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Alps Adria Acoustics Association 3rd Congress of the Alps Adria Acoustics Association 27–28 September 2007, Graz – Austria THE USE OF OPTOCOUPLERS IN MEASURING LOUDSPEAKER CONE DISPLACEMENT Milan Uskoković, M.Sc.E.E. Radio 101, Zagreb, Croatia E-mail: [email protected] Abstract The article presents a method for measuring loudspeaker cone displacement employing a photo-interrupter. The photointerrupter is set to work in the linear regime, such that any movement of the barrier between the transmitting diode and the receiving photo transistor results in a change in the collector current of the photo transistor. The barrier is fitted to the loudspeaker cone so that the change in the collector current is proportional to the movement detected. In order to achieve better linearity, temperature stability and S/N ratio, two photo-interrupters forming a differential connection are used. The paper ends with an example of the practical implementation and experimental measurement results of the proposed sensing methodology. Key words: photo-interrupter, cone displacement, frequency response, noise. 1. INTRODUCTION There are several methods for measuring loudspeaker cone movement. One of them, and the most popular, is the method with laser beam movement detectors. Although this method yields accurate and error-free results, it requires very expensive measuring equipment and is largely restricted to laboratory settings. Simpler, less costly and more practicable measuring solutions rely on the use of capacitive, inductive or optical sensors that can measure cone movement as a proportional change in the capacity, inductivity or intensity of light that is emitted from the light-emitting source to the light-receiving element. However, these methods require that additional measuring elements be mounted on the loudspeaker cone (such as electrical contacts, light transmitters, electrically conductive coatings, etc.), which may affect mechanical properties of the cone itself, degrade overall speaker performance to a certain extent and ultimately compromise measurement accuracy. The purpose of this article is to provide an overview and analysis of a method for measuring cone displacement that would be both practicable and economical and have only a minimal or negligible effect on loudspeaker properties. The method proposed in this paper is based on the use of optocouplers or, more precisely, photo-interrupters. 2. PHOTO-INTERRUPTERS 1.1. Background The structural block diagram and the schematic of a typical photo-interrupter design are shown in Figure 1. The interrupter consists of a light-emitting diode that emits light (LED) and a photo-transistor that detects said light. The value of the photo-transistor collector current depends on the amount of light emitted by the LED and the percent of the photo-transistor area obscured by the barrier that prevents the passage of light emitted by the LED. In order to make the measurement system robust to the conditions that cause interference, both the LED and the photo-transistor are made to operate in the infrared region of the electromagnetic spectrum. Fig.2 Interrupter transfer function 1.2.2 The effect of temperature on electrical properties Fig.1 Structural and functional diagrams of a photo-interrupter design 1.2. Electrical properties of photo-interrupters 1.2.1 Transfer function Interrupters are usually used to detect and count the movement of some barrier between the transmitting diode and the receiving photo-transistor, where the linear part of the transfer curve needs to be as small and as steep as possible in order to avoid counting errors. If interrupters are to be used as movement sensors, however, the opposite is required: the transfer function Ic=f(d) The internal operating temperature of a loudspeaker may vary greatly, depending on the amount of acoustic power being emitted by the loudspeaker and its efficiency. At the specific position where this photo-interrupter is placed, we can expect a relative temperature change of approximately 80 degrees Celsius, which is an important design issue that must not be overlooked. (1) where Ic is the collector current, and d is the percentage of the photo-transistor area shadowed by the barrier, should be as linear as possible in the widest working range. The linearity of the transfer function will have a direct effect on the linearity of the movement sensor and measurement accuracy. Also, the wider the range, the better the signal-noise ratio. Figure 2 shows the transfer function of the photointerrupter used in this paper. It can be observed that the transfer function is linear for 20 to 80 percent of the shadowed area, providing a linear output over the range of about 0.5mm. Fig.3 LE diode forward voltage vs. temperature characteristic Figure 3 illustrates the effect of temperature on the LE diode forward voltage whereas Figure 4 shows the dependence of the photo-transistor collector current on ambient temperature. electronic device. Its value depends on the temperature of the electronic device and the bandwidth conveyed. The Johnson noise can be calculated using the