A Wireless Passive Pressure and Temperature Sensor via a Dual LC ...

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A Wireless Passive Pressure and Temperature Sensor via a Dual LC Resonant Circuit in Harsh Environments Qiulin Tan, Tao Luo, Student Member, IEEE, Tanyong Wei, Jun Liu, Member, IEEE, Liwei Lin, and Jijun Xiong

Abstract— This paper presents a passive wireless sensor for simultaneously and remotely measuring pressure and temperature under harsh environments. The sensor consists of a dual LC (inductor and capacitor) resonant circuit, one without a cavity and the other with a cavity capacitor for temperature and pressure sensing, respectively. The low-temperature co-fired ceramic technology is used to fabricate the sensor, making it suitable for high-temperature harsh environment operations. Experimental results show the prototype sensor has temperature sensitivity of 8.15 kHz/°C and pressure sensitivity of 1.96 MHz/Bar up to 400°C. [2016-0157] Index Terms— Harsh environments, passive wireless sensor, LTCC, dual LC resonant circuit.

I. I NTRODUCTION

T

HE design and operation of harsh environment sensors working under high temperature and pressure in highspeed rotating machinery have been challenging in both literatures and practices. Specifically, silicon-based sensors can work in environments up to 300°C before issues stemming from the electrical and mechanical property changes of silicon under high temperature [1]. Several wired sensors utilizing SOI or SiC as the base materials can operate under higher temperature but they won’t work in cableinaccessible locations such as turbine blades [2], [3]. On the other hand, wireless sensors based on ceramic materials using passive detection mechanisms are attractive due to: (1) potentially better temperature stability; (2) no need for wires or power supplies; and (3) possibility for in-situ monitoring of key parameters such as pressure and temperature [4]–[7].

Manuscript received July 5, 2016; revised December 11, 2016; accepted December 18, 2016. This work was supported in part by the National Natural Science Foundation of China under Grant 61471324 and Grant 51425505 and in part by the Outstanding Young Talents Support Plan of Shanxi Province. Subject Editor C.-J. Kim. Q. Tan and T. Luo contributed equally to this work. (Corresponding authors: Qiulin Tan and Jijun Xiong.) Q. Tan, J. Liu, and J. Xiong are with the Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Tai Yuan 030051, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). T. Luo and T. Wei are with the Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong (e-mail: taoluo4-c@ my.cityu.edu.hk; [email protected]). L. Lin is with the Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2016.2642580

Fig. 1. Schematic of the sensor. (a) Perspective view and (b) cross-sectional view.

However, most state-of-art high-temperature passive wireless sensors only measure one parameter [8]–[11]. Herein an integrated passive wireless sensor [10], [11] based on the principle of a dual LC resonant circuit [12] fabricated by the LTCC technology [13] is presented for the simultaneous pressure and temperature measurements wirelessly under harsh environments. The structure design, fabrication process, and characterization of the proposed sensor is illustrated sequentially in this paper. II. S ENSOR D ESIGN AND FABRICATION A. Sensor Design The dual-sensor structure is illustrated in Fig. 1(a) with two LC resonant circuits embedded in the LTCC substrate for temperature and pressure detections. The resonant frequencies of the temperature and pressure LC resonant circuit f 01 and f 02 can be separately described as [14]: f 01 =

1 √ , 2π L 1 C1

f 02 =

1 √ 2π L 2 C2

(1)

Lumped circuit model of the sensor system is illustrated in Fig. 2, and the sensor is equivalent to two LC resonant circuits. L1 and L2 are the inductors of the sensor, R1 and R2 are the series resistances of the sensor, and C1 and C2 are the sensing capacitors of the sensor. Similarly, the readout coil is equivalent to an inductor L a and a series resistance Ra .

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

TABLE I D ESIGN PARAMETERS OF THE M ULTI -PARAMETER S ENSOR

Fig. 2. Lumped circuit model of the sensor system and schematic diagram of measuring pressure and temperature from phase of the readout coil.

