3260 IEEE SENSORS JOURNAL, VOL. 14, NO. 9, SEPTEMBER 2014 A Digital Phase Demodulation Technique for Resonant MEMS Gyroscopes Arashk Norouzpour-Shirazi, Student Member, IEEE, Mohammad Faisal Zaman, Member, IEEE, and Farrokh Ayazi, Fellow, IEEE Abstract— This paper introduces a digital phase demodulation technique for resonant MEMS gyroscopes. The proposed method converts the amplitude-modulated Coriolis signal of the gyroscope into a digital phase-modulated output by utilizing the quadrature component of the sense signal. The rate information is extracted from the digital phase-modulated output using an XOR gate as a digital multiplier. Besides offering more robustness to low-frequency amplitude noise sources due to its phasebased operation, the proposed scheme enables direct time-domain digitization of the gyroscope signal at carrier frequency to avoid additional noise folding by the down-conversion multiplier in conventional amplitude demodulation. In addition, due to its digital nature, the proposed phase-based scheme offers better design scalability for deep-submicrometer CMOS implementations. As a proof of concept, the proposed phase demodulation architecture is interfaced with a low-bias-drift mode-matched tuning fork gyroscope. A scale factor of 240 mV/°/s with sub-0.001°/s detectable rate is measured. The complete system exhibits a low√bias instability of 0.55°/h and an angle random walk of 0.12°/ h. Index Terms— Mode-matching, MEMS gyroscope, phase demodulation, quadrature cancellation, tuning-fork gyroscope. I. I NTRODUCTION M ICROMACHINED resonant MEMS gyroscopes are employed in a wide array of applications ranging from automotive to industrial and consumer electronics , . In particular, MEMS inertial sensing technology has been embedded into mobile handsets, and tablet computers. During the past few years, multiple readout and control algorithms and techniques have been developed to improve the bandwidth, sensitivity, and noise performance of MEMS gyroscopes –. To maintain the integration capability of inertial sensors with the ever-shrinking RF and digital CMOS platforms, the sensor interface circuits must also shrink in size and power consumption, while providing high dynamic range and lownoise performance required by the electromechanical sensor. Manuscript received January 9, 2014; revised March 31, 2014 and April 29, 2014; accepted May 9, 2014. Date of publication May 29, 2014; date of current version July 29, 2014. This work was supported by Qualtré, Marlborough, MA, USA. The associate editor coordinating the review of this paper and approving it for publication was Dr. Thilo Sauter. A. Norouzpour-Shirazi and F. Ayazi are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]; [email protected]). M. F. Zaman was with the Georgia Institute of Technology, Atlanta, GA 30308 USA. He is now with Qualtré, Marlborough, MA 01752 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/JSEN.2014.2326974 Fig. 1. Digital outputs are generated from the drive signal and the phasemodulated sense signal. An XOR gate is used as a digital multiplier to mix the two digital signals and convert the phase-modulated rate information into a pulse-width-modulated (PWM) output. However, at smaller CMOS technology nodes, the supply voltage reduction degrades the overall signal-to-noise ratio of the system, especially in amplitude-based architectures. In communication systems, time-based all-digital system architectures are widely used to maintain high-speed and low-power operation at reduced supply voltage levels , while avoiding the weak voltage resolution handling in deepsubmicron CMOS technologies. MEMS gyroscope interface architectures can benefit from the same approach to provide high dynamic range and low-noise performance. This paper introduces a digital phase demodulation technique for resonant MEMS gyroscopes. The proposed method utilizes the relatively large amplitude of the quadrature component of the gyroscope sense signal to convert the small amplitude-modulated Coriolis component into a digital phasemodulated output. Consequently, the rate information can be demodulated directly at carrier frequency from the phase variations of this digital signal by using a time-to-digital converter (TDC) backend. While direct digitization at carrier frequency can be used to systematically reduce the overall noise and power consumption in gyroscope interface circuits, the proposed digital phase demodulation scheme offers a reduced dynamic range requirement for the TDC backend as compared to an amplitude-based direct digitization scheme. This will be explored in more detail in Section II of this paper. In this work, as