TYPICAL RESPONSE OF THE ADXRS300 MICROELECTROMECHANICAL SYSTEMS
GYROSCOPE IN ACOUSTICALLY HARSH ENVIRONMENTS
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
Simon Thomas Castro
Certificate of Approval:
George T. Flowers
Professor
Mechanical Engineering
Robert Dean, Chair
Assistant Professor
Electrical and Computer Engineering
Thaddeus Roppel
Associate Professor
Electrical and Computer Engineering
George T. Flowers
Dean
Graduate School
TYPICAL RESPONSE OF THE ADXRS300 MICROELECTROMECHANICAL SYSTEMS
GYROSCOPE IN ACOUSTICALLY HARSH ENVIRONMENTS
Simon Thomas Castro
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
August 10, 2009
TYPICAL RESPONSE OF THE ADXRS300 MICROELECTROMECHANICAL SYSTEMS
GYROSCOPE IN ACOUSTICALLY HARSH ENVIRONMENTS
Simon Thomas Castro
Permission is granted to Auburn University to make copies of this thesis at its
discretion, upon the request of individuals or institutions and at
their expense. The author reserves all publication rights.
Signature of Author
Date of Graduation
iii
VITA
Simon Thomas Castro, son of Thomas Frank Castro and Elizabeth Ann Hawkins was
born September 26, 1981, in Nacogdoches, Texas. He graduated from Robertsdale High
School as Valedictorian in 2000. He attended Auburn University in Auburn, Alabama for
five years from September 2000 to August 2005. During this time, he spent three semesters
in the cooperative education program working for VT Miltope in Hope Hull, Alabama. He
graduated magna cum laude with a Bachelor of Science degree in Electrical and Computer
Engineering and a cooperative education degree. In September of 2006, he enrolled in the
Auburn University graduate school where he has been studying MEMS-based gyros and
microfabrication techniques.
iv
THESIS ABSTRACT
TYPICAL RESPONSE OF THE ADXRS300 MICROELECTROMECHANICAL SYSTEMS
GYROSCOPE IN ACOUSTICALLY HARSH ENVIRONMENTS
Simon Thomas Castro
Master of Science, August 10, 2009
(B.S., Auburn University?Auburn, 2005)
188 Typed Pages
Directed by Robert Dean
Microelectromechanical systems (MEMS)-based gyroscopes have become increas-
ingly commonplace in the last decade or so. With improvements in manufacturing tech-
niques, MEMS-based gyroscopes have improved in reliability, sensitivity, and cost. This
has lead to an abundance of commercially available MEMS gyroscopes. With an increased
presence in the marketplace, these gyros have been subjected to an ever expanding land-
scape of harsh environments. One such typical environment exists in the presence of pow-
erful acoustic noise. It will be shown that such an environment can have a great impact on
the gyro?s electrical output responses. Of singular focus will be the Analog Devices, Inc.
ADXRS300. The ADXRS300 is one of the most common commercial gyroscopes in the
global market as of this writing. The electrical output response will be fully characterized
while in the presence of acoustic noise to simulate several harsh real-life situations such as
loud music concerts, rocket firing scenarios, missile guidance systems, etc.
In this thesis, the basic theory behind vibratory MEMS gyroscopes will be discussed
to show how some of the design parameters originate. Also, a survey of commercially
available MEMS gyros will be presented. In addition, a further survey of new developments
v
in MEMS gyros that are taking place today will be put forth. Furthermore, the methods for
data extraction and sound level manipulation will be described. Next, the typical electrical
output response to various sound pressure levels will be shown. Finally, trends in the data
such as mean and standard deviation will be presented followed by conclusions and ideas
for further work.
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ACKNOWLEDGMENTS
The author would like to thank Dr. Robert Dean for his guidance, wisdom, and pa-
tience without which this thesis would not exist. Also, gratitude goes to Dr. George Flowers
for his support and knowledge of acoustics and vibrations. In no small way, many thanks
also go to Grant Roth, Ran Zhou, Brian Grantham, Mike Palmer, Charles Ellis, Dr. Anwar
Ahmed, John Crawford, Justin Russell, Nesha Hyatt, and Advanced Circuits for their in-
valuable assistance. The unconditional love and support of my family and closest friends
made this research possible by giving me an unfathomable amount of happiness. ?Happi-
ness is nothing if not shared...? and I owe all the people closest to me for making me who I
am today. Lastly, I?d like to thank the entire Auburn Family for the seven best years of my
life. War Eagle!
?The most exciting phrase to hear in science,
the one that heralds the most discoveries,
is not ?Eureka!? (I found it!) but ?That?s funny...??
 Isaac Asimov
vii
Style manual or journal used IEEE Standards Style Manual (together with the style
known as ?aums?).
Computer software used LabView 8.6, Matlab R2008A, PentaLogix ViewMaster 8.4,
NCH Tone Generator 2.11, Microsoft Word 2003, Microsoft Excel 2003, and AutoHotKey
1.0.47.06 along with the document preparation package TEX (specifically LATEX) together
with the departmental style-file aums.sty.
viii
TABLE OF CONTENTS
LIST OF FIGURES xii
1 INTRODUCTION 1
1.1 Where Are MEMS Gyros Found? . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Gyroscopic History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Gyroscope Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Motivation For The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 LITERATURE REVIEW OF MEMS GYROSCOPES 8
2.1 Theory Of Vibratory MEMS Gyroscopes . . . . . . . . . . . . . . . . . . . 8
2.1.1 Inertial Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 Coriolis Force and Acceleration . . . . . . . . . . . . . . . . . . . 10
2.1.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.5 Single-Axis MEMS Gyroscopes . . . . . . . . . . . . . . . . . . . 19
2.1.6 Dual-Axis Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Survey of Commercially Available MEMS Gyroscopes . . . . . . . . . . . 24
2.2.1 Analog Devices (http://www.analog.com/) . . . . . . . . . . . . . . 25
2.2.2 Robert Bosch GmbH (http://www.bosch.com/) . . . . . . . . . . . 25
2.2.3 Silicon Sensing (http://www.siliconsensing.com/) . . . . . . . . . . 28
2.2.4 BEI Systron Donner (http://www.systron.com/) . . . . . . . . . . . 31
2.2.5 Melexis (http://www.melexis.com/) . . . . . . . . . . . . . . . . . 32
2.2.6 InvenSense (http://www.invensense.com) . . . . . . . . . . . . . . 33
2.2.7 Honeywell(http://www.honeywell.com/) . . . . . . . . . . . . . . . 34
2.2.8 Gladiator Technologies (http://www.gladiatortechnologies.com/) . . 34
2.2.9 Delphi Delco (http://www.delphi.com/) . . . . . . . . . . . . . . . 34
2.2.10 Daimler-Benz (http://www.daimler.com) . . . . . . . . . . . . . . 36
2.2.11 Northrop Grumman (http://www.northropgrumman.com/) . . . . . 38
2.2.12 NEC-Tokin (http://www.nec-tokin.com/) . . . . . . . . . . . . . . 38
2.2.13 GyroOptics (http://www.gyro.ru/) . . . . . . . . . . . . . . . . . . 38
2.3 Survey of New Developments in MEMS Gyros . . . . . . . . . . . . . . . 39
2.4 The Analog Devices ADXRS300 Angular Rate Sensor . . . . . . . . . . . 53
ix
3 PERFORMANCE OF THE ADXRS300 IN HARSH ACOUSTIC ENVIRONMENTS 64
3.1 Harsh Acoustic Environments . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.1 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.2 Error Sources in the ADXRS300 . . . . . . . . . . . . . . . . . . . 68
3.1.3 Shock and Vibration . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2 Evaluation Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Evaluation Procedure and Setup . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.1 Overall Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.2 Evaluation Boards . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.3 Evaluation Facility . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.4 Rate Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.5 Speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.3.6 Audio Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.3.7 Data Acquisition Device . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.8 Microphone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.9 Equipment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.10 Data Collection and Sound Generation Software . . . . . . . . . . 95
3.4 Evaluation of the ADXRS300 Gyros . . . . . . . . . . . . . . . . . . . . . 106
3.4.1 Minimum and Maximum Sound Pressure Levels . . . . . . . . . . 107
3.4.2 Reference Gyro Data . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.4.3 Baseline (No Sound and 0 DPS) . . . . . . . . . . . . . . . . . . . 120
3.4.4 White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.4.5 Resonant Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 131
3.4.6 First Sub-Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.4.7 Sine Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
3.5 Evaluation Data Analysis and Results . . . . . . . . . . . . . . . . . . . . 144
3.5.1 Bias Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
3.5.2 No Noise Standard Deviations . . . . . . . . . . . . . . . . . . . . 145
3.5.3 White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.5.4 Resonant Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 149
3.5.5 First Sub-Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . 152
4 CONCLUSIONS 153
5 FUTURE WORK 160
BIBLIOGRAPHY 161
APPENDICES 164
A MATLAB NOISE GENERATION CODE 165
B DATA COLLECTION CODE 166
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C GYROS TO NI DAQ SCHEMATIC 170
D LABVIEW BLOCK DIAGRAMS 171
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LIST OF FIGURES
1.1 A Wheel?s Tendency to Precess While Spinning . . . . . . . . . . . . . . . 2
1.2 Precession of a rotating body . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Lump model of a vibratory rate gyoscope . . . . . . . . . . . . . . . . . . 10
2.2 Rotion of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Curved trajectory of a ball rolling on a spinning disk . . . . . . . . . . . . 11
2.4 Coriolis acceleration on a moving body in a rotating system . . . . . . . . . 12
2.5 Single mass gyroscope schematic . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Equations of motion and natural frequency . . . . . . . . . . . . . . . . . . 13
2.7 X- and Y-axis oscillatory responses . . . . . . . . . . . . . . . . . . . . . . 14
2.8 Gyroscope mass deflection response due to Coriolis acceleration . . . . . . 15
2.9 Tuning-fork structure for angular rate sensing . . . . . . . . . . . . . . . . 17
2.10 Die photo of the Analog Devices ADXRS300 [28] . . . . . . . . . . . . . 54
2.11 Schematic of the gyroscope elements . . . . . . . . . . . . . . . . . . . . . 54
2.12 ADXRS300 application circuit . . . . . . . . . . . . . . . . . . . . . . . . 55
2.13 Block diagram with external components . . . . . . . . . . . . . . . . . . 56
2.14 Absolute maximum ratings . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.15 RATEOUT signal v. clockwise rotation . . . . . . . . . . . . . . . . . . . 57
2.16 BGA pin diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.17 Pin Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
xii
2.18 ADXRS300 dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.19 ADXRS300 specifications taken from [28] . . . . . . . . . . . . . . . . . . 63
3.1 Sway space equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Isolation schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3 Natural frequency equation . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4 System response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 MEMS gyro schematic with forces . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Factors affecting snap-down phenomenon . . . . . . . . . . . . . . . . . . 72
3.7 ADXRS300 board schematic . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.8 ADXRS300 board layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.9 Unpopulated evaluation board photo . . . . . . . . . . . . . . . . . . . . . 77
3.10 Evaluation board populated with capacitors . . . . . . . . . . . . . . . . . 78
3.11 Flip chip bonder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.12 Chip placed on table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.13 Board placed under camera . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.14 Aligning solder balls to the board pads . . . . . . . . . . . . . . . . . . . . 82
3.15 Chip successfully placed on board . . . . . . . . . . . . . . . . . . . . . . 83
3.16 Reflow temperature profile . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.17 Packaging lab reflow oven . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.18 Ready for solder reflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.19 Placing board on the reflow oven belt track . . . . . . . . . . . . . . . . . . 86
3.20 Finished boards exiting the reflow oven . . . . . . . . . . . . . . . . . . . 87
3.21 Boards cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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3.22 The board is connected to a voltage supply (5V) . . . . . . . . . . . . . . . 89
3.23 The rate output signal is measured with an oscilloscope . . . . . . . . . . . 90
3.24 Fully Populated evaluation board . . . . . . . . . . . . . . . . . . . . . . . 91
3.25 Acoustic chamber in Wilmore labs . . . . . . . . . . . . . . . . . . . . . . 92
3.26 Acoustic chamber with open doors . . . . . . . . . . . . . . . . . . . . . . 93
3.27 Gyro testbed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.28 Configuration of the four drivers relative to the rate table . . . . . . . . . . 96
3.29 Reference gyro attached to the rate table . . . . . . . . . . . . . . . . . . . 97
3.30 Assembled gyro group . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.31 Reference gyro and group on table . . . . . . . . . . . . . . . . . . . . . . 99
3.32 Digital thermometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.33 Microphone and thermocouple . . . . . . . . . . . . . . . . . . . . . . . . 101
3.34 Data collection station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.35 NView HMI for controlling rate table startup screen . . . . . . . . . . . . . 103
3.36 NView HMI for controlling rate table . . . . . . . . . . . . . . . . . . . . 104
3.37 NCH Tone Generator Software . . . . . . . . . . . . . . . . . . . . . . . . 104
3.38 Gyros.vi data collection screen . . . . . . . . . . . . . . . . . . . . . . . . 105
3.39 PressureTransducerSUM.vi screen . . . . . . . . . . . . . . . . . . . . . . 106
3.40 10 Second Average SPL Baseline(No Sound) . . . . . . . . . . . . . . . . 108
3.41 White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.42 Single Frequency (Tone) . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.43 Reference gyro?s rate output at various angular rates without sound . . . . . 111
3.44 Reference gyro?s self-test rate out without sound . . . . . . . . . . . . . . . 112
xiv
3.45 Reference gyro with white noise . . . . . . . . . . . . . . . . . . . . . . . 113
3.46 Reference gyro?s self-test with white noise . . . . . . . . . . . . . . . . . . 114
3.47 Reference gyro sine sweep . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.48 Reference gyro?s self-test sine sweep . . . . . . . . . . . . . . . . . . . . . 116
3.49 Reference gyro sine sweep near resonant frequency (0 DPS) . . . . . . . . 117
3.50 Reference gyro?s resonant frequency (0 DPS) . . . . . . . . . . . . . . . . 118
3.51 Reference gyro?s 1st harmonic at 6951.95 Hz (0 DPS) . . . . . . . . . . . . 119
3.52 Reference gyro output at various sound pressure levels (0 DPS) . . . . . . . 120
3.53 Reference gyro two tone test (+/- 4 kHz) . . . . . . . . . . . . . . . . . . . 121
3.54 Reference gyro two tone test (+/- 3 kHz) . . . . . . . . . . . . . . . . . . . 122
3.55 Reference gyro two tone test (+/- 2 kHz) . . . . . . . . . . . . . . . . . . . 123
3.56 Reference gyro two tone test (+/- 1 kHz) . . . . . . . . . . . . . . . . . . . 124
3.57 Reference gyro two tone test (+/- 100 Hz) . . . . . . . . . . . . . . . . . . 125
3.58 Reference gyro two tone test (+/- 10 Hz) . . . . . . . . . . . . . . . . . . . 126
3.59 Reference gyro two tone test (+/- 1 Hz) . . . . . . . . . . . . . . . . . . . 127
3.60 Reference gyro two tone test (+/- 0.1 Hz) . . . . . . . . . . . . . . . . . . 128
3.61 Reference gyro two tone test (+/- 0.01 Hz) . . . . . . . . . . . . . . . . . . 129
3.62 Baseline (No Sound and 0 DPS) . . . . . . . . . . . . . . . . . . . . . . . 130
3.63 White Noise at 0 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.64 White Noise at 60 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.65 White Noise at 120 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.66 White Noise at 180 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
3.67 White Noise at 240 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
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3.68 White Noise at 300 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.69 White Noise at -60 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
3.70 White Noise at -120 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3.71 White Noise at -180 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
3.72 White Noise at -240 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.73 White Noise at -300 DPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.74 Resonant Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . 142
3.75 First Sub-Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
3.76 Sine sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
3.77 Baseline mean bias voltages . . . . . . . . . . . . . . . . . . . . . . . . . 145
3.78 Baseline standard deviations of rate output . . . . . . . . . . . . . . . . . . 146
3.79 Resonant frequencies of each gyro . . . . . . . . . . . . . . . . . . . . . . 151
3.80 First sub-harmonic frequencies of each gyro . . . . . . . . . . . . . . . . . 152
4.1 Natural frequency normal distribution . . . . . . . . . . . . . . . . . . . . 157
4.2 Standard deviation of gyros at increasing angular rates . . . . . . . . . . . 158
4.3 Standard deviation of groups E and F at increasing angular rates . . . . . . 159
C.1 Wiring diagram for gyros to NI BNC-2110 . . . . . . . . . . . . . . . . . . 170
D.1 Gyros.vi block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
D.2 Gyros.vi block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
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CHAPTER 1
INTRODUCTION
In today?s fast evolving technology market, microelectromechanical systems (MEMS)
gyroscopes are becoming everyday appliances for both the common consumer and state-of-
the-art applications. There are many causes for this phenomenon, none of which should be
overlooked. Miniaturization, low cost, improved reliability, increased sensitivity, and ease
of implementation are all combining to make MEMS-based gyros one of the most exciting
and beneficial technologies to appear in quite some time.
