Force Sensitivity and Stability of Multi-electrode Integrated Quartz Resonator Bo MA 1, Wen-jie TIAN 1,*, Qin-jiang ZHAO 2, Fu-bin CHEN 1 and Ou LEI 1

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1 2017 International Conference on Mechanical and Mechatronics Engineering (ICMME 2017) ISBN: Force Sensitivity and Stability of Multi-electrode Integrated Quartz Resonator Bo MA 1, Wen-jie TIAN 1,*, Qin-jiang ZHAO 2, Fu-bin CHEN 1 and Ou LEI 1 1 Key Laboratory for Sensor, Beijing Information Science & Technology University, Beijing, , China 2 Department of Physical Science and Technology, Kunming University, Kunming, , China *Corresponding author Keywords: Multi - electrode quartz resonator; Force - sensitive characteristics, Frequency stability. Abstract. A new multi-electrode quartz resonator and signal processing circuit is designed on the basis of analyzing the stress distribution in the wafer when the quartz wafer is subjected to force. When a plurality of resonators were simultaneously excited at room temperature and atmospheric conditions, the linearity of force-frequency characteristics and frequency stability on the resonators corresponding to the respective electrodes are excellent. After the interaction frequency difference and superposition processing to the frequency of each resonator, the force frequency coefficient of the output frequency signal can reach Hz/N, the linear correlation R is , and the frequency stability can reach the magnitude of Introduction Piezoelectric quartz resonators that has high output signal accuracy, digital output, anti-interference ability, fast output response, good stability and other advantages have attracted much attention. Quartz force sensitive sensor can be applied to the force, weighing, acceleration, attitude measurement and other fields. Based on the quartz piezoelectric effect and the force-sensitive mechanism of the quartz resonator and wafer stress simulation analysis, a cluster-type multi-electrode force-sensitive resonator and an effective digital signal processing circuit have been designed. It can improve the frequency-sensitive characteristics and frequency stability of the resonator while suppressing the influence of the interference factors of the resonator. This provides the basis for the development and application of the force-sensitive characteristics of the quartz resonator [1]. Structure and Circuit Design of Quartz Resonator Resonator Wafer Internal Stress Analysis The basic structure of the quartz resonator includes a quartz wafer, electrodes, and leads. Its core component is a quartz chip as a mechanical vibrator, the electrodes are deposited on the surface of the quartz wafer, and the leads are bonded to the electrode through the conductive adhesive. The electric excitation signal is applied to the wafer surface through the electrode. In the electric field, the wafer produces mechanical vibration, at the same time, the electrical signal is transmitted through the electrodes. When the frequency of the excitation signal is the same as the natural frequency of the wafer, resonance occurs [2]. Disc-type quartz crystal resonator structure shown in Figure 1. Figure 1. Structure of a disc - type quartz crystal resonator. 1