a proof of concept, the rate information is extracted from the digital phase-modulated output using an XOR gate as a digital multiplier, as shown in Fig. 1. Owing to its phase-based operation, the digital phase demodulation is insensitive to low-frequency amplitude noise 1530-437X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. NOROUZPOUR-SHIRAZI et al.: DIGITAL PHASE DEMODULATION TECHNIQUE 3261 sources and offsets in the amplifier stages preceding the XOR gate. Moreover, the proposed technique obviates the need for quadrature cancellation in the sense front-end, and thus reduces the overall system complexity, noise and power. II. P ROPOSED D IGITAL P HASE D EMODULATION T ECHNIQUE Conventional gyroscope interface architectures are mostly based on coherent demodulation of rate from the Coriolis signal. The drive signal is used as carrier, and the amplitudemodulated rate information is demodulated by multiplying it to the output current of the gyroscope sense axis. The demodulation is conventionally performed by an analog multiplier  or a switching scheme , followed by a low-pass filter to extract the low-frequency rate. In addition to the Coriolis component, the sense output current of a MEMS gyroscope contains an undesired quadrature component which is caused by misalignments and imperfections in the fabrication of the device. Being affected most dominantly by the mechanical spring imbalances , the quadrature component is almost 90° out of phase with the Coriolis component, hence the name quadrature. Furthermore, the amplitude of the quadrature component is typically 2-3 orders of magnitude (40-60 dB) larger than the fullscale of the Coriolis component. Considering the 90° phase difference, the quadrature component can simply be rejected in a coherent demodulation scheme where the carrier is in-phase with the Coriolis signal. However, the large amplitude of the quadrature component limits the maximum achievable gain of the sense-channel trans-impedance amplifier (TIA) frontend before demodulation , and thus limits the minimum achievable input-referred current noise . To alleviate the effect of the undesired quadrature error at the device level, quadrature-nulling electrodes can be used to counterbalance the mechanical force that generates the quadrature component by an opposite electrostatic force –. This method is used in this work to minimize misalignments for near-perfect mode-matching. However, complete cancellation of quadrature error is neither required for mode-matching, nor guaranteed by this method. Therefore, a residual quadrature still remains in the sense signal. The residual quadrature can be compensated by subtracting an identical signal from the sense current at the input of the TIA front-end , . The compensation signal can be generated from the drive-mode oscillation. However, accurate estimation and control of the amplitude and phase of this compensation signal adds to the overall system complexity and power consumption . Moreover, the quadrature cancellation blocks inject additional noise into the sense TIA front-end, which degrades its overall noise performance. A. Digital Phase Demodulation Scheme In this section, a digital phase demodulation technique is proposed as an alternative to conventional detection schemes with quadrature cancellation. The proposed method takes advantage of the quadrature signal for rate detection rather Fig. 2. Comparison operation is applied to drive and sense signals. The phase difference of drive and sense square-wave signals, f (t) and g(t), is detected by an XOR gate as a digital multiplier. The PWM output of the XOR, h X O R (t) is low-pass filtered and averaged to generate h avg (t) as the rate output. than cancelling it. At mode-matched condition, the gyroscope drive and sense outputs can be written as x Drive (t) = a D sin (ω0 t) y Sense (t) = a Q cos (ω0 t) + a (t) . sin (ω0 t), |a (t)| a Q , (1) where a D and a Q are the nearly constant amplitudes of the drive and quadrature signals respectively, and a (t) is the amplitude of the Coriolis signal generated by the applied mechanical rate, (t). The sense output can be rewritten as 2 y Sense (t) = a 2Q + a (t) cos (ω0 t − ϕ (t)), a (t) −1 a (t) ϕ (t) = tan . (2) aQ aQ Considering that the quadrature amplitude remains constant during the gyroscope operation, the Coriolis component of the sense signal can alternatively be represented by ϕ(t), which is the phase modulation of the sense signal zero-crossings with respect to the fixed zero-crossings of the drive signal. An analog multiplier can still be used to multiply the two signals and demodulate the phase information, ϕ(t). From an intuitive