Gas Sensor with Electroacoustically Coupled Resonator

Transcription

1 Gas Sensor with Electroacoustically Coupled Resonator F. Granstedt a, 1, M. Folke a, Y. Bäcklund a, B. Hök b a Mälardalens University, Box 883, S Västerås, Sweden b Hök Instrument AB, Flottiljgatan 49, S Västerås, Sweden Abstract A new configuration for a gas sensor is demonstrated. The configuration consists of an electroacoustic element coupled to an acoustic resonator, such as Kundt s tube, exhibiting a resonance frequency that is related to the velocity of sound, which, in turn, is a function of the molecular mass of the gas within the resonator. Electrical impedance measurements were performed, whereby a resonance peak attributable to the resonator was identified. Contributing effects to the quality factor, Q, of the resonance, was analyzed. Predictable shifts of the resonance frequency were observed when adding CO 2 and He to air, and when varying the resonator length. Linearity within the experimental accuracy was confirmed. The new sensor configuration offers the potential advantages of smaller size, improved dynamic response, and lower cost. Keywords: gas sensor, electroacoustic element, acoustic resonator 1. Introduction Acoustic gas sensors based on the measurement of the velocity of sound are well-known [1-6], and established in certain applications, such as measurement of composition of binary gas mixtures, humidity control at elevated temperatures [2-4], and indoor air quality control [5, 6]. These devices are all based on the classical equation c=(rtγ /M) 1/2 (1) where c is the sound velocity (m/s), R=8.314 J/mol K is the general gas constant, T is the absolute temperature, γ is the ratio between the heat capacities at constant pressure and constant volume, and M the molecular mass (kg/mol) of the gas. The sensor type can be used for measurement of small concentrations of an atypical pollutant in air, provided that the pollutant has a molecular mass (M x ) differing from that of air (M). Then the concentration C x of the pollutant can be calculated from C x =2M c/(m x -M)c. (2) where c/c are small relative variations of the sound velocity induced by the pollutant, and assuming that T and γ are constant. 1 Corresponding author. Fax: +46 (0) , fredrik.granstedt@mdh.se

2 Typically, these sensors consist of a permeable gas cell, including an ultrasonic transmitter/receiver pair. The variations of the sound velocity are measured by means of variations in transit time [2] or phase shift [6]. We are now proposing the simplified arrangement depicted in Fig 1, employing only one electroacoustic element. Main potential advantages of the arrangement of Fig 1 compared to existing designs [1-6] are reduced size, implicating improved dynamic response, and simplified assembly, which will result in lower production cost. 2. Theory The simplified arrangement with a single electroacoustic element coupled to a permeable gas cell in the form of a perforated tube with a reflecting wall, is supposed to function as an acoustic resonator. The tubular cavity with length L constitutes a classical Kundt s resonator, with resonating frequencies f n : f n =nc/2l, n=1,2,3,. (3) We have examined the detailed electrical impedance Vs frequency characteristics of the electroacoustic element. This characteristics is expected to be influenced by acoustic coupling of the resonant behavior of the cavity. An important property of acoustic resonators is the quality factor, Q, of the resonance, defined as the ratio between stored and dissipated power. The performance of the proposed sensor, e g the resolution and the sensitivity, will be highly dependent on its value. A number of determining mechanisms of power dissipation, and consequently, the Q factor, may be identified. Such mechanisms are: (a) Viscous loss due to internal friction between the gas molecules themselves and the resonator walls, (b) absorption of sound, (c) reflection loss via the resonator walls, (d) radiative loss in the case of an open geometry, and (e) loss due to the electroacoustic element coupled to the cavity. The respective contributions from the sources (a)-(d) were calculated for an operating frequency of 40 khz, using the following relations and parameters available from standard literature [7, 8, 9]: Q (a) = πρc 2 /400 η f Q (b) = 1/mλ Q (c) = 1 / 2(1-((1-Z 1 /Z 2 )/(1+Z 1 /Z 2 ))) 2 Q (d) = 100/π.. (4a).. (4b).. (4c).. (4d) ρ, η, and m are the density, viscosity and sound absorption coefficient of air, respectively, and Z 1 and Z 2 are the acoustic impedance s of air and the reflecting wall. The length and diameter of the Kundt s tube were set to be λ/2, and λ/5, respectively, λ being the acoustic wavelength. The results