1.1 Where Are MEMS Gyros Found?
MEMS gyros are so prevalent in today?s world that many people may not even real-
ize how often they interact with such devices. For instance, GPS navigation systems in
the latest automobiles all use MEMS gyros to help the navigation software determine the
direction of travel when the GPS signal itself is weak. Furthermore, many luxury vehi-
cles utilize stability control features to sense yaw, and compensate for over-steering and
under-steering on a slick road surface [1].
In the aeronautics industry, MEMS gyros are used for missile guidance, flight naviga-
tion, and radar stabilization. Likewise, in the consumer electronics industry MEMS gyros
are used for accurate electronic image stabilization in digital cameras and camcorders. Seg-
way Scooters also utilize MEMS gyros to provide natural steering based on the passenger?s
body movements [1]. All these applications and others on the horizon are relatively recent
developments and are thus becoming more and more important in this new millennium.
1
1.2 Gyroscopic History
In 1850, French Physicist, Jean Foucault, first utilized the ability of a rotor?s spin axis
to remain fixed in space in seeking a method to demonstrate that the earth rotated. Foucault
also coined the word which we now designate devices based on the properties of a spinning
rotor. He chose the word gyroscope from the Greek words ?gyros,? meaning rotation, and
?skopein,? meaning to view. Hence, the word gyroscope literally means ?to view rotation?
[2].
The traditional macroscale gyroscope is basically a mechanical device, the essential el-
ement of which is a flywheel rotating at high angular velocity about an axis. The flywheel is
mounted within gimbals which allow it one or two degrees of freedom. Gyroscopes derive
their basic applications from two inherent properties, namely precession and gyroscopic
inertia [2]. Figure 1.1 shows a wheel?s tendency to precess while rotating and attached to
only one end of its axis.
Figure 1.1: A Wheel?s Tendency to Precess While Spinning
In other words, in its simplest form, the gyroscope is nothing more than a spinning top
with both ends of its axis supported while allowing a platform to move [3]. A century ago
these crude devices were used to steer torpedoes, steady vessels, travel along a single rail
or on a wire, finding position at sea, proving the rotation of the earth, finding true North,
and stabilizing planes [3].
2
1.3 Gyroscope Basics
The play top or the flywheel with its axle mounted to a fixed structure is the classic
example of the gyroscopic effect [4]. When either device is spun with its axis out of the
vertical, the device will appear to ?rise? unaided. It will resist any attempt to make it fall,
and seems never to respond to any external stimulus. In fact, the flywheel will look to be
defying gravity if it is spun at a high enough angular velocity [4]. This is the essence of the
gyroscopic effect.
Mathematically speaking, there are several fundamental relationships that describe the
gyroscopic effect. One of the most important relationships, practically-speaking, is the re-
lationship between precession (f), the external moment (M), and the angular velocity of
the spin (W). This relationships states that for a given external moment, the greater the
spin velocity, the slower the precession. This is shown by the equation: W = MyCf where C
is a constant [5]. Another fundamental relationship is that of angular momentum (H) and
torque (M) of the gyroscope. The equation: M = dHdt describes this correlation [10]. A
third common relationship is that of the single-axis rate gyroscope. This type of gyro is
used to measure angular velocity. The fundamental equation for this gyro configuration is
simply: a = -Cnk W. Thus, when a platform is turned steadily about a single axis, the gimbal
will adopt a steady-state deflection proportional to the rate of turn. This principle can be
seen in aircraft turn-and-slip indicators, gunsights for tracking high-speed targets, stabiliz-
ing searchlights at sea, and anti-rolling devices on ships [11]. Many application specific
design rules may be derived from these equations such as satellite attitude control, gyro
blender phase stabilization, airplane propeller forces, optimally-balanced crankshafts, and
even monorails [6][7][8][9][12]. The fundamental gyroscope equations are summarized in
Equations 1.1 - 1.5.
3
W = MyCf (1.1)
M = dHdt (1.2)
a = Cnk W (1.3)
H = Iw (1.4)
T = dHdT +W (1.5)
A gyroscope as an inertial instrument is capable of sensing rotation in a number of
ways. One such way was invented by Leon Foucault in 1852. This first gyroscope was
based on the angular momentum of a spinning wheel. The angular momentum, H, is the
product of the mass moment of inertia, I, and the angular velocity, w, of the wheel: H = Iw.
Due to Newton?s laws of motion, the angular momentum of a body will remain unchanged
unless acted on by a torque, T: T = dHdT +W x H. If a torque is applied in the same axis as the
angular velocity, the effect is to accelerate or decelerate the rotating body, which is denoted
by the first term of the previous equation. However, if the torque is applied orthogonal to
the spin axis, the rotating body will precess, W, denoted by the second term of the equation.
These effects are illustrated in Figure 1.2 below.
Figure 1.2: Precession of a rotating body
4
The cross-product in the second term generates the interesting gyroscopic effects (i.e.,
W, H, and T are related by the right-hand rule). Precession or the moments generated by
precession are utilized by this form of gyroscope to measure angular rate. The spinning
wheel gyroscope is used to implement a class of high-performance gyroscopes for inertial
navigation as well as other lower performance applications. Because the fabrication of this
type of gyroscope requires precision bearings, machining, drive motors, and electronics,
it is very costly, large, and heavy. However, in the 1950?s inertial navigation for missiles,
aircraft, and submarines came to rely on this type of gyroscope [15].
1.4 Motivation For The Thesis
With advances in micromachining and other microfabrication techniques, the gyro-
scopes mentioned above were able to go from large, bulky devices with limited sensitivity
to devices that are able to be implemented in integrated circuits sized packages with ex-
tremely high precision. This fact coupled with low costs has created a boom in MEMS-
based gyroscope production.
One of the major differences between a traditional gyroscope and a MEMS gyro is
the method of movement of the proof mass. In a traditional gyroscope, the proof mass was
typically a spinning wheel or some such similar mechanical device. On the other hand,
a MEMS gyro uses a high frequency vibration as a means to move the micro-sized proof
mass. The frequency to which a proof tends to vibrate is called its natural frequency and is
dependent on a number of factors which will be described later in the thesis. This natural
frequency is often located in the acoustic spectrum which is from 0 to 20,0000 Hz.
Obviously, this could present a major problem. If a MEMS gyro finds itself in the
presence of loud acoustic noise, it may artificially vibrate and cause the angular rate output
5
to be erroneous. This could lead to system malfunction or complete failure of a desired
objective.
For instance, imagine someone is trying to film a rock concert, a trip to Niagra Falls,
or even a football game. If this person is using a digital camcorder with a MEMS gyro
image stabilization feature, the resulting video could be completely ruined by the hard-
ware ?stabilizing? the video when it was not necessary. A Segway scooter, GPS system,
or dangerous-if-not-accurate rocket guidance system could be affected in a very similar
manner. Each of these could fail in the presence of loud acoustic noise. This is one of the
primary motivations of this thesis.
One of the most popular MEMS gyros on the market today is the Analog Devices
ADXRSXXX-series of angular rate gyros. These gyros are used worldwide in an over-
whelmingly large number of commercial, industrial, and military applications. This model
was chosen as a basis for this thesis to be representative of a inexpensive, popular, commer-
cially available MEMS gyro which could be ordered by anyone through Digi-Key, Newark,
or many other common electronic supply retailers. Furthermore, a member of this ADI
gyro family would be representative of the functionality of other types of low-cost com-
mercially available MEMS gyros manufactured by other companies. As such, a complete
evaluation of this product would benefit the large community of technical designers who
are intimately familiar with it.
1.5 Thesis Statement
The primary purpose of this thesis is to present the results of a thorough evaluation of
the Analog Devices ADXRS300 series angular rate gyro in a harsh acoustic environment.
Before this is presented, a cursory review of vibratory MEMS gyroscopic theory will be
presented. Then, a survey of commercially available MEMS gyros along with a survey of
6
new MEMS gyro developments will be shown. Next, a detailed overview of the Analog
Devices ADXRS300 will be presented. Furthermore, the performance of the ADXRS300
in the presence of acoustic noise will be presented with a discussion of the methods for data
retrieval and analysis. Finally, the performance trends of the ADRXRS300 will presented
with conclusions and further work.
7
CHAPTER 2
LITERATURE REVIEW OF MEMS GYROSCOPES
In this chapter, the general theory of vibratory MEMS gyroscopes will be presented.
The fundamental principles and concepts of vibratory MEMS gyroscopes will be shown to
gain needed background into the world of MEMS gyro design.
Next, a survey of commercially available MEMS gyroscopes will be presented along
with some of their features and price points. These gyros will be examples of what con-
sumers can expect to readily find when needed.
Finally, a detailed description of the Analog Devices ADXRS300 will be presented.
This description will include a list of features, design elements, and other important char-
acteristics of the device.
2.1 Theory Of Vibratory MEMS Gyroscopes
Vibratory gyroscopes are based on Coriolis acceleration, which is an acceleration pro-
duced due to the changing direction in space of the velocity of the body relative to the
moving system. Another approach for rotation rate sensing lies in the dynamics of vibrat-
ing mechanical systems. The fact that vibrating objects are sensitive to rotation has been
known since 1890 [15]. The initial concept for an implementable vibratory gyroscope was
based on the vibration of a metal tuning fork [15]. By the 1960s, engineers were seeking al-
ternatives to the spinning mass gyroscope due to its size, fragility, and expense. Subsequent
technology developments enabled the realization of a functioning vibratory gyroscope. The
8
vibratory gyroscope was also later discovered to be the mechanism utilized by biological
systems such as a fly?s ability to sense angular rotation [15].
2.1.1 Inertial Sensors
Micromachined inertial sensors can be classified into two groups: accelerometers and
gyroscopes. Accelerometers measure translational acceleration along one or several axes.
Gyroscopes measure angular velocity along one or several axes. The focus of this thesis is
concentrated on micromachined gyroscopes. The first MEMS gyroscope was reported by
Draper Labs in 1991 [13].
2.1.2 Principle of Operation
MEMS gyroscopes are based on a mechanical structure that forcibly resonates and
excites a secondary oscillation in either the same structure or in a second one due to the
Coriolis force. This is known as the Coriolis effect. The angular rate signal to be measured
is directly proportional to the amplitude of this secondary oscillation [13]. All microma-
chined angular rate sensors have a vibrating element at their core. This is the moving body.
In a frame of reference fixed to the body of the oscillating element, a point on this element
oscillates with a certain velocity. If the frame of reference begins to rotate at a certain an-
gular rate, this oscillating element is then subject to a Coriolis force and a corresponding
acceleration [14].
Consequently, nearly all MEMS gyroscopes use a vibrating structure that couples en-
ergy from a primary, forced oscillation mode into a secondary, sense oscillation mode. In
Figure 2.1, a lumped model of a simple gyroscope suitable for a micromachined imple-
mentation is shown.
The proof mass is excited to oscillate along the x-axis with a constant amplitude and
frequency. Rotation about the z-axis couples energy into an oscillation along the y-axis
9
Figure 2.1: Lump model of a vibratory rate gyoscope
whose amplitude is proportional to the rotational velocity. Similar to closed loop micro-
machined accelerometers, it is possible to incorporate the sense mode in a force-feedback
loop. Any motion along the sense axis is measured and a force is applied to counterbalance
this sense motion. The magnitude of the required force is then a measure of the angular
rate signal [13].
2.1.3 Coriolis Force and Acceleration
The Coriolis effect, named after the French physicist Gaspard Coriolis, manifests it-
self in numerous weather phenomena, including hurricanes and tornadoes, and is a direct
consequence of a body?s motion in a rotating frame of reference. Figure 2.2 below is an
illustration of this phenomena in nature [14].
The Coriolis force is a force whose observability is dependent on the reference of the
observer. The Coriolis acceleration that gives rise to a Coriolis force acts perpendicularly
to the radial component of the velocity vector. Figure 2.3 below shows an example of this
is action.
10
Figure 2.2: Rotion of the Earth
Figure 2.3: Curved trajectory of a ball rolling on a spinning disk
11
The Coriolis acceleration is given by: ~aC = 2W x ~vr. Likewise, the Coriolis force is
given by: FC = 2mW x ~vr where F = m~a. The Coriolis Effect is summarized in Equations
2.1 - 2.4.
~aC = 2W~vr (2.1)
FC = 2mW~vr (2.2)
F = m~a (2.3)
Ay = W2AdQyw
y
(2.4)
For another example, Figure 2.4 shows the Coriolis acceleration, ~aC, produced on a
body moving around an axis with a fixed angular velocity, W, and moving radially with a
velocity ~vr as well. The detection of the deflection of an object due to Coriolis acceleration
is the basis for a vibratory gyroscope [15].
Figure 2.4: Coriolis acceleration on a moving body in a rotating system
2.1.4 Design
A vibratory gyroscope is composed of a resonator that will oscillate a body along one
axis and measure the orthogonal movement or force on the body due to Coriolis accelera-
tion. Figure 2.5 is a schematic of a plate being driven along the x-axis, the rotation rate to
12
be measured; W is along the z axis and the Coriolis acceleration response is sensed along
the y-axis. Although not indicated in the illustration, relative proof mass motion between
the proof mass itself and the attached frame is limited to translational motion only. For
a vibratory gyro, this results in a sinusoidal proof mass motion along the y-axis with an
amplitude of Ay = W2AdQywy .
Figure 2.5: Single mass gyroscope schematic
The first two equations in Figure 2.6 show the equations of motion (force balance) for
the body in the drive (x) and sense (y) axes, respectively. These are a system of coupled
second-order equations coupled via Coriolis acceleration terms.
Figure 2.6: Equations of motion and natural frequency
The physical mechanism for a vibratory gyroscope is the transfer of energy from one
resonator axis to another via the Coriolis acceleration coupling. The suspension for this de-
vice can have a unique natural frequency, wx, wy and a unique damping ratio for xx, xy for
each axis (equation 3 in Figure 2.6). The relative positioning of the proof mass-suspension
13
system?s natural frequencies is a gyroscope design decision. Frequently, the sense direc-
tion natural frequency, wy, is approximately 10 percent less than the drive direction natural
frequency, wx. This will provide a modest mechanical gain without significant bandwidth
or phase shift reductions. The damping ratio of the mass in the x and y axes depends
on the orientation of the mass relative to the substrate, which will determine the damping
mechanism involved (e.g., squeeze film vs. lateral shear damping). The implementation of
the gyroscope will require the mass to be driven in the x axis by the force Fx. For many
MEMS designs, Fx is electrostatic, such as an interdigitated electrostatic comb drive. The
drive amplitude, x, must be maintained very accurately because any variation will directly
contribute an error into the sense direction amplitude (equation 1 in Figure 2.6) and the gy-
roscope output. For this reason, the drive axis amplitude is controlled by an automatic gain
control feedback loop. Because the oscillatory drive portion of the gyroscope (equation 1
in Figure 2.6) is fixed to a high degree of accuracy by the gain control loop, Equation 2 in
Figure 2.6 governs the dynamics of the gyroscope response. Because the x-axis (drive axis)
is an oscillator, the response of the y axis (sense axis) will also be oscillatory (equation 1
Figure 2.7).
Figure 2.7: X- and Y-axis oscillatory responses
The Coriolis term that is the input to equation 2 in Figure 2.6 is twice the product of the
angular rate and the velocity of the x-axis oscillator, which produces a modulated signal.
Therefore, the gyroscope output will need to be demodulated to extract the rotation rate
signal. The velocity, ?x, of the drive signal that is the input to the Coriolis term of equation
2 in Figure 2.6 is simple harmonic motion, which will be zero at the extremes of motion of
14
the driven mass and a maximum as the mass passes through the undeflected position. The
mass x displacement and the Coriolis force, which contains an x velocity term, have a 90
degree phase difference; therefore, the y displacement due to the Coriolis force will also
have a 90 degree phase difference. These signals are said to be in quadrature. This will
lead to an oval deflection path (symmetric about the x-axis) of the mass shown in Figure
2.8 when the gyroscope is subject to a constant rotation rate. With a zero rotation rate, the
mass deflection pattern will not deflect in the y direction and oscillate entirely along the
x-axis as shown in Figure 2.8. However, if mass or stiffness imbalances exist in the system
dynamics as indicated in equation 2 of Figure 2.7, the mass deflection pattern will be as
shown in Figure 2.8.