By transformer network theory and Kirchhoff law used, the impendence Zin looking into the reader coil can be written as: −ω2 M2 M12 − j ωM1 Z 2 2 Z 1 Z 2 + ω2 M12 2 −ω M1 M12 − j ωM2 Z 1 + j ωM2 2 Z 1 Z 2 + ω2 M12 M1 = k1 L 0 L 1 , M2 = k2 L 0 L 2 , M12 = k12 L 1 L 2

Z in = Ra + j ωL a + j ωM1

(2) (2a)

where k1 and k2 are the coupling coefficients between the readout coil and the sensor coils, and k12 are the coupling coefficients between the sensor coils. Z 1 , Z 2 are equivalent impendence of pressure sensing LC tank and temperature sensing LC tank, respectively. Z 1 = R1 + j ωL 1 +

1 , j ωC1

Z 2 = R2 + j ωL 2 +

1 (3) j ωC2

By analyzing the phase of the readout coil, two curve crests will appear with sweep frequency, the peak frequencies of which are marked with f p1 and f p2 as shown in Fig. 2. There are corresponding mathematical relations existed between peak frequencies ( f p1 , f p2 ) with the sensor resonant frequencies ( f 01 , f02 ), whereas it is hard to deduce the mathematical relation currently. For practical use, the coupling coefficients k1 , k2 , k12 are very small, usually smaller than 0.2, and the quality factor of sensor circuits is tens or hundreds in the order of magnitude. Therefore, deviation of regarding peak frequencies as the resonant frequencies would be acceptable. For the design in this paper, the coupling coefficients k12 between these two LC resonant circuits is only 0.057 (calculated by using the model in [15]) for the current design and could be neglected, which is acceptable for engineering applications. Also, it is possible to further suppress the value of k12 by using specific winding-stacked inductors [16]. But this method will introduce a large overlap capacitance between two planar spiral inductors, which will degrade the pressure sensitivity of the sensor. Also, the maximum wireless readout distance of sensor will reduce because large overlap capacitance degrade the quality factor Q of the sensor. In this paper, f p1 and f p2 represent the peak frequencies of the temperature sensor and pressure sensor respectively. In the prototype process, LTCC and silver are used as the substrate and metallic materials and the five layer structure is required to construct the bottom electrode, cavity,

top electrode, and two inductor coils. The cross-sectional view in Fig. 1(b) shows that the two LTCC sheets are placed between two electrodes as the temperature sensing capacitor to have increased permittivity under elevated temperature [17]. As such, the resonance frequency of the temperature LC resonant circuit decreases as temperature increases. On the other hand, the pressure sensing capacitor has a cavity between the two electrodes. Under the externally applied pressure, the gap distance reduces and the capacitance increases. As such, the resonance frequency of the pressure LC resonant circuit increases as the applied pressure increases. Owing to that the temperature affects substrate material characteristics greatly, which causes pressure data drifting; the temperature data detected by the aforementioned temperature sensor can therefore be used to calibrate substrate degrading, thus to compensate the pressure sensor. In the proposed sensor structure, two square-shaped planar spiral inductor coils are via-connected with two square-shaped capacitor electrodes. Specific design parameters of the sensor are listed in Table I. B. Fabrication The sensor fabrication process is based on the lamination and sintering of screen-printed DuPont 951PT LTCC tapes (made of ceramic, glass and organic binder materials) of 114 μm in thickness. The LTCC is an excellent ceramic for its good miniaturization, compatibility with micro-circuits, as well as its resistance to high-temperature, and five layers of LTCC tapes were chosen to compose the proposed sensor. Fig.3 (a) shows exploded 3D diagram of the sensor structures, while Fig.3 (b) illustrates schematic diagram of the main fabrication process of the sensor. Five layers of green tapes were firstly punched to form via holes and air cavity, then the via holes were filled with DuPont 6141 Ag paste for providing metallic connection of capacitor electrodes and inductors of

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Fig. 5. Schematic diagram of the experimental setup. (a) Schematic of internal setup of the pressure tank and (b) measurement devices in the setup.

III. M EASUREMENT AND D ISCUSSION Fig. 3. (a) Exploded 3D view of the sensor and (b) the main fabrication process of the proposed sensor.

