ULTRA HIGH QUALITY FACTOR AND WIDE DYNAMIC RANGE

INERTIAL MEMS FOR NORTH-FINDING AND TRACKING APPLICATIONS

Alexander A. Trusov

MicroSystems Laboratory, University of California, Irvine, USA

Alex.Trusov@gmail.com, http://www.AlexanderTrusov.com, http://mems.eng.uci.edu

ABSTRACT We report high-Q and wide dynamic range MEMS

gyroscopes and accelerometers for development of a

very compact IMU capable of North finding and

tracking over dynamic environment. The vacuum

packaged SOI rate sensors utilize symmetric Quadru-

ple Mass Gyroscope (QMG) architecture with meas-

ured quality factors of 1.2 million and proven sub–

°/hr Allan deviation of bias. The true North detection

was accomplished in conventional amplitude modu-

lated (AM) rate measuring mode and showed 0.003

radian measurement uncertainty. The North (azimuth)

tracking over dynamic environment necessitates a wide dynamic range, for which the same QMG trans-

ducer is switched to a frequency modulated (FM) mo-

dality. The test results for FM operation experimen-

tally demonstrated a wide linear input rate range of

18,000 °/s and inherent self-calibration against tem-

perature changes. Vertical alignment of the IMU and

acceleration sensing is enabled using resonant accel-

erometers with 5 μg performance. The accelerometer

is self-calibrated against temperature variations, ena-

bled by differential frequency measurements. We be-

lieve the developed low dissipation inertial MEMS with interchangeable AM/FM modalities may enable

wide dynamic range IMUs for North-finding and iner-

tial guidance applications previously limited to sys-

tems based on optical and quartz inertial sensors.

I. INTRODUCTION

North-finding with 0.001 radian (1 mrad) preci-

sion and tracking of azimuth in a wide dynamic

range is required for targeting, dead reckoning, and

inertial guidance applications [1]. North identifica-

tion is traditionally accomplished using the magnetic

f i e ld of the Earth. However, there are a number of

spatial and temporal distortions in the magnetic field,

which limit the accuracy of this method. Practical

limitations of alternatives such as geodetic, celestial,

and GPS-based methods make high performance gy-roscopes desirable for true North seeking, or

gyrocompassing. Although conventional fiber optic,

ring laser, and macro-scale quartz hemispherical res-

onator gyroscopes can be used for precision

gyrocompassing, they are not perfectly suited for

man-portable and small platform applications.

MEMS, in contrast, have a number of b e n e f i t s

they are lightweight, low-power, batch fabricated, and

are have the potential to enable very small and

low cost IMU and INS technologies.

Gyrocompassing typically requires better than

0.05 °/hr total bias error over temperature variations

for repeatable measurements of the Earth’s rate and

0.1 mg total bias error for vertical alignment. Sev-eral groups have reported silicon MEMS gyroscopes

with sub–°/hr Allan deviation of bias [2-7]. However,

single digit mrad North-finding and tracking over dy-

namic environment is still view as unattainable by

MEMS technology [8]. We propose to tackle this

issue using the recently developed Quadruple Mass

Gyroscope (QMG) [9] and a new resonant accel-

erometer, with the resolution enhanced by high Q-

factors and wide dynamic range provided by frequen-

cy modulated (FM) operation, which is also robust to

temperature variations and shocks. Fig. 1 shows a photograph of a pyramid inertial measurement unit

(IMU) prototype comprising MEMS Quadruple Mass

Gyroscopes and resonant accelerometers. This review

paper is based on our recent publications [6, 7, 9-14]

and intends to provide a summary of the high perfor-

mance inertial MEMS development at the University

of California, Irvine MicroSystems Laboratory during

the period from approximately 2008 to 2012.

II. QUADRUPLE MASS GYROSCOPE (QMG)

Ultra-high sensitivity silicon MEMS rate sensors

are desired for inertial navigation and North-finding

Fig. 1: Photograph of a pyramid inertial measure-ment unit (IMU) prototype comprising MEMS quad-

ruple mass gyroscopes and resonant accelerometers.