3 are summarized in Table I, in which the inverse Q factors of each mechanism and their values are tabulated. The overall Q may be calculated from: 1/Q = Σ 1/Q (a)-(e).. (5) the dominating loss mechanism, as evidenced by table I, is the radiative (d) mechanism, and can be avoided altogether by choosing an acoustically closed resonator. Mechanism (e) is highly dependent on the actual transducer being used. 3. Experiments The electrical impedance characteristics of electroacoustic elements operating at approximately 40 khz (ultrasonic piezoelectric transmitters operating at approximately 40 khz SQ-40-T/10B, Low Power Radio Solution, LTD, Oxon., UK) was studied by measuring voltage and current in the frequency range khz. All measurements were performed in a gas tight chamber with a volume of 14 liters indoor air (Fig 2), at a temperature of approximately 22 C and 30 % relative humidity. To ensure proper gas mix, the chamber included a small fan. Temperature and humidity were kept constant during each of the measuring sequences that lasted about five minutes. Impedance and frequency measurements were performed with a voltmeter meter (Agilent, 34970A) connected to a personal computer. The impedance and frequency measurements were performed about two minutes after the gas administration to ensure proper gas mixing. An impedance reference measurement was performed with the electroacoustic element covered with loosely packed cotton, to exclude the influence of sound reflections. All other measurements were performed with the transmitters placed at one end of a plastic tube. The tube was perforated to make it permeable to gas. The inside diameter of the tube is dependent of the transmitter outer diameter, which is 9 mm. A reflecting surface was located at the other end of the tube. The distance between the transmitter and the reflecting surface represents 1.5 wavelengths, for indoor air, at the frequency of the transmitter to give a standing wave. To show the influence of the molecular mass, controlled volumes of carbon dioxide (CO 2 ) and helium (He) were injected into the chamber and mixed with the normal indoor air. The administration of the gas into the chamber took about two minutes. The sensor was also exposed to known concentrations of CO 2 to evaluate in more detail, the variations of the peak impedance and frequency as functions of CO 2 concentration. Equation 1 shows the relation between the molecular mass and the sound velocity. A lower molecular mass gives a higher sound velocity. Then a higher sound velocity, of course, gives a shorter wavelength when the frequency is fixed. This means that a shift in distance should have the same effect of the impedance as a change in the molecular mass. To show the correlation of the influence of the molecular mass and the distance between transmitter and reflector, the distance between the transmitter and the reflecting surface was changed ±0.5 wavelengths from the 1.5 wavelengths in small steps.

