Active Impedance Control for One-Dimensional Sound

D. Guicking K. Karcher
Drittes Physikalisches Institut, University of Gottingen, Gottingen, Federal Republic of Germany

Active Impedance Control for One-Dimensional Sound
Generalizing the concept of active sound absorption, a system for active impedance control has been developed, so far for plane waves at normal incidence. The active reflector is a loudspeaker driven by the incident sound wave. Its feeding signal is derived from a "wave separator" with two microphones splitting up the standing wave field into incident and reflected wave. This system permits easy control of the reflection coefficient and eliminates feedback instability. Arbitrary reflection coefficients between almost 0 and about 1.5 have been realized in the frequency range from below 100 Hz to more than 800 Hz.

Introduction The absorption of low-frequency sound is difficult with conventional, passive methods. Active (electroacoustic) methods are becoming more and more important. The state of entering into engineering practice has been reached especially for microprocessor-controlled active systems aiming at cancellation of repetitive noise [1] while more general projects of actively controlling random noise are still in the laboratory stage. One such system, an actively supported porous-plate absorber, has been described in a previous paper [2]. A generalization of the concept of active sound absorption toward active realization of arbitrary wall reflection coefficients is supposed to find applications not only for noise abatement but more generally in room acoustics. The acoustic quality of a room depends largely on its reverberation time, Tw. In concert halls, an increase of T60 toward lower frequencies guarantees fullness of sound, but for auditoriums such an increase is unfavorable since strong low-frequency components mask the upper frequency bands which are essential for good speech intelligibility. This effect is intensified by the asymmetry of the masking effect: Low frequencies mask higher ones more severely than vice versa. For multipurpose halls, therefore, variable reverberation time especially in the low-frequency range is desirable. Acoustic test rooms with adjustable reverberation time would be very interesting, too. The methods of "variable acoustics" used at present [3] comprise passive techniques like rotatable wall elements with different impedance faces, and active methods like "assisted resonance" [4], Passive methods allow the reverberation time to be reduced as compared to the situation of rigid walls (though not being very effective for low frequencies), while assisted resonance is an incoherent active means of retarding the decay process, i.e., increasing the reverberation time. Coherent active methods such as those to be described below are capable of increasing as well as reducing the reflection coefficient of a wall, and hence the reverberation time of a room. It is the final aim of the investigation part of which is reported here to develop an active wall lining which consists of a two-dimensional array of loudspeakers working as active reflectors. They shall be driven by the incident sound wave via microphones and suitable electronics in order to realize prescribed values of the acoustic input impedance. In a first step, such a system has been implemented for onedimensional sound. Its construction and performance is described in the following sections. The extension to threedimensional sound fields presents several problems some of which have not yet been solved satisfactorily. They are outlined in the final section of this paper and will be described in detail in a separate publication. Experimental Arrangement A Briiel & Kjaer impedance tube (Kundt tube) Type 4002 has been used for these experiments. The control loudspeaker, attached to the open end of the tube, is, in the simplest case fed from a microphone picking up the incident sound wave (Fig. 1). In order to determine the minimum reflection coefficient obtainable with this equipment, the amplifier gain and phase shift (combined to the complex amplification factor V) have been adjusted by hand for certain frequencies. The result is plotted in Fig. 2 as a dashed line: Values below 5 percent can be reached at low frequencies; but above 400 Hz, the tendency to feedback instability prevents the gain from being raised sufficiently so that no satisfactory results are found. An essential improvement is possible if the loudspeaker is driven by a signal determined by the incident wave only. The elimination of the reflected wave from the feedback signal is possible by a two-microphone arrangement which has the additional advantage of permitting the reflection coefficient to be measured much easier than by scanning the standing wave field in the tube. The system is described in the following section. On-the-Spot Measurement of the Complex Reflection Coefficient The separation of a standing wave field into incident and JULY 1984, Vol. 106/393

Contributed by the Noise Control and Acoustics Division for publication in the JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND RELIABILITY IN DESIGN.

Manuscript received at ASME Headquarters, December 12,1983.