Fig. 4. (a) An optical photo shown the top view of the fabricated sensor, (b) an close-up optical photo showing a portion of the inductor coil, (c) an optical photo showing the cross-sectional view of the temperature sensing capacitor, (d) an optical photo showing the cross-sectional view of the pressure sensing capacitor before sintering, and (e) schematic diagram of volatilization of the sacrificial layer during the sintering process.

different layer, which was afterward formed by screen-printing with DuPont 6142D Ag paste in step 3. The pressure sensitive cavity was then filled with a piece of ESL49000 carbon film originally as the sacrificial layer to burden the huge pressure during the afterward lamination. The lamination was for forming a physical contact of 5 LTCC layers. The whole laminated structure was finally co-fired in a furnace, with an optimized sintering process previously reported in [18], during which the sensor tapes will become porous, the carbonbased materials in the sacrificial layer can react to oxygen that penetrates into the cavity and become CO2 and escape the cavity completely. The optical photo in Fig. 4(a) shows the top view of a fabricated sensor and Fig. 4(b) shows the close-up details of the inductor coils. The cross-sectional views of the temperature and pressure sensing capacitors are shown in Fig. 4(c) and 4(d), respectively. Fig. 4(e) illustrates the volatilization process of the sacrificial layer made of organic composite. It has been found that some residual gas may be trapped inside the cavity and the LTCC tapes can densify completely after the sintering process and block gas passages [19].

The fabricated sensors have been tested by using a developed high temperature testing system which has a precise control of temperature and pressure as shown in Fig. 5. The sensor is placed in a tray inside an all-metal sealed chamber and the readout antenna is placed about 15 mm above the sensor, with two ports of which connects an agilent E5061B network analyzer through a adapter and copper leading-out wire. For room temperature and atmospheric pressure, the largest detection distance is usually close to the side length of the inductor; therefore the distance is 26 mm in the current setup. The detection distance is related to the coupling efficient k (a variable related to energy transformation from antenna to sensor inductor), and quality factor Q (a variable related to the energy losses from the sensor). Therefore, the detection distance can be increased by optimizing the sensor parameters, e.g. inductor wire spacing, width, turns etc. in order to improve the quality factor Q. The other method is to use adaptive repeater to enhance the readout distance which was already demonstrated in [20]. The temperature is heated by the heating wire placed at the bottom of the sealed chamber filled with adjustable nitrogen gas pressure. The network analyzer is used to measure and record the phase of the antenna by sending sweep frequency signal of bandwidth from 15 to 42MHz. The sensor pressure characteristics at different temperatures are measured over the pressure range of 70–200 KPa at different temperature of 20, 60, 110, 150, 200, 250, 300, 350, and 400°C, respectively. Three cycles were conducted, and the measured data kept unchanged. The robustness of the proposed sensor within 400°C is very good as a prior work had demonstrated that the LTCC-based pressure sensor can operate at 450°C [21]. Fig. 6(a) shows the phase-frequency curve of the antenna when the external pressure is increased from 0.7 to 2.0 bar at 20°C. There are two obvious peaks that correspond to the resonant points of the pressure and temperature sensors, respectively. The higher peak frequency (pressure sensor) decreases under increasing pressure, whereas the lower peak frequency remains the same (temperature sensor). Fig. 6(b) shows experimental results from the peak frequency of the pressure sensor versus applied pressure between room temperature and 400°C. There are two key observations: (1) the resonant frequency of the pressure sensor reduces linearly with respect to the pressure; and (2) the sensitivity of the pressure



Fig. 7. The C/B value versus √ Young’s modulus (black symbol and scale) and variable D = (1 + v 2 )/ (1 + 1/εr ) (blue symbol and scale) for the temperature range of 20 to 400°C.

the cavity. Using Taylor expansion and disregarding high-order terms, Eq. (5) can be written as: γ (7) C2 = C02 1+ 3 Fig. 6. Measurement results of the proposed sensor. (a) Measured phase responses versus frequency from 0.7 to 2.0 Bar at 20°C under different applied pressure magnitudes, (b) measured peak frequency from the pressure sensor versus applied pressure under different temperature, (c) measured peak frequency from the temperature sensor versus applied pressure under different temperature, (d) average frequency peak of the prototype temperature sensor versus applied temperature, and (e) correlation analysis of measured pressure and reference pressure at different temperature.