Figure 2.8: Gyroscope mass deflection response due to Coriolis acceleration
These subtle imbalances in the vibration of the sense mass produce a deflection in
the y direction known as quadrature error, which contaminates the Coriolis force measure-
ment signal, which is the measure of rotation rate. The effects of quadrature error can be
minimized by a quadrature error cancellation scheme involving the use of electrostatic ac-
tuators with properly phased signals to cancel the imbalance, or by synchronous detection
methods, which take advantage of the quadrature relationship to extract the Coriolis signal
[15].
One problem is the relatively small amplitude of the Coriolis force compared to the
driving force. Assuming a sinusoidal drive vibration given by x(t) = x0 sin (wdt), where x0
15
is the amplitude of the oscillation and wd is the drive frequency, the Coriolis acceleration
is given by aC = 2v(t) x W = 2Wx0wd cos (wdt). Using typical values of x0 = 1 ?m, W = 1
deg/s, and wd = 2p20 kHz, the Coriolis acceleration is only 4.4 mm/s2. If the sensing ele-
ment along the sense axis is considered as a second order mass-spring-damper system with
a Q = 10, the resulting displacement amplitude is only 0.0003 nm. One way to increase
the displacement is to fabricate sensing elements with a high Q structure and then tune the
drive frequency to the resonant frequency of the sense mode. Very high Q structures, how-
ever, require vacuum packaging, making the fabrication process much more demanding.
Furthermore, the bandwidth of the gyroscopes is proportional to wd/Q; hence, if a quality
factor of 10,000 or more is achieved in vacuum, the bandwidth of the sensor is reduced to
only a few Hz. Lastly, it is difficult to design structures for an exact resonant frequency,
due to manufacturing tolerances. A solution is to design the sense mode for a higher reso-
nant frequency than the drive mode and then decrease the resonant frequency of the sense
mode by tuning the mechanical spring constant using electrostatic forces [13]. An accept-
able compromise between bandwidth and sensitivity is to tune the resonant frequency of
the sense mode close to the drive frequency (within 5 percent to 10 percent). A second
fundamental problem with vibratory rate micromachined gyroscopes is due to the afore-
mentioned so-called quadrature error. This type of error originates from manufacturing
tolerances manifesting themselves as a misalignment of the axis of the driven oscillation
from the nominal drive axis. As a result, a small proportion of the driven motion will be
along the sense axis. Even though the misalignment angle is very small, due to the minute
Coriolis acceleration, the resulting motion along the sense axis may be much larger than
the motion caused by the Coriolis acceleration [13].
The vector cross product operation implies that the Coriolis acceleration and the re-
sulting displacement at that point are perpendicular to the oscillation. This, in effect, sets up
an energy transfer process from a primary mode of oscillation into a secondary mode that
16
can be measured. It is this excitation of a secondary resonance mode that forms the basis
of detection using the Coriolis effect. In beam structures, these two frequencies are dis-
tinct with orthogonal displacements. But for highly symmetrical elements, such as rings,
cylinders, or disks, the resonant frequency is degenerate, meaning there are two distinct
modes of resonance sharing the same oscillation frequency. This degeneracy causes the
temporal excitation signal (primary mode) to be in phase quadrature with the sense sig-
nal (secondary mode), thus minimizing coupling between these two modes and improving
sensitivity and accuracy [14]. Additionally, the degeneracy tends to minimize the device?s
sensitivity to thermal errors, aging, and long-term frequency drifts. A simple and common
implementation is the tuning-fork structure (see Figure 2.9).
Figure 2.9: Tuning-fork structure for angular rate sensing
The two tines of the fork normally vibrate in opposite directions in the plane of the
fork (flexural mode). The Coriolis acceleration subjects the tips to a displacement perpen-
dicular to the primary mode of oscillation, forcing each tip to describe an elliptical path.
Rotation, hence, excites a secondary vibration torsional mode around the stem with energy
transferred from the primary flexural vibration of the tines. Quartz tuning forks such as
those from BEI Technologies, Systron Donner Inertial Division of Concord, California,
use the piezoelectric properties of the material to excite and sense both vibration modes.
17
The tuning-fork structure is also at the core of a micromachined silicon sensor from Daim-
ler Benz AG that will be described later [14]. Other implementations of angular rate sensors
include simple resonant beams, vibrating ring shells, and tethered accelerometers, but all
of them exploit the principle of transferring energy from a primary to a secondary mode
of resonance. Of all the vibrating angular-rate structures, the ring shell or cylinder is the
most promising for inertial and navigational-grade performance because of the frequency
degeneracy of its two resonant modes.
The main specifications of an angular-rate sensor are full-scale range (expressed in
deg/s or deg/hr; scale factor or sensitivity [V/(deg/s)]; noise, also known as angle random
walk [deg(s  pHz)]; bandwidth (Hz); resolution (deg/s); and dynamic range (dB), the
latter two being functions of noise and bandwidth. Short- and long-term drift of the output,
known as bias drift, is another important specification (expressed in deg/s or deg/hr). As
is the case for most sensors, angular-rate sensors must withstand shocks of at least 1,000
g. Micromachined angular-rate sensors have largely been unable to deliver a performance
better than rate grade [14]. These are devices with a dynamic range of only 40 dB, a noise
figure larger than 0.1 deg(s pHz), and a bias drift worse than 10 deg/hr. By comparison,
inertial grade sensors and true gyroscopes deliver a dynamic range of over 100 dB, a noise
less than 0.001 deg/(hr pHz), and a bias drift better than 0.01 deg/hr. The advantage of
micromachined angular-rate sensors lies in their small size and low cost, currently less than
10 USD. They are slowly gaining acceptance in automotive applications, in particular, for
vehicle stability systems. The sensor detects any undesired yaw of a vehicle due to poor
road conditions and feeds the information to a control system, which may activate the anti-
lock braking system (ABS) or the traction control system (TCS) to correct the situation.
The Mercedes Benz ML series of sport utility vehicles incorporates a silicon angular rate
sensor from Robert Bosch GmbH for vehicle stability [14].
18
2.1.5 Single-Axis MEMS Gyroscopes
Early micromachined gyroscopes were based on double-ended tuning forks. Two
tines, which are joined at a junction bar, are excited to resonate in antiphase along one
axis. Rotation causes the tines to resonate along the perpendicular axis. Different actuation
mechanisms can be used to excite the primary or driven oscillation mode. Electromagnetic
actuation have the advantage that large oscillation amplitudes are easily achievable. A se-
vere disadvantage, however, is that it requires a permanent magnet to be mounted in close
proximity to the sensing element, thereby making the fabrication process not completely
compatible with that of batch processing [13]. Piezoelectric excitation has also been re-
ported, for example, by Voss., who realized a double-ended tuning fork structure with the
oscillation direction perpendicular to the wafer surface using bulk micromachining. The
prevailing approach for prototype gyroscopes, however, is to use electrostatic forces to
excite the primary oscillation. For detecting the secondary or sense oscillation, different
position measurement techniques have been used such as piezoresistive, tunneling current,
optical, and capacitive, the latter being by far the predominant method. Greiff from the
Charles Stark Draper Laboratories presented a tuning fork sensor that can be regarded as
one of the first micromachined gyroscopes suitable for batch-processing [13].
The two-gimbal structure is supported by torsional flexures. The outer gimbal struc-
ture is driven into oscillatory motion at 3 kHz out of the wafer plane by electrostatic
forces. An automatic gain control (AGC) control loop ensures that the oscillation am-
plitude is constant. In the presence of a rotation about the axis normal to the sensing
element plane, energy is transferred to the inner gimbal structure, which starts vibrating at
the same frequency at an amplitude proportional to the angular spin rate. Maximum sen-
sitivity is achieved when the drive frequency of the outer structure is equal to the resonant
frequency of the inner gimbal. The sensing element could be operated in a force-balance
19
mode. Electrostatic forces generated by voltages on the feedback electrodes counterbalance
the movement of the inner gimbal. The fixed electrodes above the inner and outer gimbal
structure were fabricated by an EDP wet-etch that removes sacrificial silicon dioxide. The
lower electrodes underneath the structure were implemented as p-type buried electrodes
and are electrically isolated by a reverse biased p-n junction from the substrate. The gap
between the fixed electrodes and the movable electrodes on the resonators is between 8 and
10 ?m. To increase the mass of the inner resonator, an inertial mass made from gold, of 25
?m height, was electroformed. The first polysilicon surface-micromachined vibratory rate
gyroscope was presented in 1996 by Clark and Howe [13]. It is a direct implementation
of the lumped model presented in Figure 2.1. Standard comb drive actuators were used
to excite the structure to oscillate along one in-plane axis (x-axis), which allows relatively
large drive amplitudes. Any angular rate signal about the out-of-plane axis (z-axis) excites
a secondary motion along the other in-plane axis (y-axis). The sensing element consists of
a 2 ?m thick polysilicon structure.
In this reference, quadrature error is discussed in detailed and it is shown that a mis-
alignment of the primary oscillation axis with the ideal x-axis of only one part in 3.6 million
will result in a quadrature error equal to the signal of a 1 deg/sec rotation about the z-axis.
No fabrication process can be accurate to such a degree, and hence, electrostatic tuning is
used to alleviate this problem. The quadrature error is proportional to the position of the
primary oscillation, whereas the Coriolis acceleration is proportional to the velocity of the
primary oscillation; hence, the resulting forces are 90 degrees out of phase (this explains
the term quadrature error). The inner interdigitated electrodes of the mechanical structure
are used to exert an electrostatic force, which is proportional to the position of the pri-
mary oscillation. Applying a biasing voltage, together with a small differential voltage,
results in an electrostatic force that allows counterbalancing of the unwanted motion of the
proof mass of the primary oscillation due to quadrature error. The paper also discusses
20
the required interface and control electronics for sustaining a constant amplitude and pri-
mary frequency oscillation. For the latter, a phase-locked loop is chosen; for the former
an automatic gain control circuit is used. Furthermore, it is possible to tune the resonant
frequencies of the primary and secondary oscillation modes by applying electrostatic neg-
ative springs. As a good compromise between bandwidth and sensitivity, a mismatch of
about 5 percent to 10 percent is suggested. Another surface-micromachined gyroscope was
presented by Geiger [13]. It was manufactured using the Bosch foundry process, which
features a polycrystalline structural layer with a thickness of 10.3 ?m. This relatively large
thickness for a surface-micromachined process is achieved by epitaxial deposition of sili-
con. Under the freestanding structures a second thinner layer of polycrystalline silicon is
used for electrodes and as interconnects. The sensing element has two decoupled rotary
oscillation modes.
The primary drive mode is around the z-axis and is excited with electrostatic forces
using the inner spoke electrodes of the inner wheel. Attached to the inner wheel, by tor-
sional springs, is a rectangular structure, which, in response to rotation about the sensitive
axis (x-axis), will exhibit a secondary rotary oscillation about the y-axis. Owing to the
high stiffness of the suspension beam in this direction, the oscillation of the inner wheel
is suppressed and only the rectangular structure can move due to a Coriolis force. With
this approach the primary and secondary modes are mechanically decoupled, which sup-
presses mechanical cross-coupling effects such as quadrature error. The oscillation of the
secondary mode is detected capacitively by electrodes on the substrate. The sensor reported
a dynamic range of 200 deg/sec, a scale factor of 10 mV/(deg/sec), and a RMS noise of
0.05 deg/sec in a 50 Hz bandwidth, which makes it suitable for most automotive applica-
tions. Another popular implementation of a micromachined gyroscope, based on a single
oscillating structure with two vibrating modes [13].
21
It is based on a ring supported by a number of semicircular springs and anchored in
the middle. The ring is excited to vibrate electrostatically in-plane, the vibration having an
elliptic shape. Any rotation about the axis normal to the ring structure transfers energy to
a secondary mode, which is 45 degrees apart from the primary mode. In other words, the
antinodes of the primary flexural mode are located at the nodes of the secondary flexural
mode. Electrodes placed at these positions are used to capacitively measure the amplitude
of the secondary mode, which is proportional to the angular rate to be measured. An ob-
vious advantage of this design is the high degree of symmetry of the sensing element. An
early version was presented by Putty and Najafi in 1994 [13]. It relied on a nickel electro-
plated ring structure, which was fabricated on a wafer containing standard CMOS circuitry
for the control and interface electronics. Subsequently, this group presented more advanced
versions of this approach. Another electroplated ring gyroscope was presented by Sparks,
which mainly improved the signal and interface circuitry [13]. More recently, improved
designs have been reported based on a high aspect ratio ring made from polysilicon [13].
The fabrication relies on the deep reactive dry etching of 50 ?m- to 100 ?m-deep trenches
with near vertical sidewalls into a low-resistive silicon substrate. The trenches are subse-
quently refilled with highly doped polysilicon over a sacrificial silicon dioxide layer. After
various patterning and etching steps of the oxide and the structural polysilicon, the sacri-
ficial oxide is removed by a HF etch step to free the ring structure and form the air gaps
between the electrodes and the ring. The ring is 1.1 mm in diameter, the support post in the
middle has a diameter of 120 ?m, and the width of the ring and support springs is 4 ?m.
Sixteen fixed electrodes are evenly located around the periphery of the ring; they are 60
?m tall, 150 ?m long, and are separated from the ring by a 1.4-?m air gap. The fabrication
technology has the advantage that the height of the ring structure and the electrodes can
be made in the order of a hundred or more microns and the air gaps can be made in the
submicron range. This results in high values of capacitance for vibration measurements;
22
thus, the sensitivity is increased considerably. The fabrication process also allows large
air gaps, which can be used to excite the structure in the primary mode with high ampli-
tude, again resulting in higher sensitivity. There is, however, a trade-off between the higher
voltages required to electrostatically drive the ring using larger air gaps. Test results were
reported for a structure 80 ?m tall, operated at a low pressure (1 mTorr), which resulted
in a quality factor for the oscillation of 1,000 to 2,000. This was lower than expected and
was attributed to anchor losses and voids inside the polysilicon beams. Improved designs
were expected to have a quality factor of up to 20,000. Similar to other micromachined
gyroscopes, the resonant frequencies of drive and sense modes were designed to be equal
in order to amplify the sense mode amplitude by the quality factor. Both resonant frequen-
cies had a nominal value of 28.3 kHz. Any mismatch due to fabrication tolerances can be
electrostatically tuned by applying suitable voltages to the electrodes around the periphery
of the ring. A 63 Hz mismatch was observed between the sense and drive modes, which
required a tuning voltage of only 0.9V. Other prototypes had a higher mismatch of up to 1
kHz for which a tuning voltage of 6V was required to match sense and drive mode resonant
frequencies. The resolution of the device was measured to be less than 1 deg/sec for a 1 Hz
bandwidth; however, with some changes in the interface circuitry this should be reduced to
0.01 deg/sec, which is then limited by the Brownian noise floor of the structure [13].
2.1.6 Dual-Axis Gyroscopes
It is also possible to design micromachined gyroscopes that are capable of sensing
angular motion about two axes simultaneously. These devices are based on a rotor-like
structure that is driven into a rotary oscillation by electrostatic comb-drives. Angular mo-
tion about the x-axis causes a Coriolis acceleration about the y-axis, which, in turn, results
in a tilting oscillation of the rotor. Similarly, any rotation of the sensor about the x-axis
causes the rotor to tilt about the x-axis.
23
An implementation of such a dual-axis gyroscope was reported by Junneau [13]. It
was manufactured in a surface-micromachining process with a 2 ?m thick proof mass.
The interface and control electronics were integrated on the same chip. Underlying pie-
shaped electrodes capacitively detect the tilting motion. To distinguish the two different
output modes, a different voltage modulation frequency (200 and 300 kHz) is used for
each sense electrode pair. The reported performance was 1 deg/sec in a 25 Hz bandwidth.
The natural driving frequency of the rotor is about 25 kHz. Similar to single-axis devices,
a high quality factor can be used to amplify the output motion. In a 60 mTorr vacuum,
Junneau et al. report a quality factor of about 1,000. Electrostatic tuning of the different
resonant frequencies can be used [13]. Cross-coupling between the two output modes is
a major problem and was measured to be as high as 15 percent. This implies that for a
commercially viable version, more research has to be done for such a dual-axis gyroscope.
