Gas sensor with electroacoustically coupled resonator F. Granstedt a,* , M. Folke a , Y. Ba Ècklund a , B. Ho Èk b a Ma Èlardalens University, P.O. Box 883, S-721 33 Va Èstera Ês, Sweden b Ho Èk Instrument AB, Flottiljgatan 49, S-721 31 Va Èstera Ês, Sweden Abstract A new con®guration for a gas sensor is demonstrated. The con®guration 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 identi®ed. 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 con®rmed. The new sensor con®guration offers the potential advantages of smaller size, improved dynamic response, and lower cost. # 2001 Elsevier Science B.V. All rights reserved. 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 tempera- tures [2±4], and indoor air quality control [5,6]. These devices are all based on the classical equation c  RT g M   1=2 1) where c is the sound velocity m/s), R  8:314 J/mol K the general gas constant, T the absolute temperature, g 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 concen- trations 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  2MDc M x  Mc 2) where Dc/c are small relative variations of the sound velocity induced by the pollutant, and assuming that T and g are constant. Typically, these sensors consist of a permeable gas cell, including an ultrasonic transmitter/receiver pair. The varia- tions of the sound velocity are measured by means of variations in transit time [2] or phase shift [6]. We are now proposing the simpli®ed 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, impli- cating improved dynamic response, and simpli®ed assem- bly, which will result in lower production cost. 2. Theory The simpli®ed arrangement with a single electroacoustic element coupled to a permeable gas cell in the form of a perforated tube with a re¯ecting wall, is supposed to func- tion 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 versus 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, de®ned as the ratio between Sensors and Actuators B 78 2001) 161±165 * Corresponding author. Fax: 46-21-10-1650. E-mail address: fredrik.granstedt@mdh.se F. Granstedt). 0925-4005/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII:S0925-400501)00807-3