2 The force sensitivity of the quartz resonator is caused by the change in the stress in the crystal when the quartz crystal is subjected to force. According to the piezoelectric effect of quartz crystal, The force sensitivity characteristic of the quartz resonator based on a certain cutting type can be expressed by the force sensitivity coefficient K F and the force-to-frequency conversion coefficient S F [3]. Under the radial force, the K F and S F of the quartz resonator can be expressed as K. (1). (2) The electrodes of the integrated multi-electrode force-sensitive resonators studied in this paper are in different positions on the same quartz crystal substrate. The analysis of the internal stress distribution when the force is applied by the crystal is the basis of the electrode position design. In this paper, a disc-type AT-cut quartz wafer is used as the vibrator element. In the actual sensor conversion structure, the contact area between the quartz wafer and the structural member is a circular, so it uses the method of applying the arc force to analyze the stress distribution inside the wafer. When using the simulation software for stress analysis, the division of the grid unit is divided into free forms on the basis of defining material performance parameters, as shown in picture 2. When a 5N pair of diameters is applied to the arc surface of the disk in the y-axis direction [3,4], the calculated stress distribution in the quartz wafer is shown in Figure 3. Figure 2. Model after dividing the grid. Figure 3. Distribution of stress in quartz crystal. When designing a plurality of electrodes on a quartz wafer, a quartz crystal resonator with a large difference in force frequency coefficient can be obtained at a position where the stress variation is large [5,6]. Design of Resonator Electrodes Compared with the traditional single-electrode quartz resonator, multi-electrode quartz resonators need to consider that each pair of electrodes. Each pair of electrodes can work independently at the same time. And it needs to consider the problems of electrode starting, the elimination of parasitic vibration caused by electrode resonance, Inter-electrode coupling, electrode-to-external coupling and non-harmonic overtone when resonating, etc. So its requirements are more stringent to the quartz wafer s size, electrode s size and position. Based on the above factors, the AT cutting quartz wafer having a radius of 7 mm, a thickness of mm, a density of 2650 kg /m 3 is selected in this experiment. The wafer surface is polished and aged, and its edges are chamfered with a width of 1 mm. While a small gap perpendicular to the X axis is cut at the position of the point where the X axis intersects the circumference in the forward direction and its chord length is 2mm ~ 3mm. The six pairs of electrodes are evenly designed on a circle with a center radius of 5 mm. Its diameter of electrodes is 1mm, and the width of electrode metal wires is 0.5mm, as shown in Figure 4. Figure 4. Structure of multi-electrode quartz resonator. 2

3 The Circuit of Excitation and Signal Processing This chapter mainly uses altium designer software to complete the circuit design and PCB board drawing. In order to suppress the interference caused by temperature, quartz crystal material and other differences, this article uses the processing method that the six groups of frequency signals first, and then sum, numerical display [7]. The circuit consists of several modules as shown in Figure 5. Figure 5. Block diagram of the processing signal. Characteristic Test of Quartz Resonator Force - Frequency Characteristics The frequency signals of six-electrode quartz resonator obtained by the oscillation circuit are f 1, f 2, f 3, f 4, f 5, f 6. f ij is the between f i and f j, that is, f 12 = f 1 -f 2, f 34 = f 3 -f 4, f 56 = f 5 -f 6. Let f=f 12 +f 34 +f 56, that is, f is the sum obtained by processing to the six frequency signals. The position of the six electrodes in this test is shown in Fig. 4. Under the action of the excitation circuit, the resonators corresponding to the six electrodes can resonate independently. And the resonant frequency of the resonator of A electrode and C electrode are subjected to the difference frequency, the difference between the B electrode and the D electrode is made, and then the A electrode and the F electrode are discriminated, inferred f AC, f BD, f AF, and their sumf=f AC + f BD + f AF. When the wafer is subjected to radial force. The frequency variation of each frequency difference is represented by f AC, f BD, f AF, f, and f= f AC + f BD + f AF. The results of the test were linearly fitted by least squares. As shown in Fig. 6, the force-frequency sensitivity characteristic linear y, the linear correlation coefficient R and the force-to-frequency conversion coefficient SF are obtained. As a result, (a) Group f AC : y = x , R=0.9996, S F = Hz/N. (b) Group f BD : y = x , R=0.9992, S F = 840.5Hz/N. (c) Group f AF : y = x , R=0.9989, S F = Hz/N. (d) Group f : y = x , R=0.9997, S F = Hz/N. 3