perspective, since the information is embedded in the zero-crossings of the sense signal, the phase difference, ϕ(t) can be alternatively detected by digital multiplication of the square-wave versions of the same sense and drive signals. As shown in Fig. 2, in the proposed scheme comparison operation is applied to the drive and sense signals to generate f (t) and g(t) square-wave signals. The phase modulation of the sense signal can be visibly seen with respect to the fixed zero-crossings of the drive signal. After comparison, the phase difference of f (t) and g(t) signals is detected by an XOR gate as a digital multiplier. The output of the XOR gate, h X O R (t) is a pulse-width modulated (PWM) signal with a duty cycle proportional to the applied rotation rate. In the presence of input rotation, the duty cycle of the PWM is modulated by ϕ(t)/π with respect to its initial 50% duty cycle in the absence 3262 of input rotation. An integrator or low-pass filter can be used at the XOR output to filter out the high frequency carrier component and extract rate from h avg (t). The functionality and effectiveness of the proposed technique can be mathematically studied by using the Fourier series representation of f (t) and g(t) signals, and representing the XOR gate as a digital multiplier. The Fourier series representation of f (t) is 4 sin 3ω0 t sin 5ω0 t sin 7ω0 t + + + ... . (3) f (t) = sin ω0 t + π 3 5 7 The sense square-wave signal, g(t) has a phase difference of π/2 – ϕ(t) with respect to f (t). Therefore, the Fourier series of g(t) can be written in part as 4 sin 3ϕ (t) g (t) = sin ϕ (t) × sin ω0 t − × sin 3ω0 t π 3 sin 5ϕ (t) sin 7ϕ (t) + ×sin 5ω0 t − × sin 7ω0 t + ... 5 7 (4) The cosine terms in (4) are eliminated, because their correlation with the sine terms in (3) is zero. The average of the XOR output representing the rate, h avg (t), can be derived as sin 5ϕ (t) sin 3ϕ (t) 8 + h avg (t) = 2 sin ϕ (t) − π 32 52 sin 7ϕ (t) − + ... . (5) 72 It can be shown that with respect to ϕ, (5) represents the Fourier series of a triangular waveform of period 2π. Therefore, the input-output characteristic is linear in a range of [−π/2, π/2], which corresponds to the span of [−∞, +∞] for a (t)/a Q , considering that ϕ(t) = tan−1 (a (t)/a Q ). It can be seen that the bandwidth of ϕ(t) is almost equal to that of a (t), which is much smaller than ω0 . Therefore with a time-varying mechanical angular rate, (t), the pulse-width modulation of the XOR output can be detected by adjusting the bandwidth of the backend low-pass filter properly. Owing to its phase-based operation, the proposed technique offers good scalability into lower supply voltages and deep submicron CMOS implementations. Moreover, the proposed scheme offers more robustness to low-frequency amplitude noise sources in the sense front-end and comparators. In particular, it can be seen from simulations that in this scheme, unlike in the conventional coherent amplitude demodulation scheme, the scale factor and bias are insensitive to any offset in the comparators and preceding amplifier chain. B. Direct Digitization at Carrier Frequency Direct digitization at carrier frequency is of interest to avoid the low-frequency baseband noise and noise folding in the demodulator, thereby improving the overall rate noise. For direct digitization in the amplitude domain, the required full-scale range of the analog-to-digital converter (ADC) is determined by the quadrature signal amplitude. Consequently, up to 40-60dB of the ADC dynamic range should be wasted to digitize the undesired quadrature signal. On the other hand, IEEE SENSORS JOURNAL, VOL. 14, NO. 9, SEPTEMBER 2014 in time-domain digitization, since a (t) a Q , rate detection takes place within a small neighborhood of only a few degrees around ϕ = 0°. Therefore, time-domain digitization can be performed on the PWM signal after the XOR, with a reduced time-domain full-scale range of only a few degrees. As a result, the time-domain full-scale range of the TDC backend can be determined only by the full-scale of the Coriolis signal. Time-domain digitization can alternatively be performed before the XOR, on the edges of f (t) and g(t) signals, which is the main motivation of the proposed technique. However, in this work, an XOR gate is used only as a proof-of-concept to show the linearity and effectiveness of the proposed digital phase demodulation scheme. III. M2 -TFG S CALING AND C HARACTERIZATION A M2 -TFG similar to the one presented in  is used in this work. The mechanical design parameters were modified to improve the sensitivity and overall noise performance. The current sensitivity of the M2 -TFG structure is