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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 [1], [2].
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
[3]–[6].
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 [7],
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
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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 [8]
or a switching scheme [9], 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 [2], 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 [10], and thus limits the minimum
achievable input-referred current noise [8].
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
[11]–[13]. 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 [10], [14]. 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 [15]. 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
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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 [12] 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 [8] 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 [16]. This package
is a smaller version of the one presented in [17], with the same
device dimensions.
NOROUZPOUR-SHIRAZI et al.: DIGITAL PHASE DEMODULATION TECHNIQUE
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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 [12]. 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 [12]. 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
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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 [8] 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.
The functionality of the proposed demodulation technique
was proven mathematically, and confirmed experimentally.
The phase demodulation scheme is able to demonstrate high
sensitivity and sub-°/hr bias drift from a M2 -TFG device.
The proposed digital phase demodulation technique offers
more robustness to low-frequency amplitude noise sources, as
compared to the analog amplitude-based coherent detection
scheme. Moreover, it obviates the need for quadrature cancellation in the sense front-end and thus reduces the power
consumption, noise and complexity of the interface circuits.
As the main objective of this work, the proposed technique enables time-domain digitization of the phase-modulated
gyroscope output at carrier frequency with optimal timedomain dynamic range requirement for the TDC backend.
Such a digital scheme can be easily adapted to deep-submicron
CMOS implementations, despite the relatively poor voltage
resolution handling of those technologies.
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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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