sensor increases as the temperature increases and the highest pressure sensitivity is 1.96 MHz/Bar under 400°C. This is expected intuitively as the stiffness of the material decreases under high temperature to result in larger cavity deformation and larger frequency changes. Analytically, the initial capacitance of the pressure sensing cavity has the capacitance: C02 =

ε0 S tg + tm /εr

(4)

where ε0 is the vacuum permittivity, εr is the permittivity of LTCC, and S is the area of the capacitor electrodes. The capacitance under a pressure difference P was derived previously as [22]: C02 √ C2 = √ tanh−1 ( γ ) γ εr γ = dP · εr tg + tm

(5) (5a)

where dP is the center deflection of the pressure sensitive membrane, and it can be derived as [23]: dP = 0.01512

Pc4 · (1 − v 2 ) Etm3

(6)

where E and v are the Young’s modulus and Poisson’s ratio of the membrane material, respectively, and c is the width of

Substituting Eq. (7) into the Eq. (1) and performing further Taylor expansion, Eq. (1) can be simplified as: ⎛ ⎞

4 1 − v2 ⎜ ⎟ 1 tm 1 - 0.01512c f 02 = 1+ ·⎜ · P⎟ ε ⎝ ⎠ r 2π L s ε0 S 1 + 1 εr Etm4 C · P) B AC AC =− P0 + Pi + AB B B 1 tm , B= A= 1 + 1 εr , 2π L s ε0 S

0.01512c4 1 − v 2 , C = Etm4 = A(B −

(8)

(8a)

Under a specific temperature, constants A, B, and C do not change and the readout frequency is linearity dependent with the outside pressure Po . Although the exerted pressure Po will cause the trapped gas pressure Pi changed to a certain extent, the variation of Pi has a slight effect on the linearity of test curve practically. Combining with Eq. (6), the expression – AC/B can be used to represent the sensitivity of the pressure sensor. It should be noted that A can be considered as a constant within 400°C for thermal expansion’s influence is insignificant to LTCC-based sensor, i.e. tm /S can be seen invariable. So the temperature enhancing sensitivity of the pressure sensor is mainly due to the variation of B and C. It can be clearly seen from Fig. 7 that Young’s modulus contributes much more to the change of C/B value, i.e. the effect of Young’s modulus changes with temperature is much more significant than the combined effect of temperature on the permittivity and poisson ratio, i.e. variable D, within 400°C. Therefore, it can be concluded that the variation of Young’s modulus of sensor substrate material at elevated

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are originated from two main aspects - the error from the temperature reading (Fig. 6(d)) and the error caused by the linear fitting for the pressure (Fig. 6(b)). IV. C ONCLUSION

Fig. 8. Slope and intercept of the pressure characteristic line of the pressure sensor at different temperatures.

temperature is the main reason for the enhanced sensitivity of the pressure sensor under high temperatures. Fig. 6(c) shows the results from the peak frequency of the temperature sensor versus applied pressure at different temperatures. It is observed that pressure has negligible effects on the temperature sensor under low temperature environment as the peak frequency of the temperature sensor remains about the same with respect to pressure. However, small decrease of the peak frequency is observed under high temperature. This phenomenon is probably attributed to the stiffness changes of the material under high temperature to cause slight deformation between the temperature capacitor electrodes. Nevertheless, the characterization results provide the foundation for the calibration of pressure and temperature sensing of the sensor up to 400°C. Specifically, the results of calculated slope and intercept for Eq. (6) based on the experimental results in Fig. 6(b) with respect to temperature can be approximated by using a quartic function for the slope and cubic function for intercept, respectively, as shown in Fig. 8. For the practical usage of the proposed sensor, the temperature is measured by the peak frequency corresponds to the temperature sensor. However, as shown in Fig. 6(c), the peak frequency from the temperature sensor changes slightly with respect to the applied pressure under the same temperature. Fig. 6(d) shows the frequency peak of the prototype temperature sensor versus temperature from Fig. 6(c) with the biggest error bar of 109.57 kHz at 400°C, which is about 3.5% of the peak frequency. It is observed that the peak frequency of the temperature resonator decreases with respect to temperature as the permittivity increases under elevated temperature. Therefore, one can use the temperature sensor to sense the temperature (Fig. 6(d)) and use the pressure sensor to sense the pressure at a particular temperature afterwards (Fig. 6(b)). Fig. 6(e) shows the correlation analysis of the measured pressure after the temperature calibration process by the aforementioned mechanism as compared with the pressure measurements by a reference precision pressure sensor. It can be seen that most pressure data fall between the 5.5% positive linearity and 5.2% negative linearity ranges. These errors