ICoriolis = 2V P Cs0 Q S x drive (A) ds0 (6) where V P is the polarization voltage, Cs0 is the static sense capacitance, ds0 is the sense gap, x drive is the mechanical drive displacement amplitude, and Q s is the sense-mode quality factor of the M2 -TFG. The mechanical noise equivalent rotation, MNE, and the electrical noise equivalent rotation, ENE of the gyroscope  are √ 4k B T 1 . BW (°/ hr ) M N E = 2x drive ω0 M Q E F F √ ds0 E N E = .I N−t ot al . BW (°/ hr ). (7) 2V P Cs0 Q E F F x drive It can be inferred from (6) and (7) that to improve the gyroscope sensitivity and electrical noise performance, the effective quality factor, the sense capacitance, and the drive amplitude must be maximized. Additionally, to further reduce the mechanical noise of the gyroscope as well, the proof-mass size should be increased additionally. Fig. 3a shows the SEM picture of the M2 -TFG used in this work, fabricated on a 120μm-thick silicon-on-glass (SOG) substrate. Each proof-mass is 550 μm × 550 μm in area. The large thickness of the device increases both the overall mass and sense capacitance, and thus reduces the mechanical and electrical noise floor values, respectively. However, because of the increased thickness of the substrate, the achievable sense gap is limited to a minimum of 4 μm. To further increase the sense capacitance, two additional parallel-plate fingers have been included to increase the overall sense electrode area by almost 3 times. To enable near-perfect mode-matching, additional quadrature electrodes, VQ1−4 are implemented on the corners of each proof-mass to partially cancel the quadrature error. The topleft inset in Fig. 3a shows the 7mm × 7mm vacuum-sealed M2 -TFG fabricated and packaged by ePack . This package is a smaller version of the one presented in , with the same device dimensions. NOROUZPOUR-SHIRAZI et al.: DIGITAL PHASE DEMODULATION TECHNIQUE 3263 TABLE I M ECHANICAL D ESIGN PARAMETERS C OMPARISON Fig. 3. (a) SEM photo of the M2 -TFG fabricated on a 120μm-thick SOG substrate. The top-left inset shows the die photo of the 7mm × 7mm vacuumpackaged M2 -TFG, (b) top: Quality factor of 65,000 at 11.68 kHz, with f = 1.5 Hz, and V P = 16.5 V; bottom: at V P = 16.9 V, the M2 -TFG shows an improved mode-matched quality factor of 77,000 at 11.68 kHz. The vacuum-packaged M2 -TFG device has been characterized across a temperature range of 0 °C to 70 °C. Modematched condition is maintained with slight modification of the polarization voltage, V P within ±20 mV, at each temperature. Fig. 4a shows qualitatively the reduction of the gyroscope resonant frequency, and the increase in the insertion loss, noise floor, and mode-matched sensor bandwidth with increase of the temperature. The resonance frequency and quality factor of the modematched gyroscope are plotted versus temperature in Fig. 4b. The resonant frequency of the gyroscope shows a TCF of −22 ppm/°C, while the mode-matched quality factor decreases from 97,000 at 0 °C to 54,000 at 70 °C. Table I summarizes the mechanical design parameters of the M2 -TFG used in this work, in comparison with the one presented in . Based on (6) and (7), and using the design parameters presented in Table I, the M2 -TFG used in this work can provide up to 7 times higher current sensitivity, 7 times lower electrical noise floor, and 2.5 times lower mechanical noise floor than the M2 -TFG used in . With mechanical drive amplitude of almost 3 μm, the MNE of the gyroscope and the ENE of the interface √ √ electronics are estimated to be 0.21°/hr/ Hz and 0.023°/hr/ Hz respectively. IV. P ROPOSED D IGITAL P HASE D EMODULATION A RCHITECTURE AND S YSTEM I MPLEMENTATION Fig. 4. (a) The M2 -TFG device was characterized at different temperatures from 0 °C to 70 °C. Mode-matched condition is maintained with slight adjustment of V P , within ±20 mV at each temperature. (b) A TCF of −22 ppm/°C is measured from the M2 -TFG, while the mode-matched quality factor changes from 97,000 at 0 °C to 54,000 at 70 °C. Fig. 3b (top) shows the frequency response of the drive and sense modes of the TFG device with a split of 1.5 Hz, at V P = 16.5 V. The drive and sense modes show quality factors of 65,000 and 28,000 respectively. For complete matching of the gyroscope drive and sense modes V P is increased to 16.9 V, while additional quadrature-nulling electrodes are also used to reduce the misalignments caused by fabrication imperfections. As can be seen in Fig. 3b (bottom), an increased effective quality factor (Q E F F ) of 77,000 is measured from the M2 -TFG device at mode-matched condition, at 11.68 kHz, in a vacuum level less than 10 mTorr. The block diagram of the overall gyroscope