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active system control setting source loudspeaker jPZ£Zrj] measuring amplifier

probe microphone
Fig. 1 Active impedance control with one microphone (open-loop control, adjustment by hand)

0.8 0.6 0.4

with one / / microphone-/
/ /

/

/

IEI
0.2

^ ' '

with two microphones --. The total sound pressurep tol is the sum of both: Plot (X,t) =Pi (X,t) +Pr (X,t). (3) If r means the complex amplitude reflection coefficient at x = 0, we have pr(0,t)=rPi(0,t). (4) The microphones pick up the sound pressure signals p,U)=Pi(0,t)+pr(0,t) and p2(t) =Pt (Ax,t) +pr (Ax,/) =Pi (0,/ + r) +pr (0,t-r) (6) where r = Ax/c is the travel time of the sound wave between 394/Vol. 106, JULY 1984 (5) (1)

the microphones (c = sound velocity). If/?, (t) is delayed by T, we have PiT=Pi(t-T)=Pi(0,t-T)+pr(0,t-T), and the difference
/MO=PII-P2=P/(0,/-T)-/?,(0,/ + T) (8)

(7)

represents the incident wave only. Similarly, we delay p2U) by T: Pir =Pi(t-r) and form the difference PA U) =Pir - P i =Pr(0J - 2T) -Pr (0,/) (10) which is free from the incident wave. With equation (4), we have P4(O=r[p,(0,/-2T)-p,(0,0]. Ifp 3 (t) is delayed once more by r t o give ps(t)=pi(t-T)=pi(0,t-2T)-pi(0,t), =Pi (0,/) +pr (0,t - IT)

(9)

(ID
(12)

we see that the ratio of p4 andp$ yields the complex reflection coefficient:

EL
PS

(13)

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active system
Pi (incident) p r (reflected)

,

!

Mi

—1 M2 I

ir
P5~Pi P r P r
Fig. 3 Electronic separation of a standing wave field into incident and reflected wave without compensation of the weighting factor

i ji i .«

' - Pr

p r

control setting
Fig. 5 Active system with two feedback microphones and open-loop control

Pi(X,t)
*«- Pp ( X ( r )

P ;=p.(o.t>

P ;=p r (o,t)

Fig. 4 Standing wave separator with flat frequency response; stability filter omitted

For a harmonic incident wave with amplitude a, pi(x,/)=«e ' 'l" '+h), p r t o ) = r « e i ( u * " t o l , the signals p 4 and/>5 are pAt)=Pr(0,t)[e-2Jwr-l]=pr(0,t) 'e p5 U) =Pi (0,0 [e~Var - l] =Pi(0,t) -e yV z +

(14)

(i "). /.2sina)T,
(15)
2

(17) PA = -PA +P4e~v"7 =Pr (0,0, r (18) Pi= -Ps+pie-V« =piW,(). Thus, the circuit of Fig. 4 separates the standing wave field into incident and reflected wave independent of frequency, provided that Ax does not equal a multiple of A/2 (or, the frequency / does not equal a multiple of 1/2T) where the output signals vanish theoretically. However, at these frequencies feedback instability occurs, which can be avoided by low-pass filters or by inserting attenuators, e.g., after the second pair of difference amplifiers. The experiments to be described below have been performed with the system of Fig. 3. The delay units are approximated by all-pass filters with group delay T = 0.29 ms corresponding to the travel time of sound signals in air for the microphone distance of Ax = 10 cm. For frequencies up to 600 Hz, first-order active filters are good enough; secondorder filters are sufficiently linear up to 1200 Hz. This method does not only speed up the measurement of reflection coefficients in the impedance tube, but extends its range of application to lower frequencies, and it is also unambiguous in the case of active reflectors where values of I r I > 1 are possible. Comparative measurements of the complex reflection coefficient of a loudspeaker (acting as a passive reflector) by (a) scanning the standing wave field, and (b) recording the amplitude ratio and phase difference of p 4 andp 5 in Fig. 3, gave the same results within experimental scatter. The loudspeaker mostly used is a moving-coil woofer with a 9-cm membrane radius in a damped box. Its amplitude reflection coefficient varies between 0.6 and 0.8 in the frequency interval from 100 through 800 Hz. Active Impedance Control With the Two-Microphone System Modifying the arrangement of Fig. 1 by utilizing the twomicrophone system, we get the setup outlined in Fig. 5. The box fed by the microphone signals contains the circuit of Fig. 3, supplying not only the reflection coefficient r but also the feedback signalp5 which is proportional top,. The amplifier gain and phase (combined in the complex factor V) are set by hand. Readjusting V for each frequency of measurement, the lowest possible values of Irl are plotted as a solid line in Fig. JULY 1984, Vol. 106/395

' • 2sincor. (16) We see that they indeed represent the reflected and incident wave, respectively, but weighted with a common complex factor depending on frequency. Similar systems have been proposed in [5-7]. The weighting factor can be compensated by a feedback which leads to the system of Fig. 4. Comparison with Fig. 3 reveals immediately that p4 and p5 are replaced by \

