2nd Pan-American and Iberian meeting on Acustics

November 2010

METHOD FOR MEASURING SENSITIVITY OF LOUDSPEAKERS IN DIFFUSE FIELD FRANCISCA BASCUÑAN V. 1 [email protected] ALEJANDRO OSSES V. 1,2 [email protected] NICOLÁS RAMÍREZ B. 1 [email protected] VÍCTOR ESPINOZA C. 1,3 [email protected] 1

2

Departamento de Sonido y Acústica, Universidad Tecnológica de Chile, Sede Pérez Rosales, Santiago, Chile. Laboratorio de Metrología Acústica, Sociedad Acustical S.A. Villaseca 21, Oficina 505, Ñuñoa, Santiago, Chile. 3 Centro Tecnológico, Facultad de Artes, Universidad de Chile, Santiago, Chile.

Abstract – A method for measuring the sensitivity of loudspeakers in diffuse field conditions is proposed. This method uses sweeps as excitation signals capturing information related not only to the loudspeaker, but also related to the room (reverberant chamber). To approximate this measurement to a free field condition, digital signal possessing techniques are used to remove the components that are related to the room. The results are compared with measurements done following the method described in the international standard IEC 60268-5 for a free field condition.

1. Introduction The measurement of a loudspeakers sensitivity is commonly done on free field under controlled environmental conditions (temperature and humidity), which usually are recreated in an anechoic chamber. These rooms are designed to have no reflections (Dry), so they are very expensive to build. This research proposes an alternative method for measuring sensitivity of speakers in diffuse field conditions. To emulate this condition, the measurements will be done in a reverberation room. These rooms represent just the opposite of an anechoic chamber, having highly reflective surfaces. Even so, the proposed method has been developed following methodology in anechoic chamber, applying windowing techniques to the measured signal to remove all information captured during the evaluation that does not belong to the speaker. The the proposed method performs well if in diffuse conditions and the results are nearly equal to the results obtained in the anechoic chamber.

frequency response. These parameters give useful information for electroacoustic designs. The measurement of the sensitivity and directionality of the speaker must be done following the guidelines of the IEC 60268-5 international standard for semi anechoic or anechoic conditions. Because of this, an alternative method is developed and evaluated, using the same procedure described by the standard method,   but allowing measurements under diffuse field conditions. For the recreation of a diffuse environment, a reverberation chamber is used. 2.1 Sensitivity and frequency response Sensitivity represents the efficiency degree on an electroacoustic transduction of a loudspeaker, i.e. measures the ratio between the input power level in volts and the sound pressure obtained in pascals. It is measured at a nominal power of 1 W and a distance of 1 m [3]. Following this, the sensitivity can be interpreted as the frequency response of a loudspeaker.

2. Previous concepts

2.2 Directionality

Within the parameters that characterize a loudspeaker, the sensitivity and directionality deliver relevant information on the transduction ability of the speaker, presenting a close relationship with its

The directional characteristic of a speaker is related to the sensitivity, being the sensitivity a parameter that is dependent on the angle of incidence. For example, if an auditor is at a distance of 1 m at an 1

 

angle of 0 ° in the axis of the speaker (front of the speaker) the measured sound presure will be different to the case when the auditor is at a distance of 1 m, but at an angle of 30 °. This information is encoded in a directional response pattern, which can be presented for a specific frequency band from 0 ° to 360 ° or for the frequency responses at angles of (at least) 0 ° 360 ° [3]. The first option was chosen for presenting the results in this investigation. 2.3 Sensitivity measurement in free field As has been mentioned, the measurement sensitivity and directionality of speakers are described in the international standard IEC 60268-5:2007 [3]. It presents the electro-acoustic requirements whose main features are listed below: -The measuring acoustic environment must have the condition of free field, which means that the sound pressure should decay inversely proportional to the propagation distance. -The measurement must be done using a pressure microphone properly calibrated (i.e., with a known calibration). -Elements used in electro-acoustic measurement chain (signal generator, power amplifier and the set microphone preamplifier) should have a controlled frequency response with a variation not greater than ± 0.5 dB in the range of frequencies that the speaker is evaluated. Moreover, these instruments should have a low level of harmonic distortion (THD) and present a negligible measurement error less than 1 dB.