interface system is shown in Fig. 5. An oscillator loop is used to actuate the drive mode of the gyroscope, and a differential TIA sense front-end followed by an XOR demodulator is used to detect rate from the M2 -TFG device described in Section III. The drive loop consists of a drive TIA, followed by a noninverting gain-stage, and an inverting variable-gain amplifier (VGA) that is controlled by an automatic level control (ALC) circuit. The above amplifier chain configuration ensures 360° of phase shift across the drive mode, and provides sufficient transimpedance gain to compensate for the relatively large drive-mode motional resistance of ∼47 M caused by the low coupling of drive-axis comb actuators. The ALC circuit consists of an active peak-detector circuit to monitor the peak amplitude of the gyroscope drive input, and an integrating 3264 IEEE SENSORS JOURNAL, VOL. 14, NO. 9, SEPTEMBER 2014 Fig. 5. M2 -TFG (center) and the interface circuit block diagram. Drive loop (left) with ALC circuit, and a pseudo-differential sense TIA front-end (right) followed by the proposed digital phase demodulator (XOR demodulator). Fig. 6. PCB implementation of the proposed gyroscope interface architecture; the right inset shows the experiment setup with the PCB mounted inside an Ideal Aerosmith 1291BR rate table for z-axis sinusoidal rotation testing. control loop to stabilize the peak drive amplitude with respect to an external reference voltage, Vre f . A differential TIA sense front-end, followed by post-amplification gain-stages detect and amplify the output current of the M2 -TFG differential sense electrodes. The post-amplification gain-stages are not shown in the schematic of Fig. 5, to be concise. A voltage comparator is used at the output of the gain-stages to generate a phasemodulated square-wave signal from the sense output, for the XOR demodulator. Another comparator compares the drive oscillation to mid-rail, and generates the reference square-wave input to the XOR. The XOR gate converts the phase variations of the sense signal with respect to the drive signal into a PWM, which is low-pass filtered to provide rate. In this implementation, the low-pass filter is a simple R-C network, followed by a 2nd -order Sallen-key Butterworth low-pass filter, with 3-dB bandwidth of 4Hz, above an order of magnitude larger than the M2 -TFG bandwidth, i.e. ∼150 mHz. Fig. 6 shows the PCB implementation of the proposed digital phase demodulation interface for a M2 -TFG. The right inset in Fig. 6 shows the PCB clamped on an Ideal Aerosmith 1291BR rate table for z-axis rotation testing. All of the analog discrete amplifiers operate from ±5V supply voltages. For the drive and sense TIAs, OPA656 opamp from TI (Texas Instruments, Dallas, TX) is used for its good frequency stability performance and low input-referred voltage noise. In both drive and sense TIAs, a feedback resistance of 500 k is used, which provides a low input-referred current √ noise  of ∼180 fA/ Hz majorly dominated by the resistor current noise. In the drive loop, VCA810 voltage-controlled amplifier from TI is used to provide automatic level control (ALC). The amplifiers used for peak detection, amplification and integration in the ALC control loop are implemented by OPA2704 dual opamps from TI. For post-TIA voltage amplification in the sense path, OPA2704 dual opamps are used in cascaded inverting and noninverting configurations, providing an overall voltage gain of 30 V/V. The differential TIA gain of 1 M followed by the post-TIA voltage gain of 30 V/V is large enough to provide a 5 V p- p sinusoidal input to the sense comparators. This large input swing ensures that the comparator generates a low-jitter square-wave output for the subsequent XOR demodulator. To achieve good timing resolution and high slew rate for the comparator stages, considering the low frequency of operation, i.e. 11.68 kHz, OPA657 opamps from TI are used in openloop comparator configuration. For digital XOR multiplication, 3-input SN74LVC XOR gate from TI is used. V. M EASUREMENT R ESULTS The M2 -TFG device interfaced with the digital phase demodulation system is characterized for rate sensitivity and bias stability. Fig. 7a shows the closed-loop sinusoidal drive oscillation at 11.68 kHz, the sense TIA output, the output of the sense comparator, and the XOR output. As can be seen, at mode-matched condition, the sense zero-rate output NOROUZPOUR-SHIRAZI et al.: DIGITAL PHASE DEMODULATION TECHNIQUE 3265 √ Fig. 8. Bias drift of 0.55°/h and ARW of 0.012°/ h were measured from 2 the M -TFG device interfaced with the proposed digital phase demodulation. M2 -TFG device, interfaced with digital