A conceptually similar implementation was reported by An [13]. The authors reported a
higher resolution, of 0.1 deg/sec, which was mainly due to a thicker proof mass (7 ?m)
[13].
2.2 Survey of Commercially Available MEMS Gyroscopes
Here is brief survey of commercially available MEMS gyroscopes in the industry to-
day. Product lines from the following companies will be considered: Analog Devices,
Robert Bosch GmbH, Silicon Sensing, BEI Systron Donner, Melexis, InvenSense, Hon-
eywell, Gladiator Technologies, Delphi Delco, Daimler-Benz, Northrop Grumman, NEC-
Tokin, and GyroOptics.
24
2.2.1 Analog Devices (http://www.analog.com/)
The company has recently introduced the ADXRS family of integrated angular rate-
sensing gyros, in which the mass is tethered to a polysilicon frame that allows it to resonate
in only one direction. Capacitive silicon sensing elements interdigitated with stationary
silicon beams attached to the substrate measure the Coriolis-induced displacement of the
resonating mass and its frame [16].
One of these products is the ADXRS610 300 deg/sec Yaw Rate Gyro. This sensor is
an electrostatically resonated surface micromachined polysilicon rate gyro with integrated
electronics. The actual mechanical structure utilizes two resonating microstructure to can-
cel common mode effects, such as translational acceleration. This particular model has a
measurement range of +/- 300 deg/sec and is intended for automotive and other applica-
tions. The proof mass structures are resonated at approximately 14 KHz, which is in the
audio frequency range. The measurement bandwidth can be tuned over the range of 0.01
Hz to 2500 Hz. The sensor can be calibrated to achieve an accuracy of 40 deg/hour or
better, with a typical rate noise density of 0.05 deg/sec/root(Hz). This sensor also includes
built is self test (BIST) functions and is available in a BGA package [23].
2.2.2 Robert Bosch GmbH (http://www.bosch.com/)
Robert Bosch has been very active in the design and fabrication of silicon vibratory
gyroscopes. They currently control 50 percent of the gyro market for the automotive indus-
try and related applications. Bosch has developed both Z axis and X/Y axis rate sensors.
Its Z-axis design was introduced in 1998 and uses electromagnetic drive with capacitive
sensing.
The X/Y-axis gyro is a rotary vibrating mass. The MEMS sensor element along with
its custom ASIC and all the discrete components are packaged in a hermetically sealed
25
metal can which is then placed inside its automotive style plastic housing with integral
connectors and mounting brackets [16].
This sensor is unique in its implementation of a mechanical resonant structure equiva-
lent to a tuning fork. An oscillator system consists of two identical masses coupled to each
other by a spring and suspended from an outer frame by two other springs.
Such a coupled system has two resonant frequencies: in phase, and out of phase. In
the in-phase oscillation mode, the instantaneous displacements of the two masses are in
the same direction. In the out-of-phase mode, the masses are moving, at any instant, in
opposite directions. A careful selection of the coupling spring provides sufficient separa-
tion between the in-phase and out-of-phase resonant frequencies. Lorentz forces generated
by an electric current loop within a permanent magnetic field excite only the out-of-phase
mode. The oscillation electromagnetically induces a voltage in a second current loop that
provides a feedback signal proportional to the velocity of the masses. The resulting Cori-
olis forces on the two masses are in opposite directions but orthogonal to the direction of
oscillation. Two polysilicon surface-micromachined accelerometers with capacitive comb
structures (similar in their basic operation to the Analog Devices ADXL family of sensors)
measure the Coriolis accelerations for each of the masses. The difference between the two
accelerations is a direct measure of the angular yaw rate, whereas their sum is proportional
to the linear acceleration along the accelerometer?s sensitive axis. Electronic circuits per-
form the addition and subtraction functions to filter out the linear acceleration signal. For
the Bosch sensor, the out-of-phase resonant frequency is 2 kHz, and the maximum oscil-
lation amplitude at this frequency is 50 ?m. The measured quality factor of the oscillator
at atmospheric pressure is 1,200, sufficiently large to excite resonance with small Lorentz
forces. The stimulated oscillation subjects the masses to large accelerations reaching ap-
proximately 800G. Though they are theoretically perpendicular to the sensitive axis of the
accelerometers, in practice, some coupling remains, which threatens the signal integrity.
26
However, because the two temporal signals are in phase quadrature, adopting synchronous
demodulation methods allows the circuits to filter the spurious coupled signals with a re-
jection ratio exceeding 78 dB. This is indeed a large rejection ratio, but it is still insufficient
to meet the requirements for inertial navigation. The peak Coriolis acceleration for a yaw
rate of 100 deg/s is only 200 mG. This requires extremely sensitive accelerometers with
compliant springs. The small Coriolis acceleration further emphasizes the need for per-
fect orthogonality between the sense and excitation axes. Closed-loop position feedback
of the acceleration sense element compensates for the mechanical poles and increases the
bandwidth of the accelerometers to over 10 kHz. The fabrication process simultaneously
encompasses bulk and surface micromachining: the former to define the masses and the
latter to form the comb-like accelerometers.
The process sequence begins by depositing a 2.5 ?m layer of silicon dioxide on a sil-
icon substrate. Epitaxy over the oxide layer grows a 12 ?m thick layer of heavily doped
n-type polysilicon. This layer forms the basis for the surface-micromachined sensors and
is polycrystalline because of the lack of a seed crystal during epitaxial growth. In the next
step, aluminum is deposited by sputtering and patterned to form electrical interconnects
and bond pads. Timed etching from the back side using potassium hydroxide (KOH) thins
the central portion of the wafer to 50 ?m. Two sequential DRIE steps define the structural
elements of the accelerometers and the oscillating masses. The following step involves
etching the sacrificial silicon dioxide layer using a gas phase process (e.g., hydrofluoric
acid vapor) to release the polysilicon comb structures. Finally, a protective silicon cap
wafer that contains a recess cavity is bonded on the front side using a low temperature seal
glass process. A glass wafer anodically bonded to the back side seals the device. The final
assembly brings together the silicon sensor and the electronic circuits inside a metal can
whose cover holds a permanent magnet. The sensitivity of the device is 18 mV/(deg/s)
in the range of +/- 100 deg/s over 40 to +85 degrees C. The temperature dependence of
27
the uncompensated sensor causes an offset amplitude of 0.5 deg/s over the specified tem-
perature range, but signal conditioning circuits reduce this dependence by implementing
appropriate electronic temperature compensation schemes [14].
Their most current product, the SMG040, is a micromachined angular rate sensor
especially designed for roll-over automobile applications.
The sensor is based upon a two-chip concept: the micromachined sensing element and
a separate evaluation ASIC. The sensing element is an oscillating polysilicon mass with the
sensitive axis lying in the chip plane. The micromachined structure is sealed under vacuum
at wafer level. The Sensor chip and read-out ASIC are packaged in a standard PLCC44
package. The sensing element has a symmetrical layout with only one suspension at the
pivot point. By applying electrostatic forces to comb structures, the mass is forced to a
rotational oscillation around this pivot point in the center of the mass. This oscillation is
stabilized by an electronic control loop (drive control loop) [17].
2.2.3 Silicon Sensing (http://www.siliconsensing.com/)
Silicon Sensing Systems is a joint venture between Sumitomo and British Aerospace.
They have brought to market an electromagnetically driven and sensed MEMS gyro with
a permanent magnet that sits above the MEMS device. Current passing through the con-
ducting legs creates a force that resonates the ring. This Coriolis-induced ring motion is
detected by induced voltages as the legs cut the magnetic field [16].
Silicon Sensing Systems has also launched two new silicon MEMS angular rate sen-
sors, the CRG20 and CRS09, which are based on a patented silicon ring gyro technology.
Derived from technology used in the automotive industry, the CRG20 device uses full
digital closed-loop control, which the supplier claimed can eliminate any temperature and
28
aging effects associated with analog devices. There is also built-in temperature compensa-
tion. The CRS09 angular rate sensor is targeted at applications such as stabilization, navi-
gation and testing. It uses a combination of a silicon MEMS gyro and discrete electronics.
The device?s temperature stability combined with a provision of both internal temperature
and silicon ring frequency data as additional outputs allow for very accurate calibration of
the gyro over its operating temperature range. CRS09 is suitable for platform stabilization,
measurement and test, and high-performance general aviation applications [18].
The CRS family of yaw-rate sensors from Silicon Sensing Systems, a joint venture
between BAE Systems of Plymouth, Devon, England, and Sumitomo Precision Products
Company of Japan, is aimed at commercial and automotive applications. It also uses a
vibratory ring shell similar to the sensor from Delphi Delco but differs on the excitation and
sense methods. Electric current loops in a magnetic field, instead of electrostatic electrodes,
excite the primary mode of resonance. These same loops provide the sense signal to detect
the angular position of the vibration pattern.
The ring, 6 mm in diameter, is suspended by eight flexural beams anchored to a 10-
mm-square frame. Eight equivalent current loops span every two adjacent support beams.
A current loop starts at a bond pad on the frame, traces a support beam to the ring, continues
on the ring for one eighth of the circumference, then moves onto the next adjacent support
beam, before ending on a second bond pad. Under this scheme, each support beam car-
ries two conductors. A Samarium-Cobalt permanent magnet mounted inside the package
provides a magnetic field perpendicular to the beams. Electromagnetic interaction between
current in a loop and the magnetic field induces a Lorentz force. Its radial component is
responsible for the oscillation of the ring in the plane of the die at approximately 14.5 kHz,
which is the mechanical resonant frequency of the ring. The sensing mechanism measures
the voltage induced around one or more loops in accordance with Faraday?s law: As the ring
oscillates, the area of the current loop in the magnetic flux changes, generating a voltage.
29
Two diametrically opposite loops perform a differential voltage measurement. One can
simplistically view an actuating and a sensing loop as the primary and secondary windings
of a transformer; the electromagnetic coupling between them depends on the ring vibration
pattern and thus on the angular rate of rotation. Closed-loop feedback improves the overall
performance by increasing the bandwidth and reducing the system?s sensitivity to physical
errors. Two separate feedback loops with automatic gain control circuits maintain a con-
stant oscillation amplitude for the primary mode of resonance and a zero amplitude for the
secondary resonance mode. The feedback voltage required to null the secondary mode is
a direct measure of the rate of rotation. The fabrication of the sensor is relatively simple.
A silicon dioxide layer is deposited on a silicon wafer, then lithographically patterned and
etched. The silicon dioxide layer serves to electrically isolate the current loops. A metal
layer is sputter deposited, patterned, and etched to define the current loops as well as the
bond pads. A layer of photoresist is spun on and patterned in the shape of the ring and sup-
port flexural beams. The photoresist then serves as a mask for a subsequent DRIE step to
etch trenches through the wafer. After removal of the photoresist mask, the silicon wafer is
anodically bonded to a glass wafer with a previously defined shallow cavity on its surface.
Little is available in the open literature on the packaging, but it is clear from the need to
include a permanent magnet that the packaging is custom and specific to this application.
The specification sheet of the CRS03-02 gives an output scale factor of 20 mV/(deg/s) with
a variation of +/- 3 percent over a temperature range from 40 degrees to +85 degrees C. The
noise is less than 1 mV rms from 3 to 10 Hz. The nonlinearity in a rate range of +/- 100
deg/s is less than 0.5 deg/s. The operating current is relatively large: 50 mA at a nominal 5
V supply [14].
Another Silicon Sensing model uses magnetic actuation and detection, which may
prove to be problematic for further device size reduction. The ring has a diameter of 6 mm
and is connected by eight radially compliant spokes to a support frame with the dimensions
30
of 10 x 10 mm. It is fabricated by deep reactive ion etching of a 100 ?m thick silicon wafer.
Current-carrying conductor loops are deposited on the surface of the ring structure. These
loops, together with the magnetic field, set up by the permanent magnet provide the signal
pick-off and primary oscillation mode drive. This gyroscope has a resolution of 0.005
deg/sec, a bandwidth of 70 Hz, and a noise floor of 0.1 deg/sec/pHz in a 20 Hz bandwidth.
Currently, they are developing a capacitive sensor without a permanent magnet, thereby
allowing for further size reduction [13].
2.2.4 BEI Systron Donner (http://www.systron.com/)
BEI Systron Donner is a major manufacturer of rate sensors for automotive applica-
tions. Their gyroscope design is based on using a one-piece quartz inertial sensor. These
micromachined inertial sensing elements measure angular rotational velocity, using tuning
fork vibratory principals and piezoelectric actuation and sensing. These sensors generate a
signal output proportional to the rate of rotation sensed. Each sensor element is packaged
in a hermetically sealed metal header which is then combined with discrete electronic to
produce the finished modules products [16].
Systron Donner?s family of quartz inertial sensors use a one piece, micromachined
inertial sensing element to measure angular rotational velocity. These sensors produce a
signal output proportional to the rate of rotation sensed. SDI?s unique quartz inertial sensors
are micromachined using photolithographic processes, and are at the forefront of MEMS
(Micro Electro-Mechanical Systems) technology. These processes are similar to those used
to produce millions of digital quartz wristwatches each year. The use of piezoelectric quartz
material simplifies the sensing element, resulting in exceptional stability over temperature
and time, and increased reliability and durability. The GyroChip uses vibrating quartz
tuning tines to sense angular rate, acting as a Coriolis sensor, coupled to a similar fork
as a pickup to produce the rate output signal. Each comprised of a pair of tuning forks,
31
the GyroChip along with their support flexures and frames are batch fabricated from thin
wafers of single-crystal piezoelectric quartz. The piezoelectric drive tines are driven by
an oscillator to vibrate at a precise amplitude, causing the tines to move toward and away
from one another at a high frequency. This vibration causes the drive fork to become
sensitive to angular rate about an axis parallel to its tines, defining the true input axis of
the sensor. Vibration of the drive tines causes them to act like the arms of a spinning ice
skater, where pulling them in causes the skater?s spin rate to increase, and pushing them out
causes a decrease in rate. For vibrating tines (?arms?), an applied rotation rate causes a sine
wave of torque to be produced, resulting from the oscillating torque at the frequency of the
drive tines, in turn causing the tines of the pickup fork to move up and down (not toward
and away from one another) out of the plane of the fork assembly. The pickup tines thus
respond to the oscillating torque by moving in and out of plane, causing electrical output
signals to be produced by the Pickup Amplifier. Those signals are amplified and converted
into a DC signal proportional to rate by use of a synchronous switch (demodulator) which
responds only to the desired rate signals. The DC output signal of the GyroChip is directly
proportional to input rate, reversing sign as the input rate reverses, since the oscillating
torque produced by the Coriolis force reverses phase when the input rate reverses [19].
2.2.5 Melexis (http://www.melexis.com/)
Melexis of Belgium recently has developed a MEMS angular rate sensor for use with
GPS navigation systems. The gyroscope works in tandem with an electronic magnetometer
(compass) to ensure vehicle position even when the GPS signal is lost. The system com-
putes the direction, speed, and angular rate of the vehicle and maps this to the navigation
software. The compass essentially ?zeros? the gyro to ensure proper initial heading after
GPS signal is lost. The MLX90609 Angular Rate Sensor is a full gyroscopic system.
32
A single SMD package contains a high performance silicon micro-machined sensor
with signal conditioning circuitry. It operates from 5V supply and is designed for demand-
ing automotive applications. The MLX90609 delivers two output signals proportional to
the angular rate parallel to the assembly surface. One of the output signals is in an analog
voltage format (the output is 2.5V at zero angular rate and the full scale angular rate pro-
duces an output of 4.5V or 0.5V depending on direction of rotation) and the other one is in
a digital SPI format [20].
2.2.6 InvenSense (http://www.invensense.com)
InvenSense provides motion sensing solutions for mobile applications. The com-
pany?s patented motion sensing technology and its novel Nasiri-Fabrication addresses many
emerging mass-market applications such as gaming, image stabilization, and smart user in-
terfaces that use hand motion and gesture-based commands for mobile applications, such
as smart phones, digital cameras, and 3D remote control devices. Their IDG-600 multi-axis
MEMS rate gyroscope has started shipping in mass production quantities to Nintendo for
its Wii MotionPlus accessory.
The addition of InvenSense?s multi-axis rate gyroscope solution to the Wii Motion-
Plus accessory allows high precision 3D tracking of rapid gaming gestures. InvenSense
pioneered its patented manufacturing platform, known as Nasiri-Fabrication, which en-
abled the company to bring the world?s first and smallest integrated multi-axis gyroscopes
to consumer products. Using Nasiri-Fabrication allows for the integration of MEMS and
CMOS structures at the wafer level with a proprietary bonding technology resulting in
several thousand gyroscopes simultaneously produced on a single wafer [21].