Table 1: Comparison of the 3 main design parame-

ters for 3 different architectures of MEMS gyro-

scopes (Tuning Fork Gyroscope, Disk Resonator Gy-

roscope, and Quad Mass Gyroscope).

applications. An optimal architecture of a high resolu-

tion vibratory rate gyroscope comprises a symmetric

mechanical structure with combination of very high

Q-factors and decay time constant, high Coriolis cou-

pling (angle gain), drive- and sense-mode degeneracy,

and frequency tuning capability [4]. Most of these

requirements can be satisfied by continuous structures

such as disks or rings operated in balanced wine-glass

modes. However, optimization of the performance parameters for such architectures is challenging due to

the inherent coupling of the natural frequency, Q-

factor, and drive-amplitude, Table 1. Frequency

trimming and tuning is also quite nontrivial for solid

structures as both mass and stiffness are collocated.

An alternative approach investigated in this work

is to use a lumped, four quadrant symmetric QMG

architecture [12], Fig. 2. It comprises four symmetri-

cally decoupled tines synchronized by anti-phase lev-

er mechanisms, providing a unique combination of

ultra-low energy dissipation due to the elimination of

anchor loss and isotropy of both the resonant frequen-cy and damping. The QMG is expected to provide

ultra-high Q-factors and enable high precision rate

measurements.

II-A. Rate Sensitivity Analysis and Optimization

The operating principle of a vibratory MEMS gy-

roscope is based on energy transfer between two vi-

bratory modes. The drive-mode is continuously excit-ed at resonance, and the sense-mode is used for rate

detection. The amplitude of the sense-mode motion

(y) is proportional to the rotation rate (z), with the

angular gain factor (0 < k 1) and the drive-amplitude (x):

yzeff xkQy 2, (1)

where y is the resonant frequency. Here, Qeff is the gain of the sense-mode at the drive-mode frequency:

22 )(41 yyyeff QQQ , (2)

which reaches maximum Qy for zero mismatch

( = 0).

It follows from (1) that the rate sensitivity is en-hanced by maximizing the Q-factor and reducing the

resonant frequency. Q-factors above 100,000 were

previously realized for both continuous and lumped

type MEMS gyroscopes [12, 15]. In contrast to con-

tinuous structures, lumped, mass-spring type devices

operate at lower frequencies, and thus, promise supe-

rior rate sensitivity. For instance, the scale factor im-

proves by 60 dB for a 1 kHz operational sensor com-

Fig. 2: SEM image of a fabricated SOI Quadruple

Mass Gyroscope or QMG (die size is 8.68.6 mm).

Fig 3: Photograph of a vacuum packaged QMG used

in the experiments. Insets: die before sealing of the ceramic package; glass lid wafer with getters.

Fig. 4: Block diagram of QMG signal processing for

rate measurements, showing drive- and sense-mode

control loops.

pared to a 1 MHz sensor. The trade-off between fre-

quency and sensitivity is a limited bandwidth, which

can be resolved by operating in a closed loop, or

force-rebalance (FRB) mode. In addition, mass-

spring, lumped architectures can provide high Coriolis

coupling (k ~ 1) and large amplitude of motion (up to 10 microns), which also increase the rate sensitivity.

Based on these considerations, we investigate a

lumped design approach for high precision applica-

tions.

II-B. Mechanical Design and Symmetry

Mode-matched operation over a wide temperature

range is desired for high-Q MEMS gyroscopes. Fre-

quency mismatch induced by fabrication imperfec-tions is typically compensated by electrostatic tuning,

which often requires high voltages and active con-

trols. In this work, we evaluate a design-level solution,

where structural symmetry of the lumped mechanical

element provides identical drive and sense tempera-

ture coefficients of frequency for increased robustness

to the temperature-induced drifts [13].