J

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computer simulation of sound fields. The measurement of the reflection coefficient turned out to be impossible with the twomicrophone system of Fig. 3, and attempts to measure it with an intensity probe failed, too, because of the complicated nearfield in front of the loudspeaker array. This problem has been solved by scanning the sound pressure along a line normal to the "wall" and fitting to the experimental data a model function which comprises, besides incident and reflected wave, also diffraction terms. One of the parameters 0 200 400 600 Hz 800 to be fitted is the reflection coefficient. Details of this investigation will be presented in a separate paper. f The successful implementation of one-dimensional active Fig. 6 Maximum energy absorption of the active broadband system impedance control not only for sinusoidal signals but also for with nonideal compensation filter broadband sound, also suggests another pursuit, namely the 2: The line stays below 5 percent through the whole frequency application to active noise control in ducts. A lot of work has range from 100 to 800 Hz, between 150 and 750 Hz even already been devoted to this problem. The systems developed so far employ a single control microphone and either below 2 percent. Variation of Irl is possible by simply changing the am- directional loudspeaker arrangements or a single loudspeaker plifier gain. No instability occurred within the frequency and a special electronic filter [10] to overcome the problem of range from below 100 Hz through more than 1000 Hz for feedback instability. An alternative is the application of a directional microphone system like the one described in this values of Irl up to 1.5. A certain phase of the reflection coefficient will usually not paper. This may provide also a solution to the severe problem be prescribed in practice, but it can be realized by appropriate in ducts with flow that the active system converts turbulent pressure fluctuations into sound. The arrangement of Fig. 3 phase setting of V. Readjustment of V for each frequency is meaningful only or 4 can be extended to a chain of three or more microphones for laboratory tests. For practical applications, a fixed setting with coherent enhancement of the signal required for feeding should be valid for a broad frequency band. This demands the loudspeakers, cancellation of the acoustic wave traveling that a flattening filter be inserted between microphone and in opposite direction, and incoherent superposition of turloudspeaker. In order to determine the filter characteristic bulent pressure fluctuations. The signal-to-noise ratio imrequired, the open-loop gain of the active system in Fig. 5 has proves with the square root of the number of microphones involved, and this number can even be raised by averaging been measured. It happened to be rather flat in amplitude ( ± 3 dB) and phase ( ± 1 0 deg) so that a broadband phase shifter over several microphones arranged along the circumference of was sufficient as an approximative correction filter. With either cross section. An experimental study has been started to optimum matching of the active acoustic loudspeaker im- realize this concept and to test its applicability. The results pedance to pc of air, the amplitude reflection coefficient was will be published in a subsequent paper. lowered from approximately 0.8 (passive system) to less than 0.2, again in the frequency interval from 100 through 800 Hz. Acknowledgments The corresponding energy absorption coefficient is plotted in Thanks are due to Prof. Dr. M. R. Schroeder for initiating Fig. 6; it exceeds 95 percent throughout. this work and for his pertaining interest in its progress. Similar results have been obtained with a specially Financial support has been given by the Deutsche Fordeveloped electret loudspeaker [8] instead of the moving-coil schungsgemeinschaft. system. In order to get a reflection coefficient below 0.2 in the same frequency range as above, a third-order all pass filter References appeared to be necessary. 1 Chaplin, B., "Anti-Sound—The Essex Breakthrough," Chartered Since the system of Fig. 5 is an open-loop control, the Mechanical Engineer, Vol. 30, 1983, pp. 41-47. complex amplification V has to be readjusted if a parameter 2 Guicking, D., and Lorenz, E., "An Active Sound Absorber With Porous of the transmission path changes. From this reason, a closed- Plate," this issue ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND loop feedback control (with a different two-microphone RELIABILITY IN DESIGN, pp. 389-392. 3 Peutz, V. M. A., "Variable Acoustics: Mechanical (Centre Pompidou, arrangement) has been built, and it works well [9]. The Paris) and Realizations," in control circuit in mixed analog and digital technique is too FASE/DAGA Electro-Acoustic 1982, pp. 143-154. Fortschritte der Akustik— '82, GOttingen involved to be described here. 4 Parkin, P. H., and Morgan, K., "Assisted Resonance" in the Royal Conclusion and Outlook It has been mentioned in the introductory chapter that this investigation was performed mainly as a preliminary study for the development of two-dimensional active arrays controlling the acoustic impedance of walls. Proceeding from the onedimensional tube to the three-dimensional free-field, one encounters several complicating effects: Instead of plane waves at normal incidence and constant intensity along the propagation path, we have oblique incidence, spatial energy spreading, interaction of different sound sources, and diffraction waves emerging from impedance discontinuities on the walls. A mainly experimental study with a 3 x 3 loudspeaker array in an anechoic room has been started, assisted by
Festival Hall, London: 1965-1969, Journal of the Acoustical Society of America, Vol. 48,1970, pp. 1025-1035. 5 Schroeder, M. R., "System for Determining Acoustic Reflection Coefficients," US Patent No. 3 346 067, 1967. 6 Tachibana, H., Suzuki, C , and Ishii, K., " A New Method of Sound Absorption Coefficient Measurement in Acoustic Tube," 10th ICA Congress, Sydney 1980, Paper No. E-l 1,2. 7 Suzuki, C , Yano.H., and Tachibana, H., " A New Method of Measuring Normal Incident Sound Absorption Characteristics of Materials Using Acoustic Tube," Journal of ihe Acoustical Society of Japan, (E), Vol. 2, 1981, pp.161-167. 8 Guicking, D., and Albrecht, M., "An Electret Loudspeaker for Active Acoustic Systems," this issue of ASME JOURNAL OF VIBRATION, ACOUSTICS,
STRESS, AND RELIABILITY IN DESIGN, pp. 397-398.