33
2.2.7 Honeywell(http://www.honeywell.com/)
The Honeywell GG5200 MEMS Rate Gyro Package is a two axis inertial sensor prod-
uct for seeker stabilization, antenna pointing, gun/turret stabilization, and flight controls.
The Honeywell GG5300 MEMS Rate Gyro Package is a three axis inertial sensor product
[22].
This device has a specified angle random walk of 0.2 deg/root(Hr).
2.2.8 Gladiator Technologies (http://www.gladiatortechnologies.com/)
The G50Z High Performance Single Axis Gyro is a MEMS rate sensor.
Designed for commercial stabilization and aircraft applications, the unit utilizes stan-
dard +5V DC power and has a voltage output. The -200 model features a +/- VSG compat-
ible signal. The signature features of the G50Z are low noise, impressive bias over temper-
ature performance, low power consumption, excellent g-sensitivity and light weight. The
unit is highly durable and can withstand environmental vibration and shock typically asso-
ciated with commercial aircraft requirements. The unit has no inherent wear-out modes for
long life and the rate output is also free from bias steps. The MEMS G50Z offers a stan-
dard angular rate range of +/- 20, 100, 175 or 350 deg/sec. Other angular rate ranges are
available. The G50Z is designed for automotive testing, commercial aircraft applications,
platform and antenna stabilization and pointing, and general aviation.
2.2.9 Delphi Delco (http://www.delphi.com/)
The sensor from Delphi Delco Electronics Systems of Kokomo, Indiana [29], a divi-
sion of Delphi Corporation of Troy, Michigan, includes at its core a vibrating ring shell
based on the principle of the ringing wine glass discovered in 1890 by G. H. Bryan. He ob-
served that the standing-wave pattern of the wine glass did not remain stationary in inertial
34
space but participated in the motion as the glass rotated about its stem. The complete theory
of vibrating-ring angular-rate sensors is well developed [30]. The ring shell, anchored at its
center to the substrate, deforms as it vibrates through a full cycle from a circle to an ellipse,
back to a circle, then to an ellipse rotated at right angles to the first ellipse, then back to the
original circle.
The points on the shell that remain stationary are called nodes, whereas the points that
undergo maximal deflection are called antinodes. The nodes and antinodes form a vibra-
tion pattern or standing-wave pattern around the ring. The pattern is characteristic of the
resonance mode. Because of symmetry, a ring shell possesses two frequency-degenerate
resonant modes with their vibration patterns offset by 45 degrees with respect to each other.
Hence, the nodes of the first mode coincide with the antinodes of the second mode. The
external control electronics excites only one of the two modes, the primary mode. But
under rotation, the Coriolis effect excites the second resonance mode, and energy transfer
occurs between the two modes. Consequently, the deflection amplitude builds up at the
antinodes of the second mode. The overall vibration becomes a linear combination of the
two modes with a new set of nodes and antinodes forming a vibration pattern rotated with
respect to the pattern of the primary mode. It is this lag that Bryan heard in his spinning
wine glass. In an open-loop configuration, the deflection amplitude at the nodes and antin-
odes is a measure of the angular rate of rotation. Alternatively, the angular shift of the
vibration pattern is another measure. In a closed-loop configuration, electrostatic actuation
by a feedback voltage applied to the excitation electrodes nulls the secondary mode and
maintains a stationary vibration pattern. The angular rate becomes directly proportional to
this feedback voltage. A total of 32 electrodes positioned around the suspended ring shell
provide the electrostatic excitation drive and sense functions. Of this set, eight electrodes
strategically positioned at 45 degrees intervals, at the nodes and antinodes, capacitively
35
sense the deformation of the ring shell. Appropriate electronic circuits complete the sys-
tem control functions, including feedback. A phased-locked loop (PLL) drives the ring into
resonance through the electrostatic drive electrodes and maintains a lock on the frequency.
Feedback is useful to electronically compensate for the mechanical poles and increase the
closed-loop bandwidth of the sensor. Additionally, a high mechanical quality factor in-
creases the closed-loop system gain and sensitivity. The fabrication process is similar to
the electroplating and molding process described in Chapter 3, except that the substrate
includes preprocessed CMOS control circuitry. The mold is made of photoresist, and the
electroplated nickel ring shell is 15 to 50 ?m thick. Finally, packaging is completed in
vacuum in order to minimize air damping of the resonant ring and provide a large quality
factor. Researchers at the University of Michigan demonstrated a polysilicon version of the
sensor with improved overall performance. The demonstrated specifications of the Delphi
Delco sensor over the temperature range of 40 degrees to +125 degrees C include a resolu-
tion of 0.5 deg/s over a bandwidth of 25Hz, limited by noise in the electronic circuitry. The
nonlinearity in a rate range of +/- 100 deg/s is less than 0.2 deg/s. The sensor survives the
standard automotive shock test: a drop from a height of one meter. The specifications are
adequate for most automotive and consumer applications [14].
2.2.10 Daimler-Benz (http://www.daimler.com)
The sensor from Daimler Benz AG of Stuttgart, Germany, is a strict implementation
of a tuning fork using micromachining technology.
The tines of the silicon tuning fork vibrate out of the plane of the die, driven by a thin-
film piezoelectric aluminum nitride actuator on top of one of the tines. The Coriolis forces
on the tines produce a torquing moment around the stem of the tuning fork, giving rise to
shear stresses that can be sensed with diffused piezoresistive elements. The shear stress is
maximal on the center line of the stem and corresponds with the optimal location for the
36
piezoresistive sense elements. The high precision of micromachining is not sufficient to
ensure the balancing of the two tines and the tuning of the two resonant frequencies. The
vibration modes of a tuning fork are not degenerate. An imbalance in the tines produces
undesirable coupling between the excitation and sense resonant modes, which degrades
the resolution of the device. A laser ablation step precisely removes tine material and
provides calibration of the tuning fork. For this particular design, all resonant modes of the
fork are at frequencies above 10 kHz. To minimize coupling to higher orders, the primary
and secondary modes are separated by at least 10 kHz from all other remaining modes. The
choice of crystalline silicon for tine material allows achieving a high quality factor (approx.
7,000) at pressures below 0.01 mbar. The fabrication process is distinct from that of other
yaw-rate sensors in its usage of SOI substrates.
The crystalline silicon over the silicon dioxide layer defines the tines. The thickness
control of the tines is accomplished at the beginning of the process by the precise epitaxial
growth of silicon over the SOI substrate. The thickness of the silicon layer, and conse-
quently of the tine, varies between 20 and 200 ?m, depending on the desired performance
of the sensor. Lithography followed by a shallow silicon etch in tetramethyl ammonium
hydroxide (TMAH) defines 2 ?m deep cavities in two mirror image SOI substrates. Silicon
fusion bonding brings these substrates together such that the cavities are facing each other.
The cavity depth determines the separation between the two tines. An etch step in TMAH
removes the silicon on the front side and stops on the buried silicon dioxide layer which
is subsequently removed in hydrofluoric acid. The following steps define the piezoelectric
and piezoresistive elements on the silicon surface. Diffused piezoresistors are formed using
ion implantation and diffusion. Piezoelectric aluminum nitride is then deposited by sputter-
ing aluminum in a controlled nitrogen and argon atmosphere. This layer is lithographically
patterned and etched in the shape of the excitation plate over the tine. Aluminum is then
sputtered and patterned to form electrical interconnects and bond pads. Finally, a TMAH
37
etch step from the back side removes the silicon from underneath the tines. The buried
silicon dioxide layer acts as an etch stop. An anisotropic plasma etch from the front side
releases the tines. The measured frequency of the primary, flexural mode (excitation mode)
was 32.2 kHz, whereas the torsional secondary mode (sense mode) was 245 Hz lower. Typ-
ical of tuning forks, the frequencies exhibited a temperature dependence. For this particular
technology, the temperature coefficient of frequency is 0.85 Hz/degrees C [14].
2.2.11 Northrop Grumman (http://www.northropgrumman.com/)
Northrop Grumman is another U.S. based commercial manufacturer of MEMS gy-
roscopes. Their MAG-16 is a single axis MEMS gyro designed for applications such as
platform stabilization and inertial navigation.
This MEMS gyro has an angular rate measurement range of 150 deg/sec and a band-
width of 350 Hz (min). It has a specified angle random walk of 1.8 deg/root(Hr). This
MEMS gyro is designed and/or packaged to operate in environments possessing unfriendly
acceleration, mechanical shock and vibration conditions [24].
2.2.12 NEC-Tokin (http://www.nec-tokin.com/)
NEC-Tokin is a Japanese company that produces a MEMS gyro consisting of a minia-
ture ceramic rod that is piezoelectrically vibrated to induce sinusoidal motion along one
axis. Application of an angular rate about an orthogonal axis results in sinusoidal motion
along a third orthogonal axis. Electrical circuitry, printed onto the column?s surface, detects
the sinusoidal motion along the sense axis due to the Coriolis effect [25].
2.2.13 GyroOptics (http://www.gyro.ru/)
Gyrooptics LTD is a Russian company that produces a MEMS electrostatic rotary
gyro [15]. In a MEMS rotary gyro, the actuator assembly vibrates the proof mass about a
38
torsional suspension system so that it experiences a rotary sinusoidal motion instead of a
translational sinusoidal motion. Otherwise, it operates in a similar fashion to other MEMS
vibratory gyros [26].
2.3 Survey of New Developments in MEMS Gyros
It is believed that in future years, major innovations will involve multiaxis sensors,
both for linear and angular motion. Three-axis accelerometers using a single proof mass
have been presented already as prototypes, but a commercial version has not yet been im-
plemented. As an ultimate goal, a single sensor capable of measuring linear and angular
motion for six degrees of freedom is envisioned. Such a sensor can be fully integrated
with the control and interface electronics on the same chip. There are reports of a five-axis
capacitive motion sensor [13]. Linear acceleration is sensed in this way: out-of-plane ac-
celeration causes the proof mass to move along the z-axis, and in-plane acceleration along
either the x- or y-axes makes the proof mass tilt. Additionally, the proof mass is vibrated
along the z-axis with electrostatic forces. Angular motion about the x- or y-axes induces
a Coriolis-based tilting oscillation of the proof mass. The oscillatory signals are of much
higher frequency (about 2 kHz) as the signals caused by linear acceleration, and hence,
they can be separated easily in the frequency domain using electronic filters. In this way,
linear acceleration and angular rate signals can be measured concurrently. Another very
promising approach towards such a sensor is to use a micromachined disk that is levitated
by electrostatic or magnetic forces and spun about its main axes. This is similar to macro-
scopic flywheel type gyroscopes; however, the lack of a good bearing in the microworld
has excluded this approach so far for micromachined gyroscopes. Using a levitated object
alleviates this problem. Any angular motion perpendicular to the spin axis of the disk will
cause it to recess, and this can be detected by a capacitive position measurement to provide
39
a measure of the angular velocity. Force feedback is used with this type of gyro to keep the
flywheel in the same position relative to the surrounding frame. The angular rate measure-
ment is embedded in the control signal(s). Using a levitated object for inertial sensing has
several advantages. First, since there is no mechanical connection from the substrate to the
disk, the effective spring constant is solely dependent on the electrostatic forces set up by
voltages or currents applied to surrounding electrodes or coils; hence, the characteristics
of the sensor, such as bandwidth and sensitivity, can be adjusted in the control electronics,
according to the application requirements. Second, when used as a gyroscope, quadrature
error is inherently eliminated in this sensor architecture. The comparable effect, due to the
imbalance of the mass, will manifest itself at the rotation frequency, whereas the Coriolis
force will cause the disk to recess at the rotational speed of the body of interest. These two
frequencies are several orders of magnitude apart and are therefore easy to separate. Fur-
thermore, there is no need to tune the drive and sense resonant frequencies since the scale
factor does not depend on the matching of different modal frequencies. Linear accelera-
tion along the three axes can be measured simultaneously by measuring the displacement
of the disk [13]. Levitation of gyros using magnetic forces has been investigated and suc-
cessfully demonstrated. The electromagnetic forces are produced by currents up to 1A,
which precludes the use of standard integrated electronics, which is a severe disadvantage
of this approach. A more promising approach is to use electrostatic forces to levitate and
spin a disk [13]. A prototype of such a device has demonstrated the feasibility of using
it for simultaneously detecting linear and angular motion [13]. There is also a design and
simulation of a similar device for three-axis acceleration measurement, which is also suit-
able to detect angular motion about two axes if rotated. Here, the micromachined disk is
incorporated in a multipath sigma-delta modulator control system [13].
A number of researchers at U.S. universities are conducting research to improve MEMS
gyros. Charles Ellis at Auburn University is developing a MEMS gyro that consists of an
40
electrostatically levitated and rotating micromachined proof mass structure, similar in op-
eration to a traditional rotating proof mass gyroscope. As previously discussed, a levitated
and rotating proof mass gyro could possibly result in a better performing MEMS gyro than
is currently available in vibratory MEMS gyro technology [27].
The University of California at Berkley has been involved in was the development of a
low-noise vibratory MEMS gyro with integrated electronics to yield a digital output. This
gyro had a measured noise floor of 3 deg/s/root(Hz) [27].
The University of California at Irvine also has a successful MEMS gyro research pro-
gram. Dr. Shkel has been investigating the possibility of realizing extremely robust vi-
bratory MEMS gyros with significantly improved performance achieved by utilizing an
improved mechanical architecture instead of trying to correct for mechanical imperfections
with feedback controllers. In this particular design, multiple drive-mode and sense-mode
oscillators were utilized to realize a highly complex and robust mechanical system [27].
Dr Garry Fedder, a professor at Carnegie Mellon University, has developed a MEMS
gyro with a microfabrication process that realized the structural components of the MEMS
gyro as post processing to a fabricated CMOS ASIC. This technique allows the support
electronics to reside on the same chip as the mechanical elements of the gyro, thus mini-
mizing the size of the sensor [27].
Dr. Rajesh Rajamani, a professor at the University of Minnesota, has been researching
the development of a MEMS vibratory gyro that can not only measure angular rate, but also
absolute angular position. The operating principle is based on measuring the angle of free
vibration of the suspended proof mass with respect to the surrounding casing of the gyro
structure. This is very difficult to accomplish due to the limitations and tolerances in mi-
crofabrication technology, as well as the underlying physics of the problem. Dr. Rajamani
proposed an innovative nonlinear control system to compensate for these limitations [27].
41
Dr. Farrokh Ayazi is a professor at the Georgia Institute of Technology. He has con-
ducted a lot of research in the development MEMS gyros, both in regard to mechanical
device design and fabrication, and in regard to support electronics development. A tuning
fork style MEMS gyro was fabricated in an SOI process. The gyro was designed to use
quadrature error to achieve and maintain perfect mode matching. This was accomplished
through both the mechanical design of the gyro element and the use of a control loop
implemented in a CMOS ASIC. This exceptional gyro achieved an unprecedented 0.003
deg/root(hr) angle random walk (ARW) [27].
Dr. Tayfun Akin is a professor at Middle East Technical University in Turkey. His goal
is to improve the quality of MEMS gyros, and especially those MEMS gyros packaged at
atmospheric pressure. This research has resulted in a MEMS gyro architecture that utilizes
a symmetric design which is intended to minimize resonant frequency mismatch of the
structure between the drive and sense axes. Otherwise, frequency mismatch between the
drive and sense modes will cause mechanical coupling which leads to unstable operation
and increased zero-rate output drift. This technique was utilized to realize a symmetric and
decoupled silicon microgyroscope structure that has varying-gap type sense electrodes for
improved rate sensitivity, post-processing electrostatic frequency tuning capability, sym-
metric and folded suspensions for mechanical decoupling and a large drive-mode amplitude
[27].
Dr. Minhang Bao is a professor at Fudan University in China. He has developed
several MEMS gyros based on variants of a two-beam vibratory MEMS gyroscopic sen-
sor architecture that used piezoresistive off-axis motion sensing instead of the more widely
used capacitive off-axis sensing. These gyros were designed to operate at atmospheric pres-
sure instead of in hermetically sealed packages at low or high vacuum.. The two large proof
mass structures were electrostatically vibrated out of plane with the substrate using an elec-
trode beneath each proof mass, where each proof mass is connected to the substrate using
42
a single cantilevered beam. Application of an angular rate resulted in sinusoidal in plane
motion, which was detected by piezoresistors embedded in the neck of the cantilevered
beam for each proof mass. By using two proof mass structures in one gyro, common mode
effects, such as a translational acceleration, could be cancelled out. Additionally, Dr. Bao
has been developing novel sensing techniques for MEMS gyros, such as an architecture that
used phase detection instead of the more popular amplitude detection to measure off-axis
motion. This technique could potentially improve performance over amplitude detection
techniques, as well as improve immunity to interference and temperature sensitivity [27].