The recently introduced lumped Quadruple Mass

Gyroscope architecture, Fig. 2, comprises four identi-

cal tines, four linear coupling flexures, and a pair of

lever mechanisms for synchronization of the anti-phase drive- and sense-mode motion. Momentum and

torque balance in both x and y directions is expected

to provide ultra-low dissipation of energy through the

substrate, leading to a high resolution and equal ultra-

high Q-factors, Qx = Qy > 1 million. Symmetric lever

mechanisms and flexures ensure low operational fre-

quency (~ 2 kHz), as well as the common mode rejec-

tion of input accelerations, both required for high pre-

cision rate measurements.

II-C. MEMS Fabrication and Vacuum Packaging

Stand-alone prototypes of the QMG were fabri-

cated using an in-house 100 m SOI process with 5

m minimal gap size. The rate sensor was packaged using custom technology for robust vacuum sealing of

the high-Q gyroscopes [16], Fig. 3. First, the QMG

die was attached to a ceramic 24-pin package using

eutectic solder and wire bonded. The device was then

sealed at sub-mTorr vacuum, preceded by the getter

activation on a glass lid.

II-D. Interface and Control Electronics

All experiments were performed using a custom

PCB connected to a FPGA-based DSP unit. The vac-

uum packaged sensor was mounted on a PCB with

front-end electronics and installed on a 1291BR Ideal

Aerosmith rate table inside the thermal chamber.

Electrostatic capacitive actuation and detection were

employed along with the EAM technique for the para-

sitic feedthrough elimination. All control and signal

processing were realized using a LabView program-

mable, FPGA-based HF2 unit from Zurich Instru-ments.

Fig. 4 depicts drive- and sense-mode control

loops used for high precision angular rate measure-

ments. The PLL-based drive-loop sustained oscilla-

tion at resonance and provided reference for the side-

band demodulations. The AGC stabilized the ampli-

tude of drive-mode motion. Rotation was detected by

demodulating the sense-mode signal. Rate was pro-

portional to a feedback force used to null the Coriolis induced motion (FRB loop). The rate measurements

were performed at a 0.2 Hz separation between drive-

and sense-mode frequencies.

II-E. QMG Experimental Characterization

The damping and frequency symmetry of the

stand-alone QMG prototype with a 2 kHz operational

frequency was evaluated using ring-down tests in a

TestEquity 107 thermal chamber. Fig. 5 shows meas-ured time-domain amplitude decays of both mechani-

cal modes at the room temperature. Exponential fits

revealed identical drive- and sense-mode Q-factors of

Fig. 5: Experimental characterization of the pack-

aged QMG using ring-down tests, revealing identical

drive- and sense-mode Q-factors of 1.17 million (with

Q/Q of 1 %).

Fig. 6: Measured Q vs. temperature for a packaged

QMG. The 1/T3 dependence is attributed to the thermoelastic dissipation. Q-factors > 0.7 M were

observed up to 100 C.

1.17 million with Q/Q variation of 1 % before tuning or compensation, confirming the complete structural

symmetry. The measured Q value of 1.17 million is

within 90% of the 1.3 million thermoelastic limit es-

timated by finite element modeling for the QMG de-

sign. The ultra-high Q-factor translates into the fun-

damental mechanical-thermal resolution limit of

0.01 /hr/Hz for a mode-matched case. The temperature sensitivity of frequency and Q-

factor were characterized in the range from 5 C to

100 C. Isotropic Q-factors above 0.7 million were

experimentally observed up to 100 C for a packaged

QMG, Fig. 6. The fit to the Q(T) data revealed 1/T3 dependence, suggesting that the dominant energy loss

mechanism is thermoelastic dissipation [17]. Frequen-

cy symmetry of the QMG design was previously

evaluated in [12], and confirmed closely matched

TCFs of –22.6 0.2 ppm/C for both modes. The ultra low dissipation design and closed loop

operation of the QMG are expected to provide low

noise rate performance. Fig. 7 shows rate response of

the packaged QMG sensor performed under a 0.2 Hz

frequency mismatch in the input angular rate range of

45 /hr, demonstrating the linearity and ability to measure rates on the order of Earth’s rotation.