or pink noise) for these purposes [6]. For example, when a speaker is measured in an anechoic chamber, there are two situations that affect the SNR of the transfer function of the speaker (S / R) for low frequencies: the loss of sensitivity (about 12 to 24 dB / Oct.) below the resonance of the box and increasing the background noise due to the poor insulation of the anechoic chamber. Both situations are compensable using Sweeps,   adding a default group delay. The construction of these signals are explained in chapter[6.1]. 2.5 Windowing As a second component the windowing technique is used, which is commonly applied to approximate infinite signals, to finite blocks (that represent small pieces of the infinite signal). This procedure is made to work with finite samples for a good resolution in time domain. For this particular case the time window of Tukey is used [2]. The Tukey window is composed of three windows, a rectangular window in the middle and cosine window at the flanks, as shown in Figure 1. The parameters of these 3 windows are defined in terms of the type of signal that is processed (or windowed). Equation 1 defines a Tukey window in time domain [2]. (1)

2.4. Proposal for the measurement of sensitivity: diffuse field condition In this research a methodology for measuring the sensitivity and directionality on a non-anechoic chambers, particularly in a reverberant chamber, is proposed. This acoustic environment has no acoustic treatment, allowing a high presence of reflections. The reverberation time is a parameter that defines a   coloration due to the reflections of each room. A reverberation chamber is correlated better with the usual listening environments (theaters, recording studios, rooms, etc..), representing a less demanding measurement environment than an anechoic chamber. The method that will be proposed has a strong base in the labeling procedure specified on the technical standard IEC 60268-5, uses Sweeps as an excitation signal and also a windowing technique, where the Tukey window is used. 2.4 Sweeps The proposed method uses a frequency sweep as excitation signal. There are precedents that support undesirability of using a random signal (white noise

Figure 1: Tukey window built at the flanks by a cosine window with α = 2 (Hanning window) and in the center by a rectangular with a length of 384 samples (75% of total samples).

3.

Proposed method

The measurements are performed in a diffuse environment recreated by a reverberant chamber, following the guidelines of standard IEC 60268-5. The free field condition, is obtained in an approximate way, removing the color components of the room (present in the measurement), by applying 2

 

 

the windowing technique, using a Tukey window with parameters specified in Table 1. Window Type

Cosine (right)

Rectangular

Cosine (left)

Start Time

1,7 ms

1,75 ms

8.0 ms

Decay interval

0,5 ms

0,5 ms

0,5 ms

Table 1: Characteristics of the windows that make up the Tukey window

The mounting conditions and instrumentation are kept (the same used at the standard). The excitation signal (which will be reproduced by the speaker for the assessment) corresponds to a frequency sweep. This exitation signal presents variable delays depending on the frequency (the concept of Group Delay), which can be used to improve the signalnoise ratio [6]. The sweep x[n] has a length of 218 = 262.144 samples, assuming a sampling frequency of 44,100 Hz which also has 5 seconds of zeros added at the end, to avoid a truncation at the measurement, because when the sweep ends, the system is not fast enough to grasp the refletions associated with the final acoustic stimulus. However, the length of this vector for other rooms can be determined, where the reverberation time of the measuring room should be considered. In the case of the used reverberant chamber, the T60 by frequency bands is presented in Table 2. Frequency band 500 1.000 2.000 4.000 5.000 6.300

T60 [s] 5,0767 5,4683 4,4267 2,8150 2,2733 1,7533

Deviation 0,4457 0,1641 0,1740 0,0418 0,0674 0,0437

Table 2: Reverberation time of the reverberant chamber at INMETRO for different frequency bands.