following formula: I j = 4kTB / Rsh (3) where Ij= Johnson noise (A) k = Boltzmann's constant (1.38 x 10-23 joules/K) T = absolute temperature (K) B = noise bandwidth (Hz) Rsh = photodiode shunt resistance (Ω). Apart from the above-mentioned types of noise sources, which are generated from within the emitting and receiving elements of the photo-interrupter itself, noise and interference can also be caused by outside light sources or by reflection against the wall of the coil assembly, as well as by the power supply of the lightemitting diode and photo-transistor. Because the value of the decoded useful signal is not constant but rather depends on the power emitted by the loudspeaker, and it decreases as the frequency rises, it is of utmost importance to keep noise at a minimum. Fig.4 Collector current vs. temperature characteristic The above figures clearly indicate that both the power emitted by the LED and the collector current of the phototransistor vary in response to ambient temperature changes, which may lead to measurement errors and deviation of the sensor operating point from the optimum. 1.2.3 Noise Before going further into the subject, we shall look briefly into the main sources of noise in photo-interrupters. The main sources of noise in photo-interrupters are thermal noise (or Johnson noise), shot noise and flicker noise (1/f or contact noise). These noise sources are independent of each other and the total noise current is the root of the sum of the square of each of these noise sources: 2 2 In = I j + Is + I f 2 (2) where In = total noise current (A), IJ = thermal or Johnson noise current (A), IS = shot noise current (A), IF = flicker noise current (A). The Johnson noise is dominant. It is a form of white noise generated by the random motion of electrons in an 1.2.4 Response time Another parameter of great importance in sensor design is the response time of the photo-interrupter. It determines the highest frequency of loudspeaker cone displacement and the maximum decodable slew rate ratio. To be useful for the purposes of the design discussed in this paper, the photo-interrupter must be able to detect electrical signals in the frequency range up to 200Hz, with a slew rate of 0.1V/µS. Figure 5 shows the response time of the photointerrupter for the square wave signal. It can be seen that the rise time is dependent on the collector current and that the required slew rate ratio of 0.1V/µS can be easily achieved. Fig.6 Barrier design The angle of the slit aperture (or wedge) k is determined by the coefficient of the reduction of the relative movement of the barrier, using the following equation: k=arc tan(d/xmax) (4) where d = linear movement of the photo-interrupter, and xmax= maximum cone displacement. Fig.5 Output signal rise time characteristic 2. Design of the optical movement sensor As noted earlier in the text, the amount of cone displacement depends on the power emitted by the loudspeaker and the frequency of the signal emitted. Loudspeaker manufacturers generally publish data on the peak cone displacement, xmax, for a given loudspeaker, which means that the maximum amount of cone movement that can be detected by the sensor is already known. This xmax value is usually in the range of 5 to 15mm so, for simplicity, in our further analysis we shall take the arithmetic mean of these values (i.e. xmax = 10mm) as our estimate of the average xmax value. On the other hand, the amount of cone displacement drops as the frequency increases, in accordance with the below formula: x( peak ) = Pn 4 ρ 0π 2 f 2 a 2 (5) where Pn= pressure, ρ0 = density of air, f = frequency, a = cone radius. Figure 7 illustrates the relationship between cone displacement and frequency of the loudspeaker at 1W. Figure 2 shows that the photo-interrupter has a linear characteristic for a maximum barrier movement of 0.5mm whereas the value of cone xmax is 10mm. This means that the barrier should be shaped so that for xmax=10mm the amount of its relative movement is 0.5mm. The shape of the barrier by which this is achieved takes the form of a wedge-shaped slit shown in Figure 6. Fig.7 Cone displacement vs. frequency characteristic As can be seen, a decrease in the amount of cone displacement that is caused by frequency rise will decrease the value of the output signal of the sensor and reduce the S/N ratio. To keep noise at a minimum, two photo-interrupters forming a differential connection are used. This will enable us to reduce the impact of temperature changes on measurement accuracy to the lowest degree possible, assuming that the physical properties and temperature of the photo-interrupters are equal. The barrier has the shape shown in Figure 6. The shape is first printed with a laser printer on a piece of transparent foil and then glued with binding glue to the inner surface of the coil former. The barrier is extremely light (it weighs less than 0.1g) so it does not affect any of the woofer parameters. The differential amplifier is implemented as shown in Figure 10. 