III. NORTH FINDING AND TRACKING

The QMG transducer [9, 13] was chosen for the

IMU development due to its symmetric design with

low energy dissipation and isotropy of both frequency

and damping. Stand- alone QMGs were fabricated

using an in-house silicon-on- insulator (SOI) process

with a 100 μm device layer and a 5 μm sacrificial oxide. Singulated devices were vacuum sealed using a

ceramic package technology with getters, providing

asub-mTorr vacuum sustainable over many years.

Mechanical characterization of the packaged QMGs

using ring-down tests showed drive- and sense-mode Q-factors of 1.2 million, with ΔQ/Q symmetry of 1%

[11]. The high Q-factor translates into an exceptional

mechanical-thermal resolution limit of 0.0001 °/√hr

for mode-matched operation, suggesting feasibility of

the sensor for gyrocompassing applications. Thermal

cycling confirmed Q-factor above 0.7 million for

temperatures up 100 °C (with Q of 1.7 million for –20

°C) [6].

The noise performance of the gyroscope used in

this work was evaluated using the Allan deviation

analysis. Fig. 8 shows current test results for the con-ventional amplitude modulated (AM) rate measuring

mode [6], without temperature calibration. The QMG

demonstrated angle random walk (ARW) of 0.07

°/√hr (4.2 °/hr/√Hz), in-run bias of 0.22 °/hr, and rate

random walk (RRW) of 0.3 °/hr/√hr (0.005

°/hr×√Hz). Next, we demonstrate that the low level of

noise the QMG allows North detection based on the

Earth’s rotation measurements.

The true North orientation (as opposed to the

magnetic North) is found by observing the horizontal

component of the Earth’s rotation vector. We imple-mented both “maytagging” and “carouseling” of a

gyroscope on a rotary platform for North-finding.

III-A. North-Finding Using Maytagging

“Maytagging” is discrete ±180° turning of the gy-

roscope sensitive axis, which allows for differential

azimuth detection. Following this approach, we

mounted the QMG with its input axis horizontal on a

rotary platform and separated the Earth’s rotation rate from the sensors bias by a virtue of 0° to 180° turns.

By combining the east (0°) and west (180°) readings

of platform heading, both azimuth (North direction)

and the gyroscope bias were recovered. The differen-

tial “maytagging” approach is effective for the con-

stant bias. In practice, however, bias was time-varying

and residues were still present in azimuth measure-

ments, Fig. 9 inset.

The detailed analysis confirmed temperature var-

iations to be the primary drift source. Temperature

self-compensation using the gyroscope frequency as

an embedded thermometer resolved normal distribu-

Fig 7: Measured linear rate response in 45/hr

range. Inset: time history of a gyro output with 15/hr increments.

Fig. 8: Allan deviation of the QMG rate sensor used

in this work, revealing a 0.07 °/√hr ARW, and a

0.22 °/hr bias stability in rate measuring AM mode.

tion of measurement errors. The azimuth uncertainty of 100 repeated measurements was 40 mrad before

filtering or averaging [7], Fig. 9.

III-B. North-Finding Using Carouseling

The continuous modulation of the constant

Earth’s rate for separation from the sensor bias is also

possible as an alternative to the 2-point discrete azi-

muth measurement (“may- tagging”). The continuous

rotation or “carouseling” mechanization of the plat-form allows identification of azimuth angle, bias and

scale-factor error. Specifically, the true North was

detected by rotating the QMG sensitive axis in a hori-

zontal plane with a 1 °/s rate, which modulates the

Earth’s constant rate with a 6 minute period, Fig. 10

inset. Every 6 minutes the azimuth was extracted from

a sinusoidal fit.

Probability analysis of the measurements re-

vealed a Gaussian error model without any tempera-

ture calibration [7]. By filtering a sequence of multi-

ple azimuth measurements, a progressively more pre-cise azimuth was obtained (beyond the resolution of

the gyroscope). The measurement uncertainty scaled

down as the square root of the number of turns,

Fig. 10. The experiment achieved a 3 mrad uncertain-

ty by averaging of 150 azimuth data points. Ongoing

improvements in the gyroscope layout and electronics

are projected to reduce the 3 mrad gyrocompassing

time down to one minute.