4 (a)force frequency characteristics of AC electrode after (b)force frequency characteristics of BD electrode after (c)force frequency characteristics of AF electrode after (d)the force frequency characteristics after the and summation Figure 6. Fit straight line of force frequency sensitivity feature. From the above data can be obtained, the linearity of the force-frequency characteristics of the three sets of signals is better, and the maximum force-to-frequency conversion factor is Hz / N and the minimum is Hz / N. After the sum of the three groups of differential frequency signal, the final output signal s force - frequency conversion coefficient is SF = Hz / N, the linear correlation coefficient R = If the frequency signal of the resonator corresponding to the six pairs of electrodes is differentiated by the frequency difference (15 series signals can be obtained) and then sum, the force-frequency conversion coefficient of the final output signal will be greatly improved. Frequency Stability As the core device of quartz force sensor, the stability of quartz force sensitive resonator directly determines that the performance of the force sensor is good or bad. The XHTF 3579 frequency stabilization tester was used to measure the respective force sensitive resonators on the same wafer. A data is collected every one second, and a frequency stability is calculated every ten seconds [8]. By continuous measurement, the values of eighteen frequency stability σ (τ) can be obtained. Analyzing the experimental data, the frequency stability of the force-sensitive resonators corresponding to the six pairs of electrodes is in the order of The frequency stability line diagram shown in Figure 7. (a)the frequency stability of A, B, C electrode (b)the frequency stability of D, E, F electrode Figure 7. Frequency stability of each resonator on the same chip. The average frequency stability areσ A =2.854E-10, σ =4.188E-10, B 4 σ =6.129E-10, C σ = D

5 E-10, σ =2.864E-10, σ =2.478E-10. The reasons causing fluctuations in frequency stability may E F be: (1) the noise impact of the test environment; (2) the metal film electrode oxidation of the quartz resonators; (3) the stability of the excitation circuit. Summary The stress distribution inside the wafer is simulated and analyzed using ANSYS finite element simulation software when the wafer is subjected to radial forces. Based on the traditional quartz resonator, six electrode quartz force sensitive resonators are designed. Based on the common mode rejection principle, resonator excitation circuit and the frequency difference processing circuit and the summing circuit of the resonator are designed. After testing, the resonators corresponding to the six pairs of electrodes can vibrate independently in the circuit excitation. Differential frequency circuit has better force-frequency linearity for three groups of signals by mutually different frequency difference processing to six resonators. After summing to three sets of signals, the coefficient of force-frequency conversion S F is Hz / N, the linear correlation coefficient R is , the frequency stability of six resonators can reach order, and the average is E-10 ~ E-10. Acknowledgements This research was financially supported by the National Natural Science Foundation of China ( ), Beijing Natural Science Foundation ( ), Beijing natural science foundation of key projects (B) (KZ ), Key Laboratory of Modern Measurement & Control Technology (Beijing Information Science & Technology University), Ministry of Education. References [1] Shawn Logan. The Power Consumption of Body Wave Quartz Crystal Components[J]. Today Electronics, 2010(5): [2] Zhen Feng. The Collection of 51 Single-chip Typical Application Development Examples[M]. Beijing: Press of China Railway, [3] Sun Rong, Zhou Tao. The Failure Analysis of Resonator Chip Structure Stress and the Measures to Reduce Impact[J]. High-tech Enterprises of China, 2013(5): [4] Zhao Shichao, Shang Jianguo. The Simulation Analysis of Quartz Crystal Resonator[J]. Journal of Xi'an Aeronautical Technical College, 2011, 29(3): [5] Tian Wenjie, Lu Junling, Liu Lingling, Zhang Fuxue. The Characteristics and Application of the Vibrating Quartz Crystal Resonator[J]. Piezoelectrics & Acoustooptics. 2006(10) [6] Wu Rongxing,Li Jiliang, Yu Lianzhen, Wang Ji. Three - dimensional Finite Element Analysis of High Frequency Vibration of Quartz Crystal Plate[J]. Piezoelectrics & Acoustooptics. 2013(03) [7] Wei Haichao, Zhang Jilong, Chen Youhua, Wang Yanchao, Chen Yuanyuan,Wang Zhibin. Study on Impedance Matching Characteristics of Piezoelectric Crystal with Light Modulator[J]. Piezoelectrics & Acoustooptics. 2013(02) [8] Song Xinju, Li Dong, Wang Yanlin, Liu Guili. Study on Phase Detection Technology for Quartz Crystal-Frequency Test[J]. Sensor World. 2006(11) 5