3. Implementation of the optical movement sensor The experiment described here uses a woofer driver with a diameter of 160mm. The photo-interrupters are mounted onto the pole piece just below the driver's dust cap and the connection wires are inserted through an opening in the center of the pole piece. The barrier is a piece of printed foil with two wedge-shaped slits on it, and it is glued to the coil former on the inside of the driver. The details of the test assembly are shown in Figures 8 and 9. Fig.10 Differential amplifier schematic Fig.8 Sensor placement I The signal from the emitter resistors R1 and R2 of the respective photo-transistors is amplified using the inverting amplifiers IC1A and IC1B. Resistors R6 and R7 are used to adjust the amplification of the inverting amplifiers in the circuit so that both sensors produce equal output signals for the same amount of cone displacement. Potentiometers R8 and R9 are used to null out any DC offset at the output of the amplifier. Signals from the output of the amplifier are passed to the differential amplifier IC2, at the output of which differential voltage is generated in proportion to the amount of cone displacement. The gain of the differential amplifier is adjusted so as to give the transfer ratio of 0.5V/1mm of the amount of cone displacement. For lack of more accurate methods, the linearity of the sensors was roughly checked with a micrometer to produce the transfer characteristic shown in Figure 11. Fig.9 Sensor placement II 4. CONCLUSION Fig.11 Sensor transfer characteristic Figure 11 indicates that the linearity of the sensor in the cone displacement range of ±4.5mm is fully satisfactory. In addition, a measurement microphone was used to measure the waveform and THD of the sound pressure produced by the loudspeaker at a frequency of f=100Hz so that a comparison could be made with the results from the sensor. The characteristics of the resulting waveforms are basically the same, both with comparable THD of about 1%. The frequency response of the driver was also measured both by the microphone and the sensor, with the results shown in Figure 12. Fig.12 Measured frequency responses The red line on the chart indicates the output signal from the sensor. It can be seen that the amount of cone displacement decreases at a slope of 12dB/octave above frequencies exceeding 40Hz. The green line on the chart shows the sound pressure level measured by the microphone while the blue line plots the level of noise at the output of the sensor (when the cone is not excited). The resulting S/N ratio is approximately 40dB for frequencies up to 100Hz while at the frequency of about 1kHz the ratio measures 0dB. The type of sensor described in this paper can have practical application in measuring loudspeaker cone displacement within a limited frequency range not exceeding 2-3 octaves. In the specific example presented here, the sensor has been used effectively in the frequency range from 0Hz to 200Hz. At frequencies above f=200Hz, however, sensor noise becomes an issue. To suppress the noise and ensure good temperature stability of the sensing unit, two photo-interrupters in a differential connection have been used, together with the accompanying electronic circuitry. The linearity of the sensor achieved by this design is very good, particularly for large cone displacements and low frequencies (basically all the way down to 0Hz), suggesting that this type of sensor may be efficiently employed in servo control of low-frequency drivers. In practice, such an application would also require the use of differentiators or integrators, depending on which signal is used as a reference (the one from the sensor or the signal from the output amplifier). The effect of the physical implementation of the barrier on the cone of the loudspeaker is not evident as the TS parameters of the loudspeaker have remained unchanged. With additional photo-interrupters for decoding the resting position of the cone, this sensor has the potential of a successful application in driver and power amplifier overload protection circuits as well (e.g. circuits that guard against abnormal or excessive cone excursion, DC offset and so on). 5. REFERENCES [1] L. L. Beranek: Acoustics, New York, NY: McGraw Hill, 1954. [2] M. Colloms: High Performance Loudspeakers, Fifth Edition, Chichester, England: John Wiley and Sons,1998. [3]H. F. Olson: Acoustical Engineering, Professional Audio Journals, Inc. PO Box 31718, Philadelphia, PA 19147-7718, 1991. [4]J. Borwick: Loudspeaker and Headphone Handbook, Butterworth & Co. Ltd, 1988. [5] Clark. J. Radcliffe, Sachin D. Gogate, Velocity feedback compensation of electromechanical speakers for acoustic applications, Michigan St. University, 1997. [6] C-Y Chen, G T-C Chiu, C-C Cheng, H Peng: Passive voice coil feedback control of closed-box subwoofer systems, IMechE2000, 2000. [7] D. De Greef, J. Vandewege: Acceleration feedback loudspeaker, Wireless World, 1981, 32-36. [8] M.O. Hawksford: Distortion reduction in movingcoil loudspeaker system using current-drive technology, J. Audio Engineering Soc., 1989, 37, 129148. [9] J.F. Novak: Performance of enclosures for low resonance high compliance loudspeaker, J. Audio Engineering Soc., 1959, 7, 29-37. [10] Panasonic, Siemens, Honeywell: Optocouplers, Application notes.