III-C. FM Gyroscope Operating Principle

While North-finding necessitates a very low

noise and narrow range sensor, North-tracking and

navigation through fast motion adds the requirements

for wide dynamic range and robustness. The QMG

transducers address these challenges by switching

between the high resolution AM and wide range FM

measurement modalities [10]. The frequency modulation (FM) approach tracks

the resonant frequency split between two symmetric

high-Q mechanical modes of vibration in the QMG

transducer to produce a frequency based measurement

of the input angular rate with inherent self-calibration

against temperature variations, Fig. 11. The FM oper-

ation mode eliminates the gain-bandwidth and dynam-

ic range trade-off of conventional AM gyroscopes and

enables signal-to-noise ratio improvements by taking

advantage of high-Q transducer without limiting the

measurement range and bandwidth.

III-D. Wide Dynamic Range Demonstration

The proposed FM gyroscope operation provides a

wide input rate range, limited only by the natural fre-

quency of a mechanical element [11]. For the experi-

mental validation, a vacuum packaged QMG was

mounted on an Ideal Aero- smith High-Speed Position

and Rate Table System 1571, and characterized from

0 to 18,000 °/s (50 revolutions per second). Without any compensation, the FM instrumented QMG

demonstrated less than 0.2% nonlinearity throughout

the entire range, Fig. 12.

Fig. 11: Schematic of the gyroscope operation based

on the mechanical FM of the input angular rate. In-ertial rotation causes a split between the gyroscope’s

two vibratory modes, producing an FM measure of

the input rate.

Fig. 9: Azimuth histogram with normal distribution

fit after temperature self-compensation, showing a 40

mrad error of maytagging. Inset: raw histogram.

Fig. 10:. Azimuth uncertainty as a function of filtered

measurements. A 3 mrad error is achieved after 150

data points. Inset: Earth’s rotation measurements

Theoretical analysis of the proposed FM rate sen-

sor also suggests immunity against the temperature-

induced drifts by virtue of the differential frequency detection, i.e. by measuring the frequency split [10].

To experimentally investigate this concept, a vacuum

packaged QMG sensor operated in FM mode was

characterized on a temperature controlled Ideal Aer-

osmith 1291BR rate table. Without any active temper-

ature compensation, experimental characterization of

the FM instrumented QMG revealed less than 0.2%

scale-factor change from 25 °C to 70 °C, Fig. 13. De-

spite a 30% reduction of the Q-factor and a 5 Hz

change of the nominal frequency, the scale-factor

sensitivity was less than 50 ppm/°C (limited by the experimental setup noise), demonstrating temperature

robustness of the differential FM measurements.

The interchangeable AM/FM operation of the

QMG sensor is expected to provide wide dynamic

range for North-finding and North-tracking applica-

tions. The measured 0.22 °/hr bias instability of the

AM mode combined with the measured ±18,000 °/s

linear range of the FM mode enables the dynamic

range of at least 170 dB. This makes a single high-Q

MEMS transducer fitted for demanding high precision

and wide input range applications.

IV. SILICON ACCELEROMETER WITH

DIFFERENTIAL FREQUENCY MODULATION

While silicon MEMS accelerometers have proven

themselves as commercially successful devices, sig-

nificant challenges remain in bringing them to high

performance, mission critical applications. Conven-

tional micromachined pendulous accelerometers oper-

ate as analogue Amplitude Modulated (AM) systems,

with an inherent gain-bandwidth tradeoff and dynamic

range limited by the stability of capacitive pickoff

electronics. These analogue devices typically show

poor long term and environmental stability. Packaging

requirements for the highly damped pendulous accel-

erometers contradict the vacuum sealing requirements of high performance MEMS gyroscopes, complicating

potential single die integration.

Another inherent disadvantage of conventional

MEMS sensors using amplitude-modulated signals

comes from the limited dynamic range, the ratio be-

tween the full-scale linear range and the smallest de-

tectable input stimulus change. In the best case sce-

nario, AM capacitive readout with carefully selected

low-noise electronic components can only achieve a

dynamic range of 10^6, with a practical limit of 10^5.