Dr. Alfredo Cigada, professor at Politecnico di Milano in Italy, has yielded a fast,
efficient, and reliable measurement method that allows the identification of the modal pa-
rameters of a MEMS tuning fork gyroscope both in the design phase (for statistical analy-
sis), and in the verification phase, when MEMS gyros have already been installed in their
final package. Additionally, the developed technique could be applied to any resonating
MEMS device. The electrical measurement technique was based on the measurement of
the ground currents flowing in different parts of the device when it was excited through
a step excitation. This technique was used to identify the primary mechanical parameters
(resonant frequency and quality factor) of the gyroscope and its quadrature error. There are
many uses for a technique like this, including initial performance verification, performance
optimization through autocalibration, and in-field built-in self test (BIST) [27].
Honglong Chang is a researcher at Northwestern Polytechnical University in China.
He has investigated the optimization of MEMS based systems by considering the coupling
effects in the fabrication process, the parameters of the physical structure of the device, the
packaging/operating environment and the interface electronics. This technique is called
?Multidisciplinary Design Optimization (MDO)? and uses a genetic algorithm. A MEMS
gyro was used as the demonstration vehicle for this approach. Chang has also been involved
in the development of a z-axis MEMS gyroscope that had a novel architecture (proof mass
43
suspension system) utilized to decouple the drive mode from the sense mode. Additionally,
the sensor was realized as a bulk micromachined gyroscope (a DRIE etched Si wafer anod-
ically bonded to glass) instead of a surface micromachined gyroscope, in order to achieve
greater sensitivity. Dr. Chang has also developed a bulk micromachined single chip IMU
containing three orthogonally arranged accelerometers and three orthogonally arranged gy-
roscopes. However, the sensor interface electronics did not reside on the same chip as the
micromachined sensor elements. The unpackaged micromachined chip was approximately
9mm by 9mm [27].
Dr. Dong-il Cho is a professor at Seoul National University in South Korea. Dr. Cho
has developed several MEMS gyros using various modifications to a MEMS fabrication
process called SBM (Surface/bulk micromachining). With this process, a solid (111) Si
wafer or an SOI wafer with a (111) Si device layer is used. The wafer is patterned and
DRIE etched down to some desired depth. Then the wafer is conformally coated with sil-
icon dioxide or silicon nitride. Next the wafer is further DRIE etched to define a ?release
gap.? The sidewalls in the etched trenches where the release gap will be formed are now
coated with the silicon dioxide or silicon nitride coating. The wafer is then placed in an
orientation dependent etchant, such as TMAH, which etches along the (111) crystal plane
(but only very slowly in the (111) direction), which is in the horizontal direction and below
the protective coating. This undercuts the protected features. The time dependent etch runs
horizontally and is allowed to etch until the desired features are released, but is stopped
before the desired anchor points are fully released. Several advantages are claimed for
this process, such as avoidance of the undercutting or footing problems possible in SOI
processes, a smooth bottom surface on the defined features, being able to set an arbitrary
depth for the release gap and the avoidance of stresses inherent in SOI wafers. Dr. Cho?s
researchers made various modifications to the SBM process and fabricated MEMS vibra-
tory gyroscopes. The most notable gyroscope developed was one where the SBM process
44
was used with multiple passivation and DRIE etch steps in order to realize Si teeth that
were vertically offset, which realized a vertical comb-drive actuator that was demonstrated
in the fabrication of an x-axis gyroscope. By using this technique, however, three orthog-
onal gyroscopes could be realized on the same substrate, resulting in 3-axis angular rate
measurement. The fabricated gyro was tested in a 60 mTorr vacuum chamber by applying
a 20 deg/s 30Hz angular rate. A measured bandwidth of over 100Hz was achieved, and an
equivalent angle random walk of 0.01 deg/s/root(Hz) was achieved [27].
Dr. Dzung Viet Dao is a post doctoral fellow at the Micro Nano Integrated Devices
Laboratory at Ritsumeikan University in Japan. Dr. Dao has developed a miniature two
axis gyroscope that used a forced gas flow to detect rotation, by using the resulting Coriolis
force to deflect the gas flow with regard to two micromachined Si thermistor half Wheat-
stone bridges, which detected the change in flow direction by a temperature change in the
thermistors. Neon gas was used as the fluid in the sensor. A gyroscope sensitivity of 0.15
mV/deg/s was achieved in a prototype unit, over an evaluation range of nearly +/- 400 deg/s.
The thermistors were fabricated by micromachining them in Si. The completed sensor used
MEMS components (the thermistors) but was not implemented as a completely microma-
chined gyroscopic sensor. The stated intended use of this two axis gyroscopic sensor was
for ship anti-rolling and stabilization systems [27].
Tohoku University in Japan has had some role in the development of electrostatically
levitated and rotated ring and sphere inertial sensors. A Si to glass anodic bonding proce-
dure is utilized. Electrical feedthroughs were realized in the glass substrate by RIE etching
through the glass and then plating Ni up though the vias. In this particular gyro, the 1.5 mm
diameter micromachined ring that served as the rotor was levitated and rotated at 74,000
RPM. The sensor was capable of two axis angular rate measurement ( 150 deg/s) and three
axis acceleration measurement (5 g) [27].
45
Dr. Weileun Fang is currently a professor at National Tsing Hua University in Taiwan.
Dr. Fang has designed a dual-axis sensing decoupled vibratory wheel gyroscope. The basic
architecture is that of an electrostatically driven rotary MEMS gyro. This design, however,
realizes a decoupled gyroscope that can sense angular rotation about two axes instead of
one. Since the design is decoupled, there will be no sensing interference and this eliminates
the need for feedback detection and compensation. A triple-beam-shaped torsional spring
is used to suppress the undesired in-plane linear motion of the outer ring. The natural
frequency of the device is approximately 4600 Hz. Also, the device has a quality factor of
2000 and a sensitivity of 7.4 fF/deg/s. In the range of +/- 150 deg/s the dual-axis sensing
mode has a nonlinearity of 0.04 percent [27].
Dr. Barry J. Gallacher and Dr. James Burdess are professors at the University of New-
castle Upon Tyne in the UK. They have worked together for a number of years to develop
on a 3-axis vibrating microring gyroscope. The basic structure consisted of a tethered mi-
cromachined ring that was designed to possess degenerate modes. Two of these modes
would possess the same natural frequency, but would have minimas and maximas around
the ring that were spatially offset by 30 degrees along the ring. Plate electrodes below
the ring would be used to detect out of plane vibration while in-plane electrodes would be
used to excite the ring into vibratory motion. A key to achieving the desired goals was the
use of (111) orientation Si wafers to approximate isotropic material properties in the ring
structure, which was necessary for the sensor to function well. The functionality of this
MEMS gyro architecture requires extremely tight and usually unachievable manufactur-
ing and material property tolerances. Therefore active tuning algorithms were developed
to compensate for this issue. One example was the use of active control of the damping
to increase the quality factor of the gyro. Another example was the implementation of a
method of correcting for mass and stiffness ?imperfections? in the micromachined micror-
ing gyroscope by tuning the device with electrostatic forces generated by adding additional
46
electrodes at specific locations relative to the ring structure. This active tuning method
could be used in conjunction with or in place of ?hardware tuning? during fabrication with
methods such as laser ablation or focused ion beam (FIB) trimming. Another example was
the use of an excitation and control scheme (combined parametric excitation and harmonic
forcing) to significantly reduce signal feedthrough from the primary or driven motion to the
secondary or detection motion of the vibrating structure. The researchers claimed that this
improvement would be a factor leading to a true low-cost inertial grade micro gyro [27].
Dr. Mohamed Toriq Kahn is a professor at Cape Peninsula University of Technology
in South Africa. Dr. Kahn has been investigating the realization of a FOG (fiber optic
gyroscope) in MEMS technology. Dr. Kahn theorized the realization of a MEMS FOG
system based on using ultra fine fiber optic cable. This type of fiber optic cable could be as
small as 2nm across and is based on a technique developed at the University of California
where very fine spider silk was utilized as a mold or template for creating extremely small
diameter optical fibers. By utilizing optical fiber of this size with optical MEMS and micro-
optical components, he theorized that a single chip FOG sensor could be realized where
the tiny optical fiber would be wound around a micromachined structure on a MEMS chip.
Many issues remain to be solved before such a MEMS gyro could be realized, such as
optical signal injection into the tiny fiber and propagation losses of the optical signal in the
fiber [27].
Dr. Michael Kraft is a professor at Southampton University in the U.K. His primary
research interest is the development of closed-loop MEMS sensors that employ sigma-delta
modulation (SDM) based force feedback, where the proof mass is held in a nearly constant
position by an SDM controller utilizing electrostatic forces. The SDM control signal, a
digital pulse density modulated bitstream, then contains the measurement of interest (ap-
plied acceleration(s) and/or angular rate(s)). In particular, Dr. Kraft has sought to apply
this technology to MEMS gyros. For example, he was involved in the development of
47
a DARPA funded project to design and build a 5V, CMOS z-axis gyroscope chip. The
MEMS gyro used an SDM controller, which is a common theme to much of Kraft?s re-
search. For several years, Kraft has also been involved in an on-going project to develop a
multi-axis inertial sensor consisting of a micromachined levitated and rotating disk proof
mass that utilizes an SDM controller in a force feedback configuration with electrostatic
forces to keep the levitated proof mass in approximately the same location. The potential
advantages of this approach, if successful, would probably be an inertial sensor at least
as good as the best MEMS gyros today and probably a gyroscope far superior to current
state-of-the-art MEMS vibratory gyros. This approach avoids many of the limitations of
commercially available vibratory MEMS gyros, such as fabrication tolerances in the me-
chanical springs (Dr. Kraft?s gyro architecture uses a fully controllable electrostatic spring),
quadrature errors in vibratory gyros (this design uses a levitated rotating proof mass) and
large motion induced nonlinearities (this design uses SDM force feedback to limit the proof
mass motion to small displacements) [27].
Dr. Jang Gyu Lee is a professor at Seoul National University in South Korea and
has been developing advanced control loops for MEMS gyros, such as a digital rebalance
loop for a dynamically tuned gyroscope using a Linear Quadratic Gaussian / Loop Transfer
Recovery method; an H2-based controller for a digital rebalance loop [40]; an H2 control
scheme to fabricate an analog closed-loop condition to enlarge the bandwidth, enhance lin-
earity and provide robustness over unmodeled dynamics; and a Kalman filter to reduce the
deterministic and random errors of a vibrating gyroscope used in GPS navigation systems
and autonomous mobile robots. Dr. Lee has also developed an electrostatically-driven and
electromagnetically-sensed vibratory MEMS gyro. The fabrication process is based on a
surface-bulk micromachining process. This MEMS gyro can be operated at atmospheric
pressure with good output characteristics as opposed to typical hermetically sealed low
pressure packaging [27].
48
Dr. Sheng Liu is the Director of the Institute of Microsystems and Director of MOEMS
Division at Wuhan National Laboratory of Optoelectronics which is maintained by Huazhong
University of Science and Technology in China. Dr. Liu has been developing a micro
thermo-fluidic gyroscope utilizing bidirectional liquids. The proposed gyroscope consisted
of two main flow channels that each split into two symmetrical outlet ports. Each outlet
port had a thermistor for measuring the temperature of the fluid as it flowed through that
outlet port. When the device experienced an angular rate, the mass flow rate of the sym-
metric microchannels became unequal, resulting in a temperature difference between the
two ports. By measuring the temperature difference between the symmetric thermistors,
the angular rate was obtained [27].
Dr. Helmut Seidel is a professor at Saarland University in Germany. He conducts
research in MEMS tuning fork style gyros and in particular for automotive safety appli-
cations. His research team has developed a silicon micromachined tuning fork gyroscope
that is driven by two piezoelectric thin film actuators. The applied external angular rate
was determined by sensing the resulting torsional motion around the structure?s sensitive
axis that resulted from the Coriolis effect. The shear strain was proportional to the angular
rate and was detected by piezoresistive read-out sensing. The sensor output voltage was
adversely affected by certain parasitic effects such as mechanical imbalance, actuation im-
balance and drive motion parasitics. To combat these factors, the researchers suggested
several methods of minimizing these parasitic effects, such as phase-locked loop (PLL)
electronic circuitry, tight production tolerances, post-process trimming of the sensor mass
at specific locations, stem design optimization, electrical actuator compensation and read-
out element beam positioning. The testing results showed that this tuning fork gyroscope
had outstanding behavior under external shock. It also had a CMOS-compatible fabrication
process and a relatively small chip-size of less than 15 mm x 15 mm [27].
49
Dr. Yung Ting is an associate professor at Chung Yuan Christian University in Taiwan.
Dr. Ting has been investigating the effects of a polarized electric field on the sensitivity, me-
chanical quality factor, and resonant frequency of a piezoelectric solid-beam cylinder-type
vibratory gyro. The gyro utilized for this investigation was ceramic and had the advantage
of material uniformity. His simulation analysis and experimental results of the ceramic
cylinder gyro revealed that the resonant frequency of the primary and secondary modes of
the cylinder gyroscope were nearly equal. This indicated that the axis-symmetry of the
cylinder gave it the advantage of having increased sensitivity. Besides the effect on reso-
nant frequency, it was also determined that the polarized electric field was proportional to
the sensing voltage, thus it was proportional to the sensitivity. From the ANSYS simula-
tion, it was concluded that a cylinder with a small diameter would easily achieve a high
polarized electric field, and a large diameter cylinder would need a higher applied polar-
ized voltage to preserve complete polarization. Furthermore, equal width of the electrodes
and the clearance between the adjacent electrodes would yield a better polarized electric
field. Since it was determined that a linear relationship between the sensing voltage and
the rotation speed existed, the ceramic cylinder gyro would be suitable for measurement of
rotation speed in low and medium speed applications [27].
Dr. Xue Zhong Wu is with the Laboratory of Precision Engineering and MEMS at the
National University of Defense and Technology in China. Dr. Wu has been developing a
MEMS interdigitated transducer (IDT) surface acoustic wave (SAW) two axis gyroscope.
The sensor consisted of two orthogonally mounted SAW resonators that can each act as a
SAW resonator and as a SAW sensor. When a standing wave is generated in a SAW device,
particles on the substrate in the standing wave experience oscillatory motion and respond
to the Coriolis force when the substrate experiences an angular rotation. This effect can be
detected using an orthogonally located SAW sensor. However, if the orthogonally mounted
SAW resonators are used as both SAW generators and as sensors, then two-axis angular
50
rate detection is possible. Dr. Wu used this architecture in developing his MEMS gyro and
speculated that this architecture would be resistant to mechanical shock and vibration, at
least compared to traditional MEMS vibratory gyros.
Dr. Bin Xiong is a professor at the Shanghai Institute of Microsystem and Information
Technology (SIMIT) in China. Dr. Xiong has developed a vibratory MEMS gyro designed
to operate at ambient pressure. The sensor consisted of an anchored Si proof mass that was
forced to oscillate along the in-plane x-axis by the tangential force produced by applying a
voltage waveform between the proof mass structure and offset electrodes located beneath
it. When the device was subjected to an angular rotation about the z axis (normal to the
device surface), the proof mass would experience motion along the in-plane y-axis due to
the Coriolis force, which was detected by a change in capacitance between the proof mass
and other electrodes located beneath it. A motivating factor for the development of this
gyro architecture was a desire to avoid vacuum packaging [27].
Dr. Yishen Xu is a researcher at Southeast University in China. He developed a
monolithic triaxial micromachined capacitive gyro that consisted of two uniaxial in-plane
(x and y axis) gyros and one uniaxial out-of-plane (z axis) gyro. All three gyros utilized
electrostatic force actuators and capacitive detection methods. A 300 deg/sec prototype
was fabricated using bulk micromachining technology and evaluated. Testing indicated
only a 5 percent error between the estimated resonant frequency and the realized resonant
frequency. Dr. Xu has also been developing signal processing techniques for improving the
performance of MEMS gyros. For example, he used an adaptive Kalman filter to actively
compensate for any drift signal in a particular MEMS gyro. He has also investigated the
use of a folded-flexure spring design based suspension system to minimize quadrature error
in MEMS gyros [27].