9 Karcher, K., "Aktiv beeinflu/3bare Wandimpedanz bei senkrechtem Schalleinfall," doctoral dissertation, University of GOttingen, 1982. 10 Eghtesadi, K., and Leventhall, H. G., "Active Attenuation of Noise— The Monopole System," Journal of the Acoustical Society of America, Vol. 71, 1982, pp. 608-611.

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References: appeared to be necessary. 1 Chaplin, B., "Anti-Sound—The Essex Breakthrough," Chartered Since the system of Fig. 5 is an open-loop control, the Mechanical Engineer, Vol. 30, 1983, pp. 41-47. complex amplification V has to be readjusted if a parameter 2 Guicking, D., and Lorenz, E., "An Active Sound Absorber With Porous of the transmission path changes. From this reason, a closed- Plate," this issue ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND loop feedback control (with a different two-microphone RELIABILITY IN DESIGN, pp. 389-392. 3 Peutz, V. M. A., "Variable Acoustics: Mechanical (Centre Pompidou, arrangement) has been built, and it works well [9]. The Paris) and Realizations," in control circuit in mixed analog and digital technique is too FASE/DAGA Electro-Acoustic 1982, pp. 143-154. Fortschritte der Akustik— '82, GOttingen involved to be described here. 4 Parkin, P. H., and Morgan, K., "Assisted Resonance" in the Royal Conclusion and Outlook It has been mentioned in the introductory chapter that this investigation was performed mainly as a preliminary study for the development of two-dimensional active arrays controlling the acoustic impedance of walls. Proceeding from the onedimensional tube to the three-dimensional free-field, one encounters several complicating effects: Instead of plane waves at normal incidence and constant intensity along the propagation path, we have oblique incidence, spatial energy spreading, interaction of different sound sources, and diffraction waves emerging from impedance discontinuities on the walls. A mainly experimental study with a 3 x 3 loudspeaker array in an anechoic room has been started, assisted by Festival Hall, London: 1965-1969, Journal of the Acoustical Society of America, Vol. 48,1970, pp. 1025-1035. 5 Schroeder, M. R., "System for Determining Acoustic Reflection Coefficients," US Patent No. 3 346 067, 1967. 6 Tachibana, H., Suzuki, C , and Ishii, K., " A New Method of Sound Absorption Coefficient Measurement in Acoustic Tube," 10th ICA Congress, Sydney 1980, Paper No. E-l 1,2. 7 Suzuki, C , Yano.H., and Tachibana, H., " A New Method of Measuring Normal Incident Sound Absorption Characteristics of Materials Using Acoustic Tube," Journal of ihe Acoustical Society of Japan, (E), Vol. 2, 1981, pp.161-167. 8 Guicking, D., and Albrecht, M., "An Electret Loudspeaker for Active Acoustic Systems," this issue of ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND RELIABILITY IN DESIGN, pp. 397-398. 9 Karcher, K., "Aktiv beeinflu/3bare Wandimpedanz bei senkrechtem Schalleinfall," doctoral dissertation, University of GOttingen, 1982. 10 Eghtesadi, K., and Leventhall, H. G., "Active Attenuation of Noise— The Monopole System," Journal of the Acoustical Society of America, Vol. 71, 1982, pp. 608-611. 396/Vol. 106, JULY 1984 Transactions of the ASME Downloaded 21 Dec 2010 to 130.207.50.192. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm