Meas. Sci. Technol. 11 (2000) 1565 1569. Printed in the UK PII: S0957-0233(00)15873-4 A temperature insensitive quartz resonator orce sensor Zheyao Wang, Huizhong Zhu, Yonggui Dong and Guanping Feng Department o Precision Instruments, Tsinghua University, Beijing, 100084, People s Republic o China E-mail: wangzy@post.pim.tsinghua.edu.cn Received 27 July 2000 Abstract. This paper describes a novel sel-temperature-sensing method and temperature compensation o a quartz resonator orce sensor based on dual-harmonic-mode oscillation. An AT-cut resonator, used as a orce sensing element, is excited at the undamental and the third overtone modes simultaneously by a specially designed oscillator. The beat requency between three times the undamental mode requency and the third overtone mode requency is linear with temperature and independent o the unknown orce. Consequently, the temperature and orce can be obtained simultaneously by the beat requency and the third overtone mode requency, respectively. As compared with conventional temperature compensation using a thermistor as a separate temperature sensor, the novel method can eliminate the temperature measurement error induced by the dierence in the thermal time constants and the temperature gradient between the quartz resonator and the thermistor. The implementation o the dual-mode oscillating circuit is described, as well as a special method to reduce the requency temperature anomalies. The experimental results show that, in a dynamic temperature environment, the measurement error o the orce sensor using the sel-temperature-sensing method decreases by 80% as compared with the method using a separate temperature sensor. Keywords: quartz resonator, orce sensor, sel-temperature-sensing, temperature compensation, dual-mode 1. Introduction The quartz resonator orce sensor, employing a quartz resonator as the sensing element, is a novel digital sensor with a requency output. The orce measurement is accomplished by measuring the requency shits modulated by the unknown orce diametrically applied to the rim o the quartz resonator. The historic development o the quartz resonator orce sensor originated rom the utilization o quartz resonators as requency control elements in electrical engineering. Ater the exploration o the orce requency eect, that is the requency shits are linear to the magnitude o the external orce, many investigators have contributed greatly to the research o quartz resonator orce sensors [1 4]. The key advantages o the quartz resonator orce sensors are digital output, high resolution, high accuracy, good long-term stability and low power consumption. AT-cut quartz resonators are the most commonly used sensing elements because o their high orce sensitivity and simple manuacture. Since the orce sensitivity o AT-cut quartz resonators is temperature dependent, temperature compensation should by deinitely considered in its application to orce sensors [5, 6]. The most common temperature measurement method in conventional temperature compensation makes use o a separate thermistor, placed in close proximity to the resonator, as a temperature sensor. This method induces inaccuracies due to a thermal lag stemming rom the dierences in the eective thermal time constants and the spatial location between the crystal and thermistor. To overcome these limitations, Kuster and Leach [7] proposed a method or stimulating the b-mode or the orce measurement and the c-mode or the temperature measurement simultaneously. However, activity dips o the b-mode reported later prevent this idea rom prevailing [8]. In 1989, Schodowski [9] presented a new sel-temperature-sensing method o an SCcut resonator using a pair o harmonically related c-modes in a dual c-mode oscillator. The beat requency between three times the undamental mode requency and the third overtone requency was used to precisely sense the temperature o the resonator. Due to the stress- and temperature-compensated characteristics o SC-cut resonators, the dual harmonic excitation o the c-mode avoids the activity dips. This method exhibits quite good results in temperature compensation o a microcomputer-compensated crystal oscillator and quartz crystal microbalance [10 14]. It was reported that the presence o activity dips in AT-cut crystals produce unpredictable resistance changes over the temperature range and makes them useless in thermal sensor application [11]. In this paper, the dual-harmonic-mode excitation method is proposed or temperature measurement and temperature compensation in order to develop a 0957-0233/00/111565+05$30.00 2000 IOP Publishing Ltd 1565