4 4. Results Fig 3 shows measurements of the impedance characteristics of an electroacoustic element with and without coupling to a resonator. The transmitter itself exhibits an impedance maximum at approximately 40.3 khz as dominating feature. The standard deviation when measuring on a batch of 250 elements was 500 Hz. When adding the resonator with a reflecting wall at a distance of approximately 13 mm=1.5 λ, an additional peak, having a maximum at 39.0 khz, occurred. The Q factors of both peaks, measured as relative half-value widths, were Large variations in Q factors were observed between individual electroacoustic elements. This can be seen when comparing the impedance curves of Fig. 3, 4, 5, which were recorded on different elements. Each line in the figures (4-6) represents a mean value plot of four measurement sequences, between khz in steps of 20 Hz. Measurements of the impedance change of a transmitter when 100ml CO 2 or He is mixed with the air in the gas chamber is shown in Fig 4. The resulting concentrations are approximately 0.7 % by volume in both cases. The additional peak of the resonator shifts to a higher frequency when He is added, and to a lower frequency for addition of CO 2. For different distances, between the transmitter and the reflecting surface, the impedance change as shown in Fig 5. As predicted by eq. (3), the additional peak shifts to a lower frequency when the distance increases and to a higher frequency when the distance decreases. Table 2 shows the standard deviation, mean value and median for the electrical impedance and the resonance frequency for different CO 2 concentrations. No evidence of impedance or frequency shift due to self-heating was observed. Fig 6 shows measurements of the impedance change of an electroacoustic element with a reflector at varying concentrations of CO 2 in the gas chamber. The concentration was increased by 0.7 volume % between each measurement sequence. When the concentration increases, the molecule mass increases, and the peak, as predicted, moves to the left. From the data of Fig 6, peak frequencies and impedances may be plotted against CO 2 concentration, as shown in Fig 7. Approximately linear relations can be noted within the experimental accuracy of about ±5%. 5. Discussion A new acoustic gas sensor configuration has been demonstrated, having significant potential advantages compared to existing types. Ideal performance would be obtained with a high Q resonator coupled to a transducer with a flat frequency response. From simple theoretical arguments it was shown that acoustically closed resonator structures are superior to open ones. Gas exchange to the cavity can still be obtained by perforating the sidewalls. As shown in Fig 7, a change in concentration gives approximately linear changes in peak impedance and frequency. Incomplete mixing, or temperature variations may cause observed deviations from linearity during the measurement sequence.

5 The experimental Q factors are considerably smaller than the highest theoretically possible, according to table 1. This is possibly caused by the electroacoustic element, which by definition is not an ideal reflector. The differences of the Q factors observed between individual elements also indicate that this is the dominant cause. The reproducibility shown in table 2 seems to be acceptable, although the standard deviation for the resonance frequency is quite high for some concentrations, and probably influenced by the sampling rate. The experimental model used for the present demonstration does not represent an optimized solution. Rather, it was chosen on the basis that ultrasonic devices operating at 40 khz are readily available at low cost. The 40 khz transmitter used in the experiments exhibits resonance s which by themselves dominate the overall behavior, and even mask the resonator properties. Still we have been able to verify the basic hypothesis that a single electroacoustic device combined with a resonance cavity can be used to advantage in sensor applications. However, before these advantages can be exploited, it is necessary to develop a theoretical model of the coupling between the resonator and the elctroacoustic element, in order to make predictions of the detailed behavior possible. Furthermore, it is necessary to develop a scheme for electronic interfacing to the electroacoustic element. A possible strategy is to let the resonator peak determine the frequency of a free-running oscillator. An advantage of such an approach is the frequency output, a problem could be undesired locking to the spurious peaks due to the transducer element. Using a phase-locked loop (PLL) makes it possible to reduce the capture frequency range [10], and hence to control the locking behavior. A second possibility would be to use an electroacoustic element with a flat frequency response. This would possibly result in a higher Q, with an accompanying higher resolution and sensitivity. On the other hand, it would reduce the noise immunity of the sensor. 6. Conclusion We have been able to verify the basic hypothesis that a single electroacoustic device combined with a resonance cavity can be used in gas sensor applications. Our new gas sensor configuration is expected to have significant potential advantages compared to existing types. Quite far from being optimized, a continuing R&D effort is still necessary. 7. Acknowledgments Financial support from Västmanlands FoU-Råd, NUTEK, Teknikbrostiftelsen and KK-Stiftelsen is gratefully acknowledged.