Pressure measurements in high-temperature environment have been very challenging as the temperature effects often influence the pressure detections. This work presents wireless sensing scheme of utilizing a dual LC resonant circuit fabricated by the LTCC technology to detect both pressure and temperature simultaneously with full characterizations. The fabricated prototype sensor was tested by using a developed high temperature testing system, and results show that the prototype sensor can work under the temperature up to 400°C with the considerable temperature and are sensitivity of 8.15 kHz/°C and 1.96 MHz/Bar, respectively. Temperature data measured by the sensor was used to algorithmically compensate the pressure measurement, and calibrated results show measurement errors within typical engineering practices for potential harsh environment applications. R EFERENCES [1] G. H. Kroetz, M. H. Eickhoff, and H. Moeller, “Silicon compatible materials for harsh environment sensors,” Sens. Actuators A, Phys., vol. 74, nos. 1–3, pp. 182–189, Apr. 1999. [2] H. San, Y. Li, Z. Song, Y. Yu, and X. Chen, “Self-packaging fabrication of silicon–glass-based piezoresistive pressure sensor,” IEEE Electron Device Lett., vol. 34, no. 6, pp. 789–791, Jun. 2013. [3] R. S. Okojie, D. Lukco, V. Nguyen, and E. Savrun, “4H-SiC piezoresistive pressure sensors at 800 °C with observed sensitivity recovery,” IEEE Electron Device Lett., vol. 36, no. 2, pp. 174–176, Feb. 2015. [4] H. Cheng et al., “Evanescent-mode-resonator-based and antennaintegrated wireless passive pressure sensors for harsh-environment applications,” Sens. Actuators A, Phys., vol. 220, pp. 22–33, Dec. 2014. [5] M. A. Fonseca, J. M. English, M. V. Arx, and M. G. Allen, “Wireless micromachined ceramic pressure sensor for high-temperature applications,” J. Microelectromech. Syst., vol. 11, no. 4, pp. 337–343, Aug. 2002. [6] H. Cheng, X. Ren, S. Ebadi, Y. Chen, L. An, and X. Gong, “Wireless passive temperature sensors using integrated cylindrical resonator/antenna for harsh-environment applications,” IEEE Sensors J., vol. 15, no. 3, pp. 1453–1461, Mar. 2015. [7] Y. Li, Y. Yu, H. San, Y. Wong, and L. An, “Wireless passive polymerderived SiCN ceramic sensor with integrated resonator/antenna,” Appl. Phys. Lett., vol. 103, no. 16, p. 163505, Oct. 2013. [8] G. W. Hunter, “An overview of the development of high temperature wireless smart sensor technology,” NASA Glenn Res. Center, Cleveland, OH, USA, Tech. Rep. GRC-E-DAA-TN19422, Nov. 2014. [9] Y. Zhao et al., “RF evanescent-mode cavity resonator for passive wireless sensor applications,” Sens. Actuators A, Phys., vol. 161, nos. 1–2, pp. 322–328, Jun. 2010. [10] P. Sturesson, Z. Khaji, S. Knaust, L. Klintberg, and G. Thornell, “Thermomechanical properties and performance of ceramic resonators for wireless pressure reading at high temperatures,” J. Micromech. Microeng., vol. 25, no. 9, p. 095016, Aug. 2015. [11] S.-Y. Wu, C. Yang, W. Hsu, and L. Lin, “3D-printed microelectronics for integrated circuitry and passive wireless sensors,” Microsy. Nanoeng., vol. 1, no. 1, Jul. 2015, Art. no. 15013. [12] D. A. Sanz, C. Mitrosbaras, E. A. Unigarro, and F. Segura-Quijano, “Passive resonators for wireless passive sensor readout enhancement,” Appl. Phys. Lett., vol. 103, no. 13, Sep. 2013, Art. no. 1335021. [13] B. Jiang, J. Haber, A. Renken, P. Muralt, L. Kiwi-Minsker, and T. Maeder, “Fine structuration of low-temperature co-fired ceramic (LTCC) microreactors,” Lab Chip, vol. 15, no. 2, pp. 563–574, Nov. 2015. [14] C. Zhang, J.-Q. Huang, and Q.-A. Huang, “Design of LC-type passive wireless multi-parameter sensor,” in Proc. 8th Int. Conf. Nano/Micro Eng. Molecular Syst., Suzhou, China, Apr. 2013, pp. 256–259.