After having defined the parameters of the Sweep x [n] that will be used, it must be reproduced by the speaker that is being tested in the reverberant

chamber. The measured signal y [n], will allow us to calculate the total system response Hrev(z-1), considering in Equation 2. Hrev(z-1) = Y(z-1) / X(z-1)

(2)

Where Hrev reflects the speaker and the reverberant chamber response, both are contained in this transfer function. To remove the components that belong to the reverberation from Hrev a windowing technique in the time domain is used. Because of that a prior application is required, an inverse Fourier transform (IFFT) to obtain the signal hrev[n] (time domain). Finally, to wipe out the influence of the room in hrev[n] a time window is convolved with the response hrev[n]. Then the response convolved with the window will be an approximation of the response in an anechoic chamber han[n] (Figure 2c). As has been mentioned, the time window chosen for this purpose is a Tukey window (Table 1). Finally, the speaker frequency response is obtained by applying a Fourier transform to the signal, as shown in Figure 2.d. 4. Experimental Assembly To evaluate the proposed method, a speaker was chosen for the measurement of its sensitivity and polar pattern following the guidelines of standard IEC 60268-5, then the results will be compared with the alternative proposal that is measured in a reverberation room. This speaker corresponds to a mid-range speaker and was measured in INMETRO facilities. 4.1 Instrumentation used In accordance with the standard IEC 60268-5, the instruments chosen for the electroacoustic chain, used in both environments (anechoic and reverberation chamber), are: preamplifier Brüel&Kjær 2669, laboratory microphone Brüel&Kjær 4180, CM22 interface for acoustic measurements, all properly calibrated. A computer with the software Monkey Forest used to record and store the data, a rotary table and other structures to support the speaker were also used.

Figure 2: Diagram of the proposed method (a) Transfer function Hrev(z-1) (b) Impulse response hrev[n]=IFFT(Hrev(z-1)), (c) h[n] windowing ≈ han[n] (d) Transfer function H(z-1) windowing.

   

3

4.2 Implemented electroacustic chain Both measurements in anechoic chamber and reverberation chamber used the same electroacoustic chain, varying only in some practical details such as the mounting of the microphone and amplifier. Figures 3 and 4 show the wiring diagrams of the electroacoustic chain in anechoic and reverberant chamber respectively.

signal processing techniques, so the final difference in the implementation is presented from the data analysis carried out with the Monkey Forest software. 5. Results and Discussion Figure 5 shows the variation of the speaker’s sensitivity as a function of frequency, for the two methods evaluated. It also presents the measured polar pattern in 1/3 octave bands with center frequencies at 500 Hz, 1 kHz and 4 kHz.

Figure 3: Diagram of the electroacoustic chain implemented in the anechoic chamber according to the Figure 5: Frequency response measured by the conventional method (red line) and the proposed method (blue line).

standard IEC 60268-5.

The time window parameters (length and slope) were chosen empirically, searching the combination that provided fewer differences between measurements in anechoic and measurements in reverberant chamber, and also ensure the repeatability of the procedures. Figure 6 shows directional patterns measured for midrange speaker observation.

Figure 4: Diagram of the electroacoustic chain implemented in the reverberation chamber. One variation is that the set microphone-preamplifier was mounted on pedestals over the ground.  

Sweeps as excitation signals in the frequency range of 20 Hz - 20 kHz were used. However, the results were analyzed in 1/3 octave frequency bands, from 500 Hz to 8 kHz, due to the speaker frequency response. The variation in sensitivity depending on the angle of incidence was also analyzed. The standard IEC 60268-5 recommended a variation of less than 15° of the angle. The measurements were made considering a variation of the incidence angle in steps of 5° degrees (beyond what is stipulated in the reference standard). The speaker was rotated with the help of a turntable. As mentioned, the proposed method removes the reverberation reflections of the room through digital 4

 

Figure 7: Differences between the measurement in anechoic chamber and reverberation chamber.

 

5.1. Implications of applying a window

Figure 5: Frequency Response Measured by the Conventional method (red line) and the Proposed method (blue line) at a) 500 Hz, b) 1KHz and c) 4KHz.

The differences between the curves at 500 Hz in Figure 5.a) are outstanding to the window used. For this band, there were no significant differences in the back angles. With respect to 1 kHz and 4 kHz frequency bands it can be observed that the differences in rear angles are higher, but not enough to declare the method ineffective. As seen in the graph of errors (Figure 7), it´s probably not a windowing problem. The factor with maybe more influence is the accuracy of the turntable, which is not quite perfect and makes the repetition of the experiment complicated. Repeatability errors can be caused by several factors, some may be caused by the difficulty of the turntable to repeat the same position, but changes in atmospheric pressure or temperature could also affect the results.