Zheyao Wang et al temperature insensitive AT-cut quartz resonator orce sensor. The beat requency between three times the undamental mode requency and the third overtone requency is almost linear with temperature and is orce independent. Thereore, the beat requency and the third overtone requency are used to sense the temperature and the orce, respectively. However, considering that AT-cut resonators exhibit more serious requency against temperature anomalies than SCcut resonators, the key diiculty is how to eliminate these anomalies. 2. Theory For AT-cut resonators, both the undamental and the third overtone mode requencies are unctions o the temperature and orce, that is the temperature and orce are cross sensitive. The normalized requency changes o both the undamental mode and the third overtone mode can be written as unctions o the applied orce and temperature o the resonator: = F + T where / is the total requency changes, and F / and T / are, respectively, the requency changes induced by the orce and the temperature. According to the requency unction and the relations between the requency and the dimensions and elastic stiness constants, requency changes o the undamental and the third overtone modes against temperature can be written in detail, ater a high-order truncation, as [15]: 1 1 (T 0 ) = T (2),1 T + T,1 T 2 + T (3),1 T 3 3 3 (T 0 ) = T (2),3 T + T,3 T 2 + T (3),3 T 3 (2) where T is the arbitrary temperature and T 0 is the reerence temperature. The numbers 1 and 3 in the subscripts represent the harmonic numbers. n (T 0 ) and n (n = 1, 3 are the harmonic numbers) are the resonant requency at temperature T 0 and the requency change caused by the temperature change o T = T T 0. T (i),n, which is deined as [15]: ( T (i),n = 1 i ) n (3) i! n (T 0 ) T i T 0 is the i-order (i = 1, 2 or 3) requency temperature coeicient o the nth overtone at the reerenced temperature. It can be seen that T (i),n is a unction o T 0 and T. The requency changes induced by the unknown orce are: F = S F F where F represents the unknown orce and S F = K 2 /nd is the orce sensitivity [2]. K is the Ratajski coeicient and D is the diameter o the quartz resonator. For the undamental mode and the third overtone mode, equation (4) can be written as F,1 = S F,1(T )F = [S F,1(T 0 ) + k ST,1 T ]F 1 1 1 (4) F,3 = S F,3(T )F = [S F,3(T 0 ) + k ST,3 T ]F. (5) 3 3 3 Here k ST is the temperature coeicient o orce sensitivity. By deining the beat requency as one obtains b = 3 1 3 (6) b = 3 1 3. (7) Let 3 (T 0 )/ 1 (T 0 ) = λ (8) where λ is a non-integer number and, or AT-cut quartz resonators, experiments show that λ 3. By inserting equations (2), (5) and (8) into equation, the normalized beat requency can be deduced: b b (T 0 ) = 1 3 [3T (i),1 (T 0) λt (i),3 (T 0)] T (i) + F i=1 [ 3SF,1 (T ) 1 (T 0 ) 3S ] F,3(T ). (9) 3 (T 0 ) According to the harmonic eect [15], the irst-order temperature coeicient o the third overtone mode is not equal to that o the undamental mode, while other orders temperature coeicients are identical to those o the undamental mode. Additionally, the orce requency sensitivity is proportional to the harmonic numbers, and the ratio o the requency change to the resonant requency is no more than 10 4. In consideration o the aorementioned conditions, the items containing T 2 or T 3 and the last item o equation (9) are so small that they should be neglected; thereore, equation (11) can be reduced to b (T ) b (T ) = 3T,1 λt,3 T. (10) It can be seen that the normalized beat requency is a linear unction o temperature, and orce independent. Thereore, the temperature o the quartz resonator can be obtained by the beat requency. Figure 1(a) depicts the curve o requencies o the undamental mode and the third overtone mode against temperature, and igure 1(b) depicts the beat requency curve against temperature. Consequently, by stimulating the undamental and the third overtone modes simultaneously, the unknown orce and temperature can be obtained simultaneously and the seltemperature-sensing as well as temperature compensation can be realized. 3. Dual harmonic oscillator Dual-mode excitation is based on the act that when a quartz resonator is excited, many orders o overtone resonant requencies are excited simultaneously. Only the desired requency, being equal to the eigenrequency o the tune networks o the oscillator, occupies most vibration energy and orms the main output. A dual-mode oscillator is a device consisting o two independent oscillators having dierent eigenrequencies 1566