This means that achieving a better than 10^6 dynamic range and 1 ppm stability (requirement of the naviga-

tion grade) is practically impossible with conventional

MEMS sensors architectures. These fundamental limi-

tations on the dynamic range and output stability pre-

vent the use of MEMS gyroscopes and accelerometers

Fig. 12: Experimental characterization of the QMG in FM mode reveals less than 0.2% nonlinearity in a

wide input range of 18,000 °/s.

Fig. 13: Rate characterization of the QMG in FM mode shows no drift in the response for 25 °C and 70

°C despite a 30% reduction in Q-factor and a 5 Hz

drop of nominal frequency (without any temperature

compensation).

Fig. 14: Photograph of a differential FM accel-

erometer fabricated using an in-house 100 µm SOI

process. Arrows show sensitivity to acceleration and

temperature.

Fig. 15: Concept of the differential FM accelerome-ter with temperature self-calibration. Arrows show

axes of sensitivity to external acceleration and tem-

perature.

in many important applications. An alternative ap-proach to resolving these limitations is using a fre-

quency-modulated accelerometer, where induced ac-

celeration changes the resonant frequency of the de-

vice due to changes in the total effective stiffness [18,

19].

Performance of previously reported FM accel-

erometers is limited by relatively low Q-factors and

temperature dependency. The main challenge to

overcome in silicon MEMS accelerometers with FM

operation is temperature sensitivity of the resonant

frequency, caused by the strong temperature depend-ency of the silicon's Young's modulus. In this paper

we propose a wide dynamic range, differential FM

accelerometer architecture with tunable scale factor

and inherent self-calibration against dynamic envi-

ronment changes, Fig. 14. The differential FM accel-

erometer approach relies on tracking of the resonant

frequencies of two high-Q mechanical MEMS oscilla-

tors to produce quasi-digital and decoupled FM meas-

urements of the input acceleration and temperature,

Fig. 15.

IV-A. Sensor Concept and Design

The proposed differential FM accelerometer con-

sists of two identical silicon MEMS tuning fork reso-

nators. Each of the two resonators has two mechanical

degrees of freedoms: in-phase and anti-phase motion

of the coupled tines. The anti-phase mode of the reso-

nator is dynamically balanced, eliminating dissipation

of energy due to linear and angular vibrations of the

substrate. Increase of the Q-factor up to the funda-mental thermoelastic limit improves precision, stabil-

ity, and phase noise for the anti-phase vibration. In

contrast, the in-phase vibration has a low Q-factor,

which is limited by the anchor loss [20].

Each tine includes differential lateral comb elec-

trodes for electrostatic excitation of the anti-phase

mode, differential lateral comb electrodes for capaci-

tive detection, and non-differential parallel plate ca-

pacitors for modulation of stiffness by means of the

negative electrostatic spring effect. By applying a DC

voltage bias on the parallel plates, a negative electro-

static spring is created, the stiffness of which is pro-

portional to the square of the bias voltage and inverse-

ly proportional to the cube of the capacitive gap. This makes the anti-phase natural frequency highly sensi-

tive to the gap between the fixed and moving parallel

plate electrodes. In other words, the in-phase dis-

placement of the two tines modulates the resonant

frequency of the anti-phase mode.

Finite Element Modeling (FEM) was completed

using Comsol Multiphysics to determine the vibratory

modes of this device. The 2-D model of the device

consists of 296,000 triangular mesh elements, the

structure of which was imported from the lithography

mask used to create the actual device, Fig. 16. Be-cause the device moves only along the x-axis and is

fabricated from single crystalline silicon, a uniform

Fig. 17: Photograph of a differential FM accel-

erometer fabricated using an in-house 100 µm SOI

process.

Fig. 18: Photograph of a packaged differential FM

accelerometer assembled with signal conditioning

PCBs.

(a) Anti-phase mode at 2.6 kHz, QTED=O.3 million.

(b) In-phase mode at 0.9 kHz.

Fig. 16: Finite Element Modeling (FEM) results il-

lustrating the (a) anti-phase and (b) in-phase vibra-

tory modes of the FM accelerometer.

