek et al. 16, 17, 18 with good performance in the low-frequency region. Lissek et al. 5, 18 focused on applying shunted loudspeaker to duct acoustics, controlling low-frequency noise, resonance, among other things. They analyzed the analogy between the shunt strategies and active impedance control in simulation. They found that the velocity feedback strategy performs better in noise reduc-tion and such a system was validated experimentally. Zhang 6 made a comprehensive discussion on the effect of different electrical components in the shunt circuit of a loudspeaker and proposed a strategy to suppress the system dynamic mass for improved high frequency performance.  The effort paid on low-frequency noise absorption is well noted but convenient devices are still not readily available. Resonator devices are limited in its effective bandwidth and traditional porous materials requires large space 19. We here propose a shunt-circuit-based low-frequency absorber. The circuit modifies the impedance of loudspeaker such as to match the characteristic impedance of air. A major benefit is that low-frequency absorption performance is improved a lot between 100Hz and 400Hz using a shallow cavity of 5cm in depth. Both theoretical and experimental discussions are conducted.     2. Loudspeaker with shunt circuits 2.1  General dynamic model of loudspeaker with shunt circuits Under Linear hypothesis, a moving-coil loudspeaker can be seen as a single degree-of-freedom, mass-spring system below the cut-off frequency of the loudspeaker diaphragm. The impedance of a loudspeaker with open electrical terminals can be denoted by    ,    ( )                                          (1) where s is the Laplace variable, ,     and   are the dynamic mass, damping and stiffness of the moving-coil loudspeaker, respectively. The sum of the terms of mass and stiffness is called mechan-ical reactance. When such a loudspeaker is installed at the end of an impedance tube, the normal-incidence sound absorption coefficient is                                                             21air moair moZ Z ssZ Z s                                                         (2) where            is the impedance of air and A is the cross section area of the impedance tube. From Eq. (1) we see that the loudspeaker reactance becomes larger when frequency goes to low which will decrease the absorption coefficient to zero at the DC frequency. When the back enclo-sure of the loudspeaker is small, the stiffness term is very large hence the low-frequency absorption is low. This is the problem that most resonator-type absorbers encounter and this is the issue we set out to address. The proposed device is shown in Figure 1. When the loudspeaker is connected to an electrical loading,   , at the terminals of the loudspeaker, an additional mechanical impedance will be introduced.  The system impedance becomes,   121( )s emZ s ms s Bl Z                                                (3) where    is the force factor derived from the magnetic field in the loudspeaker. Moving-coil re-sistance and inductance are contained in   . If negative impedance converter (NIC) 20 is employed,    could be any designed value, beyond the constrain of coil resistance and inductance. The full implementation of the system is shown in Figure 1. When a sound hits the loudspeaker diaphragm, electromotive force (EMF) is induced in the moving coil, which is proportional to (  )  times the mechanical excitation. Therefore, a current will flow and is inversely proportional to electrical load- 20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     3 ing    and the additional acoustic impedance is (  )     . By manipulating    we can obtain a de-sirable acoustic impedance at low frequencies.   Figure 1. Moving coil loudspeaker with shunt circuit 2.2 Stability While an active unit such as NIC is connected to the system, it’s possible to cause the system to be unstable. Without loss of generality, we here only consider an R-L-C series shunt circuit. The transfer function is Eq. (4) and the stability characteristic equation is Eq. (5)  21 1eFVms s Bl Z                                                   (4)                                                      4 3 24 3 2 04312110121 0ss ss s ss ssa s a s a s s aa mLa mR La mC R L BlC RaaCa                                                         (5) Aware that coil resistance and inductance    and    is included in     and    for the conven-ience of reading in Eq. (5). It’s a fourth order equation which is not easy to solve analytically. How-ever, we can use Routh-Hurwitz stability criterion to derive the stability boundary, according to which the stability requires  20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     4                                                      3 2 4 12 23 2 1 4 1 2 00, 0,1,2,3,400na na a a aa a a a a a a                                                            (6) It follows that                                                                                               (7) will guarantee a stable system.   2.3 Impedance design  From Eq. (2) and Eq. (3), we get:                                                 2212 1111airr eaieZ ms s Bl ZsZ ms s Bl Z                                             (8) To make good low-frequency absorption, it’s key to design    to decrease the system reactance at low frequency. Our design starts from a hybrid R-L-C circuit as shown in Figure 1. The acoustic impedance induced by the circuit is                 11221 1 1 1 1( )es s s p pmepR L s C sBR L s C slZ Bl Z                          (9) The imaginary part of     should be positive for frequencies below the eigen frequency of the unshunted loudspeaker,     , and slightly negative after that in order to reduce the magnitude of the system reactance. In Eq. (9) we can see that    is not effective at both low frequency and high frequency. Therefore, for the sake of convenient analysis, we make it zero.     is written as Eq. (10), separated into real and imaginary parts. The real part is the induced damping and the im-aginary part reactance.                                                 