51
Dr. Sang Sik Yang is a professor at Ajou University in South Korea. Dr. Yang has
developed a micro rate gyroscope (MRG) based on the surface acoustic wave (SAW) gy-
roscopic effect, for use in extremely high-shock military applications. The gyro (called the
SAWMRG) consisted of two SAW delay-line oscillators. The two surface acoustic waves
were generated by separate SAW oscillators and propagated in opposite directions on the
substrate. When the substrate experienced an angular rate about the out-of-plane z axis,
the resulting Coriolis force would cause an opposite frequency shift in the frequencies of
the two oscillators. Demodulation was used to recover an output signal whose frequency
was proportional to the applied angular rate. The 9 x 9 mm2 SAWMRG was fabricated
on a ST-cut quartz substrate and loaded into a specially designed low temperature co-fired
ceramic (LTCC) package to ensure good RF characteristics. The center frequency and the
insertion loss of the delay line were measured at 98.6 MHz and 15.2 dB, respectively. Us-
ing a rate table and stochastic noise analysis, a sensitivity of 0.431 Hz/deg/s was measured
in angular rates up to 2000 deg/s and a white noise of 0.55/deg/s/root(Hz), respectively. A
SAW-based gyroscope has an inherent shock robustness due to having no moving mechan-
ical parts. Also, the fabrication process uses only lithography and a metallization processes
like that of a conventional SAW filter [27].
Dr. Weiping Zhang is a professor at the Institute of Micro and Nano Science and Tech-
nology at Shanghai Jiao Tong University in China. Dr. Zhang has developed an electromag-
netic micromotor with an alumina rotor. It was levitated, rotated, sensed, and controlled
by independent coils and a capacitance structure. Levitated force with lateral stability was
produced by the electromagnetic interaction between the rotor and four groups of levita-
tion planar coils with inner and outer conductors carrying opposite phase high frequency
AC current. The rotation was realized by a four-phase induction micromotor composed of
the rotor and eight rotation planar coils carrying AC current. Eight sense electrodes and the
rotor created a non-contact capacitive displacement sensing system. The torque returning
52
the rotor to its equilibrium position was produced by four groups of planar coils. A proto-
type device with a rotational speed of 3035 RPM, a levitation height of 200 ?m, and a scale
factor of 0.212 V/deg, has been designed, fabricated and successfully tested. This project
illustrated that the micromotor could be used to construct a MEMS levitated and rotating
proof mass gyro [27].
Dr. Rong Zhu is a professor at Tsinghua University in China. Dr. Zhu has developed
a micromachined gas inertial sensor based on the principle of convective heat transfer that
was capable of sensing acceleration in two axes and angular rate about one axis. The sensor
consisted of a small silicon etched cavity, a suspended central heater and four suspended
thermistor wires, all of which were assembled and packaged in a hermetically sealed cham-
ber. The sensor measured temperature gradients induced by inertial forces acting on the
gas flowing in the sealed chamber. The temperature gradients were detected using the four
thermistors, and the applied two axis acceleration and one axis rotational rate were then
determined from the output signals from the thermistors [27].
2.4 The Analog Devices ADXRS300 Angular Rate Sensor
Analog Devices (ADI) is home to the ADXRS family of integrated angular rate-
sensing gyroscopes, which contains the ADXRS300 (with dynamic range of +/- 300 deg/sec)
and the ADXRS150 (with dynamic range of +/- 150 deg/sec). It is the first fully integrated
commercial gyroscope. A picture of the chip is shown in Figure 2.10.
It operates from a 5V supply over the industrial temperature range of 40 degrees C
to +85 degrees C and is available in a space-saving 32-pin Ball Grid Array surface-mount
package measuring 7 x 7 x 3 mm. Both are priced at approximately 30 dollars per unit in
thousand-piece quantities. Because the internal resonators require 14V to 16V for proper
operation, ADI includes on-chip charge pumps to boost an applied TTL-level voltage. Both
53
Figure 2.10: Die photo of the Analog Devices ADXRS300 [28]
the ADXRS150 and ADXRS300 are essentially z-axis devices based on the principle of
resonant-tuning-fork gyroscopes. In these systems, two polysilicon sensing structures each
contain a so-called dither frame that is driven electrostatically to resonance. Interestingly,
the gyroscope includes two identical structures to enable differential sensing in order to
reject environmental shock, vibration, and effects from translational motion. Figure 2.11
shows one structure schematically.
Figure 2.11: Schematic of the gyroscope elements
A rotation about the z-axis, normal to the plane of the chip, produces a Coriolis force
that displaces the inner frame perpendicular to the vibratory motion. This Coriolis motion
is detected by a series of capacitive pick-off structures on the edges of the inner frame. The
resulting signal is amplified and demodulated to produce the rate signal output [13].
54
The ADXRS300 is a complete angular rate sensor (gyroscope) that uses Analog De-
vices? surface-micromachining process to make a functionally complete and low cost an-
gular rate sensor integrated with all of the required electronics on one chip. The manufac-
turing technique for this device is the same high volume BiCMOS process used for high
reliability automotive airbag accelerometers. The output signal, RATEOUT (pins 1B, 2A),
is a voltage proportional to angular rate about the axis normal to the top surface of the
package (see Figure 2.12).
Figure 2.12: ADXRS300 application circuit
A single external resistor can be used to lower the scale factor. An external capacitor
is used to set the bandwidth. Other external decoupling and charge pump capacitors are
required for operation (see Figure 2.13).
A precision voltage reference for using an external A/D converter and a temperature
output are also provided for compensation techniques. Two digital self-test inputs elec-
tromechanically excite the sensor to test proper operation of both sensors and the signal
conditioning circuits. The ADXRS300 is available in a 7 mm x 7 mm x 3 mm BGA chip-
scale package.
55
Figure 2.13: Block diagram with external components
Figure 2.14: Absolute maximum ratings
56
Stresses above those listed under the Absolute Maximum Ratings in Figure 2.14 may
cause permanent damage to the device. This is a stress rating only; functional operation of
the device at these or any other conditions above those indicated in the operational section
of this specification is not implied. Exposure to absolute maximum rating conditions for
extended periods may affect device reliability. Applications requiring more than 200 cy-
cles to MIL-STD-883 Method 1010 Condition B (55 degree C to +125 degrees C) require
underfill or other means to achieve this requirement. Drops onto hard surfaces can cause
shocks of greater than 2000 g and exceed the absolute maximum rating of the device.
This is a Z-axis rate-sensing device that is also called a yaw rate sensing device. It
produces a positive going output voltage for clockwise rotation about the axis normal to
the package top, i.e., clockwise when looking down at the package lid.
Figure 2.15: RATEOUT signal v. clockwise rotation
The ADXRS300 operates on the principle of a tuning fork resonator gyro. Two
polysilicon sensing structures each contain a dither frame, which is electrostatically driven
to resonance. This produces the necessary velocity element to produce a Coriolis force
when the device experiences angular rate. At two of the outer extremes of each frame,
orthogonal to the dither motion, there are movable fingers that are interdigitated with fixed
pickoff fingers to form a capacitive pickoff structure that senses Coriolis motion. The re-
sulting signal is fed to a series of gain and demodulation stages that produce the electrical
57
Figure 2.16: BGA pin diagram
Figure 2.17: Pin Functions
58
rate signal output. The dual-sensor design rejects external g-forces and vibration. Fabricat-
ing the sensor with the signal conditioning electronics preserves signal integrity in noisy
environments. The electrostatic resonator requires 14 V to 16 V for operation. Since only 5
V is typically available in most applications, a charge pump is included on-chip. A charge
pump is a simple voltage multiplier. If an external 14 V to 16 V supply is available, the two
capacitors on CP1 through CP4 can be omitted and this power supply can be connected to
CP5 (Pin 7D) with a 100 nF decoupling capacitor in place of the 47 nF capacitor. After the
demodulation stage, there is a single-pole low-pass filter consisting of an internal 7 kW re-
sistor (RSEN1) and an external user-supplied capacitor (CMID). A CMID capacitor of 100
nF sets a 400 Hz +/- 3-5 percent low-pass pole and is used to limit high frequency artifacts
before final amplification. The bandwidth limit capacitor, COUT, sets the pass bandwidth.
Only power supplies used for supplying analog circuits are recommended for pow-
ering the ADXRS300. High frequency noise and transients associated with digital circuit
supplies may have adverse effects on device operation. Fig. 2.12 shows the recommended
connections for the ADXRS300 where both AVCC (+ analog supply) and PDD (charge
pump supply) have a separate decoupling capacitor. These should be placed as close to the
their respective pins as possible before routing to the system analog supply. This minimizes
the noise injected by the charge pump that uses the PDD supply. It is also recommended
to place the charge pump capacitors connected to the CP1 through CP4 pins as close to
the part as possible. These capacitors are used to produce the on-chip high voltage supply
switched at the dither frequency at approximately 14 kHz. Surface-mount chip capacitors
are suitable as long as they are rated for over 15 V.
External capacitors CMID and COUT are used in combination with on-chip resistors
to create two low-pass filters to limit the bandwidth of the ADXRS300?s rate response. The
3 dB frequency set by ROUT and COUT is shown in Equation 2.5.
59
fOUT = 1=(2 p ROUT COUT) (2.5)
The bandwidth can be well controlled since ROUT has been trimmed during manu-
facturing to be 180 kW +/- 1 percent. Any external resistor applied between the RATEOUT
(1B, 2A) and the output amplifier summing junction, SUMJ (1C, 2C) pins, results in Equa-
tion 2.6.
ROUT = (180;000 REXT)=(180;000 REXT) (2.6)
The 3 dB frequency is set by RSEN (the parallel combination of RSEN1 and RSEN2)
at about 3.5 kW nominal; CMID is less well controlled since RSEN1 and RSEN2 have been
used to trim the rate sensitivity during manufacturing and have a +/- 35 percent tolerance.
Its primary purpose is to limit the high frequency demodulation artifacts from saturating
the final amplifier stage. Thus, this pole of nominally 400 Hz @ 0.1 ?F need not be precise.
Lower frequency is preferable, but its variability usually requires it to be about 10 times
greater (in order to preserve phase integrity) than the well-controlled output pole. In gen-
eral, both 3 dB filter frequencies should be set as low as possible to reduce the amplitude
of these high frequency artifacts and to reduce the overall system noise.
The full-scale measurement range of the ADXRS300 can be increased by placing an
external resistor between the RATEOUT (1B, 2A) and SUMJ (1C, 2C) pins, which would
parallel the internal ROUT resistor that is factory-trimmed to 180 kW. For example, a 330
kW external resistor will give approximately a 50 percent increase in the full-scale range.
This is effective for up to a 4X increase in the full-scale range (minimum value of the
parallel resistor allowed is 45 kW). Beyond this amount of external sensitivity reduction,
the internal circuitry headroom requirements prevent further increase in the linear full-scale
output range. The drawbacks of modifying the full-scale range are the additional output
60
null drift (as much as 2 deg/sec over temperature) and the readjustment of the initial null
bias.
The ADXRS300?s RATEOUT signal is nonratiometric, i.e., neither the null voltage
nor the rate sensitivity is proportional to the power supply voltage. Rather, they are nom-
inally constant for dc supply changes within the 4.75 V to 5.25 V operating range. If the
ADXRS300 is used with a supply-ratiometric ADC, the ADXRS300?s 2.5 V output can be
used to make corrections in software for the supply variations.
Null adjustment is possible by injecting a suitable current to SUMJ (1C, 2C). Adding
a suitable resistor to either ground or to the positive supply is a simple way of achieving
this. The nominal 2.5 V null is for a symmetrical swing range at RATEOUT (1B, 2A).
However, a nonsymmetric output swing may be suitable in some applications. Note that
if a resistor is connected to the positive supply, then supply disturbances may reflect some
null instabilities. Digital supply noise should be avoided, particularly in this case. The
resistor value to use is approximately shown in Equation 2.7.
RNULL = (2:5 180;000)=(VNULL0 VNULL1) (2.7)
VNULL0 is the unadjusted zero rate output, and VNULL1 is the target null value. If
the initial value is below the desired value, the resistor should terminate on common or
ground. If it is above the desired value, the resistor should terminate on the 5 V supply.
Values are typically in the 1 MW to 5 MW range. If an external resistor is used across
RATEOUT and SUMJ, then the parallel equivalent value is substituted into Equation 2.7.
The resistor value is an estimate since it assumes VCC = 5.0 V and VSUMJ = 2.5 V.
The ADXRS300 includes a self-test feature that actuates each of the sensing structures
and associated electronics in the same manner as if subjected to angular rate. It is activated
by standard logic high levels applied to inputs ST1 (5F, 5G), ST2 (4F, 4G), or both. ST1
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causes a voltage at RATEOUT equivalent to typically 270 mV (-60 deg/s), and ST2 causes
an opposite +270 mV (+60 deg/s) change. The self-test response follows the viscosity
temperature dependence of the package atmosphere, approximately 0.25 percent/degrees
C. Activating both ST1 and ST2 simultaneously is not damaging. Since ST1 and ST2 are
not necessarily closely matched, actuating both simultaneously may result in an apparent
null bias shift [28].
Figure 2.18: ADXRS300 dimensions
62
Figure 2.19: ADXRS300 specifications taken from [28]
63
CHAPTER 3
PERFORMANCE OF THE ADXRS300 IN HARSH ACOUSTIC ENVIRONMENTS
In this chapter, a discussion of how the ADXRS300 is affected by mechanical shock,
vibration, and acoustic energy is presented. These factors can all impact a MEMS gyro?s
performance.
3.1 Harsh Acoustic Environments
This section will provide some background information on how harsh environments
affect MEMS devices in general and how the ADXRS300 compensates for this in its design.
3.1.1 Design Considerations
When considering vibration, acoustic noise, and mechanical shock levels, we must
pay attention to frequency bandwidth. Often the specified and/or measured environments
are limited to a bandwidth of less than 10 kHz. However, for the purpose of designing for
MEMS sensors, we need to measure frequency content to more than 10 kHz. For most
applications a 20 kHz bandwidth is sufficient. Measurement of shock and vibration in this
frequency range requires special care because much of the equipment in the industry is de-
signed for less than 5 kHz. It is important to know what steady-state acceleration (g) levels
the IMU will be exposed to. The isolated body requires sufficient space to move within the
part of the system that is rigidly mounted. This amount of space, or sway space, is a func-
tion of the natural frequency of the isolator and the magnitude of the input acceleration.
The lower the natural frequency of the isolator and the higher the g level, the more sway
64
space that is required. Also, the need for increased sway space implies increased stress and
strain on the isolator at full load. We can easily predict how much sway space is required
if we assume that the isolated system will behave like a single-degree-of-freedom, second
order system. Bottoming out of the isolation system not only eliminates the benefit of iso-
lation but it can also send an unattenuated shock pulse directly into the MEMS sensors.
This may result in severally degraded system performance as well as damage to the MEMS
sensors. The equation for sway space is shown in Fig. 3.1.
Figure 3.1: Sway space equation
If the acoustic environment is particularly severe it may be necessary for the IMU to
incorporate an internal isolation system. The choice between internal and external isolation
may also be driven by size constraints. These two basic isolation schemes are shown in Fig.
3.2.
Figure 3.2: Isolation schemes
One very important aspect of isolator design is the elastomer formulation. When
choosing the elastomer material it is very important to consider the operating tempera-
ture range. The material properties of elastomers have a much wider variation as a function
65
of temperature than typical engineering materials (metals, epoxy resins, etc.). There are
various choices of elastomers that will perform over a variety of temperature ranges. In
general, an isolation system properly designed for a limited temperature range will have
higher performance than an isolation system designed for extreme temperatures. Also,
knowing the thermal rate of change is required since the isolation system can affect the
thermal time constant and minimize thermal gradients across the MEMS sensors.
The second requirement is to determine the vibration frequencies and amplitudes to
which the MEMS sensors are sensitive. Since MEMS sensors are mechanical systems,
energy at certain frequencies can couple in and disrupt either the drive or sense loops. When
enough energy is present, these loops can go unstable and performance can be degraded. At
certain frequencies and levels these loops can be so unstable that temporary and permanent
damage to the sensors can occur. Since each MEMS sensors has unique modes, each with
a unique Q (or damping ratio), the designer must determine which MEMS sensors the IMU
will use. When dealing with MEMS sensors that are highly dampened (low Q) and/or
with sensitive excitation frequencies higher than the environment can excite, the need for
isolation diminishes. Since low-damping is equal to a high Q, when dealing with MEMS
sensors that have little damping (high Q?s) and/or with sensitive frequencies within the
frequency range of exposure, the need for isolation increases. Typically in these IMU?s
the lower the sensitive frequencies and the higher the Q?s the more isolation is required.