Young's Modulus was used with a value of 160 GPa.

The in-phase and anti-phase resonance frequency

were found to be 0.9 kHz and 2.6 kHz, respectively.

Through the suspension system design, the next mode

of vibrations was pushed to 25 kHz frequency to min-

imize cross axis sensitivity. A second FEM model

was then executed to analyze the fundamental

thermoelastic limit of the Q-factor. For the anti-phase

mode of vibrations, a Q-factor of 0.3 million was pre-

dicted.

IV-B. Self-Calibration through Differential FM

The proposed temperature self-calibration ap-

proach takes advantage of the differential design, in

which both oscillators have the same sensitivity to

temperature but opposite sensitivity to external accel-

eration, Fig. 14 and 15. The dependency of frequency

on temperature has a well known linear relationship

for single crystalline silicon, enabling direct self-

sensing of temperature. The differential FM signal processing tracks the frequency difference between

the two resonant accelerometers, enabling drift free

measurement of acceleration, Fig. 15. In this ap-

proach, the FM accelerometer provides a quasi-digital

measurement of the input acceleration as well as di-

rect measurement of the accelerometer temperature.

The sensor becomes its own thermometer, eliminating

thermal lags and hysteresis typical in compensation

schemes using an external temperature sensor.

V-C. FM Accelerometer Characterization

The fabrication of prototype FM accelerometers was performed using an in-house, wafer-level, single

mask process. Devices were fabricated using Silicon-

on-Insulator (SOI) wafers with a 100 μm single crys-

talline silicon device layer, a 5 μm buried oxide layer,

and a 500 μm handle wafer, Fig. 17. After wafer fab-

rication and dicing, sensors were attached to a ceram-

ic DIP-24 package, wirebonded, and vacuum sealed

in-house at ~1 Torr. In future fabrication runs, accel-

erometers will be vacuum sealed at 0.1 mTorr using

getter to enable ultra-high Q-factor operation. For

testing, the packaged sensors were assembled with

signal conditioning electronics, Fig. 18.

A standard multi-point tumble test was carried

out for a single tuning fork (non-differential) FM ac-

celerometer using an Ideal Aerosmith 2102 Series

Two-Axis Position and Rate Table System. The sen-

sor was tested by measuring the change of the anti-phase resonant frequency as a function of inclination

angle with 10 o increments. The resonance frequency

of the accelerometer was recorded for each orientation

within a range from -g to g. This experiment was per-

formed for three different tuning voltages (28, 25 and

20 V), revealing linear response to acceleration with

tunable scale factors of 4.4, 2.0 and 1.2 Hz/g, respec-

tively, Fig. 19.

To evaluate the proposed self-calibration concept,

a differential FM accelerometer with two tuning fork

oscillators was placed into a TestEquity 107 tempera-ture chamber. The temperature was set to 70 °C for

the duration of 3 hours. The temperature control was

then turned off and the output signals from both tun-

ing forks were recorded Fig. 20. Each oscillator

showed an identical 500 mg drif over the temperature

change. Differential FM demodulation provided au-

tomatic calibration against temperature by canceling

common frequency drifts between the two sensors. As

shown in Fig. 21, the drift over temperature was re-

duced to approximately 1 mg, currently limited by the

noise performance of oscillators sealed with 1 Torr

Fig. 19: Measured input-output characteristic of FM

accelerometer for different stiffness modulation DC

voltages. Inset: scale factor vs. modulation DC volt-

age.

Fig. 20: Measured output of two differential FM

channels during dynamic temperature ramp. Bias

drifts track each other, enabling self-calibration.

Fig. 21: Measured differential FM output during a

dynamic temperature ramp, showing self-calibration

against temperature with a low drift rate of 30 µg/hr.

pressure. Testing of differential FM accelerometers

sealed with getter is expected to improve the bias sev-

eral orders of magnitude.