phase demodulation √ architecture. The measured ARW corresponds to 0.72°/hr/ Hz overall noise density of the sensor and electronics. VI. C ONCLUSION Fig. 7. (a) Sinusoidal closed-loop drive oscillation at 11.68 kHz and ZRO at mode-matched condition are 90° out of phase. The XOR output has twice higher frequency than the square-wave sense output. (b) Input rotation rates lower than 5 × 10−3 °/s are applied to the M2 -TFG at 100 mHz frequency. The M2 -TFG system can detect sub-0.001°/s rotation rates. (ZRO) is 90° out of phase with the drive actuation signal. This quadrature phase relationship provides maximum rate sensitivity and minimum offset at the demodulator output. Rate measurements were taken on Ideal Aerosmith 1291BR rate table. For all measurements, sinusoidally-varying rotation is applied at different peak angular rates, and the peak value of the sinusoidal output of the demodulator is measured. Fig. 7b shows the spectrum of the rate output to sinusoidally varying angular rotations with peak amplitude of 0.625×10−3 −5 × 10−3 °/s, applied at a frequency of 100 mHz. As can be seen, sub-0.001°/s rotation rates can be detected, while every twice increase of the angular rate amplitude results in 6dB increase in the magnitude of the 100-mHz rate component. As shown in the bottom right inset of Fig. 7b, a large scale factor of 240 mV/°/s is measured for angular rates from 2.5×10−3°/s to 2°/s. Considering a maximum applicable rate of 10°/s for the M2 -TFG, the overall system shows close to 80 dB dynamic range. Fig. 8 shows the Allan variance plot of the M2 -TFG system. The output of the stationary gyroscope was measured for 1.5 hours at a sampling rate of 2 kSa/s. A bias drift of √ 0.55°/hr and an ARW of 0.012°/ hr were measured from the This paper introduced a novel digital phase demodulation architecture for the interface of resonant MEMS gyroscopes. 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Zaman, F. Ayazi, and K. Najafi, “A low-power oven-controlled vacuum package technology for high-performance MEMS,” in Proc. IEEE 22nd Int. Conf. MEMS, Jan. 2009, pp. 753–756. Arashk Norouzpour-Shirazi (S’09) received the B.S. and M.S. degrees in electrical and computer engineering from the University of Tehran, Tehran, Iran, in 2005 and 2008, respectively. He is currently pursuing the Ph.D. degree in electrical engineering at the Georgia Institute of Technology, Atlanta, GA, USA. His research interests are in the areas of analog and mixed-signal integrated circuit design, and the design and implementation of high-performance interface systems for MEMS resonators and inertial sensors. Mohammad Faisal Zaman (S’97–M’08) is currently the Lead Applications and Systems Engineer at Qualtré Inc., Marlborough, MA, USA. He was the Lead MEMS Design Engineer, involved in the development of the BAW gyroscope. He is an alumni of the Integrated MEMS Laboratory at the Georgia Institute of Technology, Atlanta, GA, USA, where he received the B.Sc. and Ph.D. degrees in electrical and computer engineering in 2001 and 2007, respectively. He has numerous technical conference and peer-reviewed journal publications, and holds multiple patents in the field of MEMS gyroscope design and implementation. Farrokh Ayazi (S’96–M’00–SM’05–F’13) is a Professor of Electrical and Computer Engineering and the Director of the Center for MEMS and Microsystems Technologies at the Georgia Institute of Technology (Georgia Tech), Atlanta, GA, USA. He received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, MI, USA, in 1997 and 2000, respectively. His main research interest lies in the area of integrated micro and nanoelectromechanical systems (MEMS and NEMS), with a focus on resonators and inertial sensors (gyroscopes and accelerometers). He has authored over 200 refereed technical and scientific articles. He and his students have received several best paper awards at international conferences. He is an Editor of the IEEE T RANSACTIONS ON E LECTRON D EVICES and a past Editor of the IEEE/ASME J OURNAL OF M ICROELECTROMECHANICAL S YSTEMS . He was the General Chair of the IEEE Micro-Electro-MechanicalSystems (MEMS) Conference in 2014. He was a recipient of the National Science Foundation CAREER Award, and Outstanding Junior Faculty Member Award, and the Richard M. Bass/Eta Kappa Nu Outstanding Teacher Award from the School of Electrical and Computer Engineering at Georgia Tech. He is the Co-Founder and CTO of Qualtré Inc., a spinout from his research laboratory that commercializes bulk-acoustic-wave silicon gyroscopes and inertial sensors for personal navigation systems. He holds 42 patents.
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