One of the problems in the application of windows is the loss of information at low frequencies, when the window is very narrow. The envelope of the impulse response is divided into two areas of interest, the components that represent the high frequency and components that represent the low frequency. Impulsive samples of high-frequency decay rapidly, contrary to the low sample frequency, which decay slowly, thus if a very narrow window is applied the resolution at low frequencies can be quite low. It is noteworthy that at low frequencies the speaker has a point source behavior [5], so a nearfield measurement could be a good result at low frecuencies without the influence of reflections. This condition can only be considered true when the environments are quasi-acoustic, not in a reverberant chamber. 6.

Future work

The proposed method sets the optimal window in relation to the comparison between the anechoic chamber and reverberation chamber windowing, the chosen window will be the one that delivers the smallest differences for the most extreme conditions of diffuse field (reverberant room). It is important to note that the everyday environments will likely have a reverberation time less than a reverberation chamber. Therefore, setting the length of the window automatically in relation of the reverberation time of the acoustic environment would help to increase the size of the window, which means that more components that represent the low frequency will be considered in the measurement. To implement the automatic adjustment of the window it is necessary to 5

 

develop an application that calculates the reverberation time of the room in which the measurement will be carried out. Then this result will choose an optimal window from a database which relates the reverberation time with the best window for this case in particular. 7.

Conclusion

The method presented in this paper has been validated for measurements in the horizontal directivity patterns, including measurements of sensitivity (incidence of 0 °) in a measuring range between 20 Hz and 20,000 Hz. For the directionality measure at 500 Hz it is possible to visualize the effect of the temporal window. Even so, the proposed method shows similar results to those obtained in free field conditions, according to the IEC 60268-5 standard, making it possible to dispense the use of an anechoic chamber. The advantage of this method over the method presented in the IEC 60268-5 standard for measuring free field consists in the possibility of measuring the sensitivity of a loudspeaker in any room fairly diffuse and without acoustical treatment, without requiring the infrastructure to measure in free field. The approach to free field given by this method might work better if the acoustic dimentions of the environments are large enough and the influence of normal modes are considerably minimum. 8.

This work was conducted under the supervision of Ricardo Villela and Zemar Soares, in addition to continued support from the rest of the team DIAVI, including Marco Nabuco and Swen Müller. We are grateful to Maria Paz Raveau, the Universidad Tecnologica de Chile, INACAP, by Grant our stay in Brazil during the practice period. 9.

References

[1] Bascuñan F., Ramírez N. “Propuesta de un método alternativo para medición de sensibilidad y direccionalidad de alto parlantes”, INMETRO, Rio de Janeiro, Brasil. Marzo de 2010. [2] Harris F.,“On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform”, Proceedings of the IEEE 66 (1):51-83. Enero de 1978. [3] International Electrotechnical Comission, IEC. “IEC 60268-5 Ed.3.1 Consol. with am1: Sound System Equipment-Loudspeakers”, 2007. [4] Kahrs M., Brandenburg K. “Applications of digital signal processing to audio and acoustics”, Kluwer Academic Publishers, 2002. [5] Kinsler L., Frey A. “Fundamentals of acoustics”, Editorial John Wiley & Sons, Ed. 4, 1999.

Acknowledgements

This research was done during the professional practice of two students of Sound and Acoustic Engineering, Francisca Bascuñan and Nicolás Ramírez, developed at the Acoustics and Vibration Division DIAVI National Institute of Metrology and Industrial Quality INMETRO, located in Rio de Janeiro, Brazil, during February and March 2010.

[6] Müller S., Massarani P. “Transfer-Function Measurement with Sweeps”. Journal Audio Engineering Society 49(6):443-471, 2001. [7] Orfanidis S., “Introduction to Signal Processing”, Editorial Prentice Hall, Edición 1, Agosto de 1995.

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