Self-calibration by differential FM also applies to

the scale factor. The anti-phase resonant frequencies

of both tuning fork oscillators were characterized as

functions of applied acceleration at two different tem-

peratures of 30 °C and 75 °C, Fig. 22(a). The meas-

ured frequency split between the nominally equal modal frequencies was proportional to the input ac-

celeration, Fig. 22(b). Without any active temperature

compensation, experimental characterization of the

FM accelerometer at 30 °C and 75°C revealed less

than 0.5 percent response fluctuation (within the accu-

racy of the experimental setup) despite a 4 Hz drop of

the nominal frequency, Fig. 22(b).

Allan deviation analysis of FM accelerometer in-

run performance at constant temperature is shown in

Fig. 23. For a single tuning fork (non-differential) FM

accelerometer, three regimes are identified: a -1/2

slope white noise of frequency for time constants of several seconds, a zero slope flicker noise floor, and a

+1 slope temperature ramp at time constants above 10

seconds. Differential FM demodulation using two

tuning forks removes the +1 slope temperature ramp,

revealing the bias instability of 6 µg at 20 s. In com-

bination with the design linear range of 20 g, the sen-

sor demonstrates a wide dynamic range of 130 dB

dynamic range.

V. CONCLUSIONS

We demonstrated low dissipation silicon MEMS

gyroscopes and accelerometers with interchangeable

AM/FM modality for wide dynamic range IMU de-

velopment. The current performance results for vacu-

um sealed Quadruple Mass Gyroscope (QMG)

showed Q-factors of 1.2 million and total bias error of

0.5 °/hr over temperature variations [7]. Continuous rotation (“carouseling”) and discrete ±180° turning

(“maytagging”) were implemented for true North de-

tection, demonstrating a 3 mrad azimuth uncertainty.

Once North has been identified, it can be tracked by

the same transducer using FM method of detection

with a proven 170 dB dynamic range. Vertical align-

ment and acceleration sensing is enabled by the pro-

posed resonant accelerometers, with accuracy ensured

by differential frequency measurements of the accel-

eration.

Inspired by the progress on the low dissipation

inertial MEMS, we are currently developing a multi-axis MEMS based IMU with inherently quasi-digital

FM operation, Fig. 24. Currently we are developing a

single-die system comprising a gyroscope and two

resonant accelerometers in a shared vacuum package.

Due to the inherent FM nature of the system, it is ex-

pected to provide dynamic range and stability unprec-

edented in conventional inertial MEMS, while simul-

taneously reducing the power consumption of the ana-

log-digital interface.

VI. ACKNOWLEDGMENTS

The author would like to thank his collaborators

and colleagues at the University of California, Irvine

MicroSystems Laboratory. Especially valuable con-

tributions to this work were made by Prof. Andrei M.

Shkel, Dr. Sergei A. Zotov, Dr. Gunjana Sharma, Igor

P. Prikhodko, and Brenton R. Simon. The work has

(a) Measured resonant frequencies f1,2 as a function

of the input acceleration for 30 °C and 75 °C. Differ-

ential frequency split f1-f2 is invariant to tempera-

ture.

(b) Measured acceleration responses for 30 °C and

75 °C using the differential frequency split.

Fig. 22: Characterization of the differential FM ac-

celerometer at 30 °C and 75 °C, demonstrating self-

calibration to temperature. There is less than 0.5%

response fluctuation.

Fig. 23: Measured Allan deviation for a vacuum sen-

sor. Differential FM demodulation removes tempera-ture ramp and achieves a 6 µg bias at 20 sec.

been supported by various grants from NSF, NSWCDD, DARPA, and SPAWAR. The author

would also like to acknowledge valuable assistance

from several exceptional vendors, including Dr.

Flavio Heer and Stephan Senn of Zurich Instruments,

Heather Florence of SAES Getters, Zappella Pierino

and David Muhs of SST International. The gyro-

scopes and accelerometers were designed and charac-

terized at the MicroSystems Laboratory, University of

California, Irvine.

VII. REFERENCES

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Fig. 24: Single chip multi-axis MEMS IMU combin-

ing wide dynamic range gyroscopes and accelerome-

ters with frequency modulated operation. Total die size is 1 by 1 cm.