6 8. Biography of the authors Fredrik Granstedt has been a Ph. D student at Department of Electrical Engineering, Mälardalens University, Sweden since His research field is electroacoustic gas measurement mainly for medical applications. Mia Folke has been a Ph. D student at Department of Electrical Engineering, Mälardalens University, Sweden since Her research field is electroacoustic gas measurement mainly for medical applications. Ylva Bäcklund was born in Västerås, Sweden, in Her Ph D degree in1992, on silicon micromachining for sensors, was followed by leadership of a research group at Ångström laboratories, Uppsala University. In Dec she appointed as at professor in electronics at Mälardalens University. Bertil Hök was born in Molkom, Sweden, in His Ph. D degree in 1975, on medical manometry, was followed by sensor research and development work at Siemens-Elema and ASEA. In 1986 he formed a company, Hök Instrument AB, Västerås, Sweden. The company is developing, producing and marketing instruments for patient monitoring, based on new sensors. Since 1984, he has also been an associate professor at Uppsala University, and has conduced research on micromechanics, sensors an actuators, mainly for medical applications.

7 References [1] P. Hauptmann. Sensoren: Prinzipien und Anwendungen. C. Hanser Verlag, München, 1991, pp [2] L. Zipser, J Labude. Technisches messen, 58 (1991) [3] L. Zipser, J Labude. Technisches messen, 58 (1991) [4] L. Zipser, Sensors and Actuators B7 (1992) [5] B. Hök, M. Tallfors, G. Sandberg, A. Blückert. A new sensor for indoor air quality control, Proc. Eurosensors XII, Southampton, U.K. Sepember 1998, [6] B. Hök, M. Tallfors, G. Sandberg, A. Blückert. Acoustic Gas Sensor with ppm Resolution, Proc. Eurosensors XIII, The Hague, The Netherlands. Sepember 1999, [7] H. F. Olson, Music, Physics and Engineering, 2 nd Ed., Dover Publications, Inc., New York, [8] L. L. Beranek, Acoustics, Mc Graw-Hill, New York, [9] A. B. Bhatia, Ultrasonic Absorption: An Introduction to the Theory of Sound Absorption and Dispersion in Gases, Liquids, and Solids, Dover Publications, New York, [10] F. M. Gardner, Phaselock Techniques, 2 nd Edition,Wiley&Sons, New York, 1979.

8 Loss mechanism 40kHz Viscous Absorption Wall reflection Radiation Table 1.

9 Reference 0.7% CO 2 1.4% CO 2 2.1% CO 2 2.9% CO 2 Resonance frequency Electrical impedance Resonance frequency Electrical impedance Resonance frequency Electrical impedance Resonance frequency Electrical impedance Resonance frequency Electrical impedance Standard deviation Mean value 8,94 0,48 11,55 0,50 0 0,26 0 0,10 10,95 0, , , , , ,9 Median , , , , ,9 Table 2

10 Table 1. Contributions to the Q factor from various loss mechanisms of acoustic resonators at 40 khz. Table 2. Standard deviation, mean value and median for the resonance frequency and the electrical impedance for different CO 2 concentrations.

11 Electroacoustic element Perforated tube Reflector 12 mm 28 mm Fig 1.

12 Fig 2.

13 Electrical impedance (Ω) Frequency (Hz) Fig 3.

17 Reconance frequency (Hz) Electrical impedance (Ω) CO2 concentration (%) Fig 7.

18 Fig 1. Gas sensor consisting of a two-terminal electroacoustic element coupled to a tubular resonator. Fig 2. Photograph of the measurement setup. Fig 3. Electrical impedance (Ω) as a function of frequency (Hz) for the 40 khz electroacoustic element with and without resonator. Fig 4. Electrical impedance (Ω) as a function of frequency (Hz) for the assembled sensor in air and additions of 0.7 % CO 2 and He, respectively. Fig 5. Electrical impedance (Ω) as a function of frequency (Hz) for the electroacoustic element when changing the distance to the reflecting wall of the resonator. Fig 6. Electrical impedance (Ω) as a function of frequency (Hz) for the additional peak when changing the CO 2 concentration. Fig 7. Resonance frequency [ ] and Electrical impedance [-] as a function of CO 2 concentration.