A temperature insensitive quartz resonator Figure 1. Frequency shits o AT-cut quartz resonators against temperature. (a) The requency shits o the undamental mode and the third overtone mode. (b) The beat requency between three times the undamental mode requency and the third overtone mode requency. (a) (b) Figure 2. (a) Block diagram o dual-mode excitation. (b) A dual-mode exciting oscillator. Figure 3. The wave orms o the dual-mode exciting oscillator: (a) the undamental mode, (b) the third overtone mode and (c) the pin o the quartz resonator. coupled to each other by an AT-cut quartz resonator. A block diagram o the dual-mode oscillator and a practical circuit are shown in igure 2. To obtain low power consumption and small dimensions, integrated gate circuits are used. Figure 3 shows the waveorm o the undamental mode, the third overtone mode and the output o the pins o the resonator. It is clear that the undamental mode modulates the third overtone mode. In practice, to acilitate the design and obtain pure resonant requencies, two dierent quartz resonators are used as selective elements in a band pass ilter rather than LC circuits that serve to decouple the adjacent mode signal. The requency o one o the two resonators is equal to the undamental mode requency o the orce sensing resonator, and the other s requency is equal to the third overtone mode requency. Dierent dual-mode oscillators were introduced in [9] and [13]. 4. Elimination o requency anomalies Although Forster [16] reported that as compared with SC-cut resonators, AT-cut resonators display no real disadvantage, AT-cut resonators have no abilities o stress and temperature compensation. Thereore, the requency temperature anomalies and the hysteresis become the key actors which are obstacles to AT-cut resonators in dual-mode temperaturesel-sensing. The reasons or the anomalies and hysteresis cannot be well explained [17]. However, it has recognized that the stresses remaining in the crystal or the platings are important impact actors. In order to compensate or the eect o temperature on the orce sensor, it is necessary to decrease the anomalies and hysteresis and improve the repeatability o the resonant requency. To decrease the anomalies and hysteresis a special method is used. First, place the resonators into a chamber 1567
Zheyao Wang et al Figure 4. The eect o the treatment on the motional resistance and the quality. (a) Changes o the motional resistance. (b) Changes o the quality actor. Figure 5. Block diagram o the temperature compensation o a quartz resonator orce sensor. at a temperature o 120 C or 20 min, then change the temperature to 20 C or 20 min, and repeat this step or 20 times. Secondly, put the resonator in at 120 C or 48 h. This special method is intended to decrease the remained stresses in the crystal or platings. This treatment can improve quality actor (Q value) o both the undamental mode and the third overtone mode and decrease motional resistance. The discontinuous resistance curve in igure 4(a) or the discontinuous quality actor curve in igure 4(b) show that, beore the treatment, the motional resistance o the third overtone mode o a quartz resonator was so great that the resonator could not vibrate at the dual-mode over the whole temperature range. Ater the treatment, the motional resistance decreased and the quality actor increased remarkably, as shown in igure 4(b). The dual-mode vibration occurred at all temperature points. Experimental data show that the treatment can improve the temperature measurement accuracy. 5. Experiments and discussion Figure 5 shows the implementation o the temperature compensation o the quartz resonator orce sensor. The orce sensor uses an AT-cut quartz resonator with a 3.35 MHz undamental mode requency as the orce sensing element. The temperature measurement is accomplished by the seltemperature-sensing o the AT-cut quartz resonator by exciting the undamental mode and the third overtone mode Figure 6. The orce measurement error o quartz resonator orce sensors with dierent temperature measurement methods. requencies simultaneously. The requency shits o the third overtone mode give the magnitude o the unknown orce and the beat requency, which is obtained by multiplying the undamental mode requency by three and then mixing this requency with the third overtone mode requency, gives the magnitude o the temperature. A microprocessor is used to determine the temperature according to the beat requency and then compensate the temperature dependent orce requency sensitivity. As compared with quartz crystals, the separate thermistor used as the temperature sensing element in the conventional temperature compensation method has a larger eective thermal time constant, so in the process o increasing 1568