2 22 2 2 2 2 22 22 2 2222 2 2 21mep psp pp ps ss p pp qZ Bl i Blp q p qR Lp RR LR LL CqC R L                                (10) where   is the angular frequency. Making   smaller and larger than the unshunted loudspeaker (henceforth ‘open loudspeaker’) resonance, we can get approximations of    :                                              2 22 2 2 2 2 2( ) ( )1 1rs smes s s sBl R Bl CZ iC R C R                                             (11)  222 22 22 2 2 2 2 22 2( )( ) ( )( ) ( ) ( ) ( )rpss p pmep ps p s s p sp pRBl LBl R R LZ iR RR R L R R LL L                   (12)  20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     5 Eq. (11) shows that the induced reactance is positive at low frequencies, and the series capaci-tance and resistance are important for this purpose. When the frequency is higher, the reactance becomes negative as we want. The by-product is an extraordinary damping spectrum introduced. The situation is complex in the mid frequency range, the ranges of ‘low’, ’high’ and ‘mid’ being relative to the design frequency.  3. Experimental validation    Figure 2. Measurement setup. In what follows, we will conduct simple numerical calculations to predict the performance of the designed loudspeaker as absorber, which will be validated experimentally. First, the impedance of the open-circuit loudspeaker is measured, and the impedance data are extracted to predict the absorption coefficient of the shunted loudspeaker. The sample loudspeaker used is Visaton WS-17 whose technical data are shown in Table 1. The loudspeaker is sealed in a rigid box whose depth is adjustable, the value used in this study being 5cm. The shunted loudspeaker is installed at the end of a rectangular impedance tube, as illustrated in Fig. 2. Two microphones are mounted in the tube for standing-wave measurement and decomposition. A computer controls the driving excitation and data collection. The shunted circuit is connected to the loudspeaker terminals and the designed cir-cuit parameters are shown in Table 2.  Table 1. Technical data of WS-17 according to http://www.visaton.com/en/chassis_zubehoer/tiefton/ws17e_8.html Dynamic moving mass Nominal impedance D.C. resistance Voice-coil inductance 13 g 8 Ω 5.8 Ω 0.9 mH Force factor    Effective piston area Resonance frequency   3.9 Tm 143 cm2 45 Hz  The measured absorption coefficient of the open circuit loudspeaker is shown in Fig. 3 and the reactance and damping shown in the figure are all dimensionless. Fig. 3 shows that, because of the large reactance below 150 Hz, the absorption performance is poor. Meanwhile, its dimensionless damping is below 1 which is not sufficient. Therefore, a shunt circuit is designed to connect the loudspeaker to modify its mechanical impedance.    20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     6   Figure 3. Absorption coefficient and impedance of open termination loudspeaker The shunt circuit parameters are listed in Table 2. We use Eq. (8) to predicte the absorption co-efficient and impedance, shown in Fig. 4. The experimental results of the shunted loudspeaker are shown in the same figure.   Table 2. Shunt circuit parameters Op-amp          LM358 1 Ω 0.9 mH 0.7mF R          0.32 Ω 0.5 Ω 0.18 mH absent  When the output of the operational amplifier (op-amp),    and    , are too large to be supplied by the chosen op-amp, the op-amp goes into saturation. In our design,   should be kept small and    should avoid being too small 6.    and    are not important in determining properties of shunt circuit . However, we still keep them in the analytical analysis and experiments for the sake of completeness in analysis.     20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     7  Figure 4. Impedance and sound absorption for the open-circuit and shunted loudspeakers. The legends shown between the first two sub-figures apply to all. We find that the absorption coefficient is improved a lot and it is above 0.7 in the range of 100~420 Hz. The predicted coefficient agrees with the experimental result well while the effective band is found to be broader in experiments. In Fig. 4, it is clear that the low-frequency reactance is decreased as we anticipated, and the damping gets larger. A good absorption performance is achieved in the low frequency range considering the thin structural design. 4. Conclusion In this paper, a shunt-circuit-based strategy to achieve broadband low-frequency absorption is proposed, and the numerical prediction is validated experimentally using an impedance tube. The proposed devices have thin structure and simple implementation which can effectively reduce sys-tem reactance and increase damping. Series capacitor and resistor are found to be key to overcome large reactance provide by the shallow enclosure, realizing low-frequency absorption.     Acknowledgement:  The project is supported by a National Key Basic Research Scheme of China (Grant no. 2012CB720202).  20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013   ICSV20, Bangkok, Thailand, 7-11 July 2013                                                                                     8  REFERENCES 1. H. Leventhall, Low frequency noise and annoyance, Noise and Health, 6,  59-72, (2004). 2. L. Fok, M. Ambati, and X. Z. M. Bulletin, Acoustic Metamaterials., MRS Bulletin, 33, 931-934, (2008). 3. Z. Liu, X. Zhang, Y. Mao, Y. Zhu, Z. Yang, C. Chan, et al., Locally resonant sonic materials, Science, 289, 1734-1736, (2000). 4. J. Mei, G. Ma, M. Yang, Z. Yang, W. Wen, and P. Sheng, Dark acoustic metamaterials as super absorbers for low-frequency sound,  Nature Communications, 3,  756, (2012). 5. H. Lissek, R. Boulandet, and R. 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Low-frequency noise absorption by a shunted loudspeaker

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Low-frequency noise absorption by a shunted loudspeaker

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