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Qiulin Tan received the B.S., M.S., and Ph.D. degrees from the North Universtiy of China, Shanxi, China, in 2002, 2006, and 2009, respectively. He was a Post-Doctoral Researcher with Tsinghua University, Beijing, China, from 2013 to 2015, and a Visiting Scholar with the University of California at Berkeley from 2015 to 2016. He is currently a Professor and a Doctoral Supervisor with the North University of China. His research interests include microwave backscattering sensor, LC resonant hightemperature pressure sensor, infrared gas sensor, and intraocular pressure monitoring sensor.

Jun Liu (M’10) was born in the Inner Mongolia Autonomous Region, China, in 1968. He received the B.S. degree from the North University of China, and the M.S. and Ph.D. degrees from the Beijing Institute of Technology, Beijing, China, in 2001. He was a Post-Doctoral Researcher with Peking University from 2003 to 2007. As the Team Leader, he has worked on around 20 different projects funded by the National 863 Project, National Nature Funds, and National 973 Project. He is currently with the Vice Director of the Key Laboratory of Instrumentation Science and Dynamic Measurement of the Ministry of Education, North University of China and also the Secretary-General of the Chinese Academy of Ordnance Industry. His research interests focus on MEMS and MIMU.

Liwei Lin received the B.S. degree in power mechanical engineering from National Tsing Hua University, Taiwan, in 1986, and the M.S. and Ph.D. degrees in mechanical engineering from the University of California at Berkeley (UC Berkeley) in 1991 and 1993, respectively. He was a Senior Research Scientist with BEI Electronics, Inc. He served as an Associate Professor with National Taiwan University and an Assistant Professor with the University of Michigan. He was a faculty member with UC Berkeley in 1999. He was the Vice Chair of Graduate Study with the Mechanical Engineering Department from 2006 to 2009. He currently serves as a Chancellor’s Professor with the Department of Mechanical Engineering, UC Berkeley, and also the Co-Director of the Berkeley Sensor and Actuator Center. He holds 19 patents in MEMS and has authored or co-authored over 160 journal publications. His research interests and activities at UC Berkeley include MEMS, NEMS, nanotechnology, design and manufacturing of microsensors and microactuators, development of micromachining processes by silicon surface/bulk micromachining, micromolding process, and mechanical issues in MEMS, such as heat transfer, solid/fluid mechanics, and dynamics.

Tao Luo (S’15) received the B.S. and M.S. degrees from the North University of China in 2012 and 2015, respectively. He is currently pursuing the Ph.D. degree with the Department of Mechanical and Biomedical Engineering, City University of Hong Kong. His research interests include sensors for harsh environments and microfluidic chip for biological applications.

Tanyong Wei received the B.S. and M.S. degrees from the North University of China in 2013 and 2015, respectively. He is currently pursuing the Ph.D. degree with the Department of Mechanical and Biomedical Engineering, City University of Hong Kong. His research interest is in ceramic-based LC resonant pressure sensor, backscattering sensor, and micro-robot for biomedical applications.

Jijun Xiong received the B.S. and M.S. degrees in electrical engineering from the North Universtiy of China, Shanxi, China, in 1993 and 1998 respectively, and the Ph.D. degree in precision instruments and mechanology from Tsinghua University, Beijing, China, in 2003. He was a Post-Doctoral Researcher with Tsinghua University, Beijing, China, from 2003 to 2005. He is currently a Professor, the Academic Leader, and the Vice Director of the Key Laboratory of Instrumentation Science and Dynamic Measurement of the Ministry of Education, North University of China. His research interests include high-temperature pressure sensor, infrared gas sensor, and searching, and positioning technology toward aerospace field.