A temperature insensitive quartz resonator temperature, it measures a higher temperature than the real temperature o the resonator, which leads to over compensation. Similarly, deicient compensation will occur in terms o decreasing temperature. Since the dual-mode seltemperature-sensing method can decrease the error induced by the dierent eective thermal time constants and the thermal gradient, in the dynamic temperature process it can eectively decrease the measurement error. Figure 6 shows the orce measurement error as the temperature changes rom 20 Cto+50 C ater temperature compensation by a conventional thermistor and the dual-mode sel-temperaturesensing method separately. It can be seen that the dualmode sel-temperature-sensing method can decrease the orce measurement error rom 2%FS (ull scale) to 0.3%FS. Thus, the method improves the accuracy signiicantly, and the orce sensor is nearly temperature independent. 6. Conclusion A temperature insensitive AT-cut quartz resonator is accomplished by dual-mode sel-temperature-sensing and microprocessor temperature compensation. It eliminates the thermal lag compared with a conventional, separate sensing element and signiicantly improves the measurement accuracy, especially in a wide temperature range or in an environment in which the temperature changes rapidly. As a result o the inability to compensate or stress and temperature, AT-cut resonators should be subjected to special treatment to reduce the anomalies and the hysteresis. Reerences [1] Karrer E and Ward R 1977 A low-range quartz resonator pressure transducer ISA Trans. 16 90 8 [2] EerNisse E P, Ward R W and Wiggins R B 1988 Survey o quartz bulk resonator sensor technologies IEEE Trans. Ultra. Ferroelectr. Freq. Control 35 323 30 [3] Bens E, Groshl M, Burger W and Schmid M 1995 Sensors based on piezoelectric resonators Sensors Actuators A 48 1 21 [4] Clayton L D and EerNisse E P 1998 Quartz thickness-shear mode pressure sensor design or enhanced sensitivity IEEE Trans. Ultra. Ferroelectr. Freq. Control 55 1196 203 [5] Dulmut B, Bourquin R and Shibanova N 1995 Frequency-output orce sensor using a multimode doubly rotated quartz resonator Sensors Actuators A 48 109 16 [6] Besson R J et al 1993 A dual-mode thickness-shear quartz resonator pressure sensor IEEE Trans. Ultra. Ferroelectr. Freq. Control 40 584 91 [7] Kuster J A and Leach J G 1978 Dual mode operation o temperature and stress compensated crystals Proc. 32nd Ann. Frequency Control Symp. pp 389 97 [8] Vig J R, Filler R L and Kosinski J A 1982 SC-cut resonator or temperature compensated oscillators Proc. 36th Ann. Frequency Control Symp. pp 181 6 [9] Schodowski S S 1989 Resonator sel-temperature-sensing using a dual-harmonic-mode crystal oscillator Proc. 43th Ann. Frequency Control Symp. pp 2 7 [10] Pierce D E, Kim Y and Vig J R 1997 A temperature insensitive quartz microbalance Proc. 51st Ann. Frequency Control Symp. pp 41 8 [11] Azcondo F J, Blanco J C and Peire J 1995 New digital compensation technique or the design o a microcomputer compensated crystal oscillator IEEE Trans. Industrial Electron. 42 307 15 [12] Kosykh A V and Abramson I V 1996 Dual-mode excitation o quartz crystals without dips o activity on the C and B modes Proc 1996 10th Eur. Frequency and Time Forum paper 418, p 238 [13] Filler R L and Vig J R 1989 Resonators or the microcomputer compensated crystal oscillator Proc. 43rd Ann. Frequency Control Symp. pp 8 15 [14] EerNisse E P and Ward R W 1985 Resonator transducer system with temperature compensation US Patent Speciication 4535638 [15] Ballato A and Lukaszek T 1975 High-order temperature coeicients o requency o mass-loaded piezoelectrical crystal plates Proc. 26th Ann. Frequency Control Symp. pp 10 20 [16] Forster H J 1982 Thermal hysteresis o AT+SC-cut quartz crystal resonators automated measurement method and results Proc. 36th Ann. Frequency Control Symp. pp 140 58 [17] Kuster J A and Vig J R 1990 Thermal hysteresis in quartz resonators a review Proc. 44th Ann. Frequency Control Symp. pp 165 75 1569