Additionally, when the MEMS sensors are underdamped (Q greater than 5,000) then the
isolation system is extremely critical and requires increased design margin to assure proper
IMU performance. Since a MEMS IMU can employ multiple technologies, different for
accelerometers and rate sensors, the isolation system must be designed to maximize the
performance of the entire IMU.
Mass properties are critical parameters since they play an important roll in the design
of the isolation system. A 3-degree of freedom system can have different masses, but this is
66
usually undesirable. The mass is used, in conjunction with the spring constant, to determine
the three axial natural frequencies of the system. Since the goal is to minimize the delta
between each of the axial natural frequencies, we need to design the isolation system to
have the same spring constant in the 3 axial degrees of freedom. Therefore, to adjust the
natural frequencies we can either adjust the material properties or adjust the mass of the
isolated body. The equation for isolator natural frequency is shown in Fig. 3.3.
Figure 3.3: Natural frequency equation
Inertia is also an important parameter since we need to control the three radial natural
frequencies of the isolation system. These radial natural frequencies are less important than
the axial natural frequencies but they still need to be known and controlled. The goal is to
design the isolation system to minimize the delta between the 3 radial natural frequencies as
well as place them near the axial natural frequencies. And since the inertias of the isolated
portion are seldom symmetric in the 3 degrees of freedom, the isolation system geometry is
the most appropriate method to adjust the radial frequencies. Also, note that larger isolation
schemes allow for lower radial frequency systems and visa versa.
The center of gravity of the isolated body is also very important and needs to be known
and controlled. We need to align this center of gravity with the isolation system?s center
of elasticity. The center of elasticity is the three dimensional point, or node, in which the
isolation system reacts. We want to align these two points as best as possible. If these
points are not aligned, axial vibration can generate rocking, coning, and/or skulling of the
67
isolation system, which can degrade performance. By minimizing the offset between these
two points we can maximize the MEMS IMU performance.
From knowing all the required information, a designer can determine the proper pa-
rameters of the isolation system. The most important parameters are the natural frequency
of the isolation system and its Q, or damping, and how both these parameters vary as a
function of all the others. Once these two parameters are established, everything else can
be tweaked by changing the isolator?s material properties and geometry. By using the trans-
missability equation in Fig. 3.4, the effects of altering the natural frequency or Q can be
determined from the system?s response [29].
Figure 3.4: System response
3.1.2 Error Sources in the ADXRS300
Analog Devices began their gyro development with the ground rules that the instru-
ment should be inexpensive and it should satisfy automotive applications. To minimize
expense, ADI?s accelerometer CMOS and polysilicon process was mandated. In the mid-
1990s, the process focused on 2-?m-thick suspended parts. Based on performance consid-
erations, Analog has moved to 4-?m thick suspended polysilicon parts. The 4-?m thickness
results in smaller moving parts, shorter beams, and smaller deflections compared to other
commercially available tuning fork gyros (TFG?s). To incorporate on-chip circuitry, the
substrate must be silicon. The moving elements, electrical traces, and bonding pads are
68
isolated from the conducting silicon substrate by an oxide layer. The gyro mechanism
consists of two independent mechanical structures.
For each structure, the inner member is driven and sensed electrostatically. The sens-
ing frame supports the driven member. An angular rate about an axis perpendicular to the
substrate moves the driven mass along the sense direction, which is parallel to the substrate
plane. As discussed below, the suspension is designed so that the sensing frame does not
move in the drive direction, but follows the proof mass in the sense direction. Electrostatic
combs detect the frame position. Eliminating trimming to reduce quadrature error was a
dominant decision in ADXRS design. With crab leg or folded beam suspension, differing
beam stiffnesses can cause sense-axis motion when driving the proof mass. Because this
motion is in phase with displacement, it is in quadrature to the desired rate-induced motion.
The ADXRS beam widths are 1.7 ?m, and width tolerances are 0.2 ?m so that quadrature
reduction was a major design goal. Straight beams between the sense and drive elements
result in very little sense-axis motion. The beams have stress relief at their ends to reduce
longitudinal stresses from polysilicon thermal expansion and from drive motion. Although
ADI has not employed it, a fine quadrature trim is possible by fingers excited to exert a
sense force that is modulated by the drive motion. In the ADXRS, both the sense and drive
motions are parallel to the substrate?s plane; thus, all critical dimensions are done in one
masking and etching operation. If the polysilicon thickness is off, all frequencies move
together so that mode ordering is maintained. While the proof mass is driven at a 7-?m
amplitude, the sense motion for angular rate is roughly 10 10 ?m/rad/s, an order of magni-
tude lower than for TFG?s. This smaller motion is attributed to smaller drive amplitude, the
fact that the drive mass must also drive the additional sense mass, and 20 to 30 percent sep-
aration of sense and drive resonant frequencies. The greater separation is consistent with
a 2-?m beam width and with a 4-?m thickness and the resulting proof mass and suspen-
sion dimensions. The gyro consists of two mechanically independent mechanisms whose
69
drive frequency is roughly 14 kHz and whose quality factor is 45. The units are electrically
cross-connected so that the proof masses move anti-parallel to common mode reject linear
acceleration. To achieve common mode rejection with a Q of 45, the two drive resonant
frequencies should be within 1 percent of each other. If the moving drive teeth are not
centered with respect to the stationary teeth (i.e., the entire proof mass is moved relative to
the stationary combs), a large coupling to sense force results. Since the drive force is large
because of the high damping and since the drive force is in phase with the drive velocity
and, hence, the Coriolis acceleration, the proof mass must be centered to very tight levels.
With 1.7-?m-wide beams, achieving the geometric control for sense drive frequency sepa-
ration, matching drive frequencies, and centering the combs is challenging. The ADXRS
is hermetically sealed at 1 atmosphere. Because of the resulting damping, noise is limited
by Brownian motion. To achieve drive amplitude, the 5-V supplies must be boosted to
approximately 12 V. Damping adds phase shift between sense and drive axes. Electronics
design and increasing separation between sense and drive frequencies reduce the effect of
this additional phase shift. The resulting damping renders the ADXRS tolerant of oper-
ating shock. The ADXRS relies heavily on its on-chip electronics to overcome the small
size and low scale factor of the mechanical parts. The sense displacement per rate input
is 10 percent and the capacitance variation is 1 percent of the 20-?m thick TFG?s. Analog
measures displacement resolution similar to the TFG?s, but with much smaller capacitors
[30].
3.1.3 Shock and Vibration
The MEMS tuning fork gyro (TFG) is an electromechanical device that measures an-
gular rotation rate. A proof-mass attached to springs is forced to oscillate in the horizontal
plane.
70
A voltage is applied to a sensing electrode (sense plate) below the proof mass, creating
an electrical field. The Coriolis force imparted by angular rotation causes the proof-mass
to oscillate in the vertical direction, which, in turn, changes the gap between the proof
mass and the sense plate. This generates an AC current with amplitude proportional to the
rotation rate. The bias voltage also generates an electrostatic force between the proof mass
and the sense plate. This force acts to pull the proof mass toward the sense plate as shown
in Fig. 3.5.
Figure 3.5: MEMS gyro schematic with forces
If the sense gap gets too small, a catastrophic failure will occur when the proof mass
touches the sense plate. Since the gyro is a mechanical device, it is sensitive to external
stimuli. These stimuli include vibration, acoustic excitation, and acceleration due to me-
chanical shock. For some applications, the acceleration levels at the gyro can be as large as
500 g?s. These stimuli will increase or decrease the sense gap depending on amplitude and
frequency. Additionally, as the rotation rate increases, the sense gap decreases. In order to
successfully operate at high rates (up to 50 revolutions per second) and in high g environ-
ments, the maximum proof mass displacement (minimum sense gap) must be determined.
71
The sense bias voltage and the motor amplitude can be used to control the maximum dis-
placement but, if the maximum displacement is exceeded, snap-down will occur. Proof
mass snap-down is a catastrophic failure that occurs when the electrostatic force between
the proof mass and the electrode is larger than the restoring force provided by the springs
that suspend the proof mass. When this happens, the proof mass touches the sense plate
and the gyro has snapped-down. The minimum sense gap required to prevent snap-down
can be determined for each gyro design and is affected by the factors listed in Fig. 3.6 [32].
Figure 3.6: Factors affecting snap-down phenomenon
The ADXRS gyros employ a novel approach to angular rate-sensing that makes it
possible to reject shocks of up to 1,000 g. They use two resonators to differentially sense
signals and reject common-mode external accelerations that are unrelated to angular mo-
tion. This approach is, in part, the reason for the excellent immunity of the ADXRS gyros
to shock and vibration. The two resonators are mechanically independent, and they oper-
ate anti-phase. As a result, they measure the same magnitude of rotation, but give outputs
in opposite directions. Therefore, the difference between the two sensor signals is used to
measure angular rate. This cancels non-rotational signals that affect both sensors. Thus, ex-
treme acceleration overloads are largely prevented from reaching the electronics, thereby
72
allowing the signal conditioning to preserve the angular rate output during large shocks.
This scheme requires that the two sensors be well-matched, precisely fabricated copies of
each other [31].
3.2 Evaluation Goals
The main goal of this research effort is to determine the typical response of the ADXRS300
MEMS gyro in an acoustically harsh environment. It is commonly known that the ADXRS300
can be adversely affected by high frequency mechanical vibrations and sufficiently loud
acoustic noise, but the average or typical response of this device in this harsh environment
has not been quantified. The following sections will address this by attempting to answer
these questions:
 Is the frequency or amplitude of the sine wave in the output signal sound level de-
pendent?
 How close above and below the resonant frequency of the sensor does this occur?
 Does it occur at the two other minor resonant frequencies?
 What happens if a two-tone signal is applied, where one tone is above and one below
the resonant frequency?
 Does a single tone far away from the resonant frequencies have any effect on the gyro
output at any realistic sound power level?
For each test case, the mean and standard deviation for each set of gyros will be
computed. The mean equates to the bias voltage and output signal components of the gyro
output. The standard deviation would be related to the noise in the output signal. For all the
tested gyros, a distribution plot of the standard deviation will be developed for each case.
73
This should then reveal the variance in the ADXRS300 performance in an acoustically
harsh environment. From this set of graphs and data, performance trends can then be
ascertained accordingly.
3.3 Evaluation Procedure and Setup
This section will describe in detail the procedures and equipment used for the experi-
ments.
3.3.1 Overall Procedure
Twenty-four Analog Devices ADXRS300 were acquired for testing. These were stan-
dard packages ordered via Digi-Key. Once the gyros were gathered, an evaluation board
was designed to accommodate the testing. Essentially, access to the gyro?s rate output sig-
nal and self-test inputs were required. Also, the boards were designed to provide power and
signal conditioning along with easy daisy-chaining of multiple boards. These boards were
then fabricated externally. The ADXRS300 chips were then assembled on the boards in-
house at Auburn University. One of the boards was designated as a control board and was
labeled board ?1?. The boards were then separated into groups (A through E) of three or
four, with the control board number ?1? as a member of each group. The groups were then
attached to an aluminum CDG plate via screws. Consequently, the plate was mounted on
an industrial rate table which provided precision-controlled spinning of a group of boards
to stimulate a rate output from the gyros.
An acoustic sound chamber in Wilmore Labs housed the rate table. The rate table is
bolted to an aluminum slab to provide stability to the system. Once inside the chamber,
the signal lines are fed through the rate table to a port which leads outside the chamber.
74
Connected to the lines inside the chamber are power and ground signals from an analog
power supply. The outside lines are then interfaced to the data collection equipment.
Inside the chamber, a three-dimensional speaker mount encloses the rate table. From
above the rate table, the speakers used to generate the acoustic noise are positioned for
maximum sound levels and a minimum of sound wave cancellation. A powered micro-
phone and digital thermometer are also mounted in close proximity to the boards. The
microphone is used to measure the sound pressure levels that the gyros are experiencing.
The microphone?s signal line is also fed though the port to the data collection center. The
chamber is then sealed from the outside.
The data collection center consists of four main components: rate signal data collec-
tion, sound level data collection, noise generation, and rate table control. All four compo-
nents are processed by two personal computers, audio amplifiers, and National Instruments
data acquisition devices. Various software packages are used to control the process and
will be discussed in a later section.
In a typical procedure, the rate table was activated, noise was generated, and data was
collected.
3.3.2 Evaluation Boards
The ADXRS300 evaluation board is two-layer printed circuit board (PCB). The board
was designed using The board was manufactured by Advanced Circuits (www.4pcb.com)
in Aurora, Colorado. Fig. 3.7 shows the schematic for the board. The capacitor values
CP1 - CP4 are charge pump capacitors for a 5V source. These can be omitted with a 15V
source. The power pins each have a decoupling capacitor. CMID and COUT are used to
set the output frequency bandwidth.
The physical board layout is shown in Fig. 3.8.
75
Figure 3.7: ADXRS300 board schematic
Figure 3.8: ADXRS300 board layout
76
The unpopulated evaluation board can be seen in Fig. 3.9. Each board is fitted with
the appropriate 1206-size surface mount capacitors as shown in Fig. 3.10.
Figure 3.9: Unpopulated evaluation board photo
Next, a flip chip bonder with a split optic alignment system (Fig. 3.11) was used place
the gyro on the board with solder balls accurately lined up on the pads.
Fig. 3.12 through Fig. 3.15 illustrate this process.
Next, the boards are sent through the reflow oven. The reflow oven melts the solder
balls from the BGA array which self-align to the pads. The surface mount capacitors are
attached in the same manner. The temperature profile shown in Fig. 3.16 was used.
The procedure for operating the reflow oven is shown in Fig. 3.17 through Fig. 3.21.
77
Figure 3.10: Evaluation board populated with capacitors
78
Figure 3.11: Flip chip bonder
79
Figure 3.12: Chip placed on table
80
Figure 3.13: Board placed under camera
81
Figure 3.14: Aligning solder balls to the board pads
82
Figure 3.15: Chip successfully placed on board
Figure 3.16: Reflow temperature profile
83
Figure 3.17: Packaging lab reflow oven
84
Figure 3.18: Ready for solder reflow
85
Figure 3.19: Placing board on the reflow oven belt track
86
Figure 3.20: Finished boards exiting the reflow oven
87
Figure 3.21: Boards cooling
88
Lastly, each board is tested to verify functional operation. Wires are soldered to all
the signal and power lines. The boards are hooked up to a power supply and the output is
measured with an oscilloscope. This is depicted in Fig. 3.22 and 3.24.
Figure 3.22: The board is connected to a voltage supply (5V)
3.3.3 Evaluation Facility
The acoustic chamber is located in Wilmore Labs on the Auburn University campus.
The chamber itself is primarily made of wood. It is approximately 8 inches off the ground
and is supported by a small number of legs to isolate the room from seismic and machine
vibrations. The floor of the chamber rests on a bed of compressed air. This makes the
chamber totally suspended from the ground. The chamber walls are insulated with fiber-
glass for further noise isolation. It also utilizes a double door system which has insulation
89
Figure 3.23: The rate output signal is measured with an oscilloscope
90
Figure 3.24: Fully Populated evaluation board
91
between the two doors when closed. There is a small circular port in room for external
access. The chamber is shown in Figs. 3.25 and 3.26.
Figure 3.25: Acoustic chamber in Wilmore labs
3.3.4 Rate Table
The rate table used is based on the Aerotech ADR160 mechanical-bearing rotary stage.
The ADR160 has a feedback rating of 23,600 lines/revolution. It also has a resolution of
13.1 ?rad and an accuracy rating of +/- 24.3 ?rad. 800 RPM?s (17,280,000 deg/s) is its
maximum rotary speed. It is a brushless direct-drive system [33].
92
Figure 3.26: Acoustic chamber with open doors
3.3.5 Speakers
Four speakers were used in the testing of the gyros. Two of the speakers are high-
frequency drivers. There is also a mid-range driver and a low-frequency driver to encom-
pass the acoustic spectrum (200-20 kHz). The mid-range speaker is a Community EM282
high power compression driver. It has a maximum output of 134 dB SPL (sound pressure
level) and a frequency response of 1 to 12 kHz. The low-frequency Community M4 high
power compression driver has a maximum output of 137 dB SPL and an operating range of
200 to 2000 Hz. The high-frequency Community VHF100 driver has a maximum output
of 131 dB SPL and an operating range of 1.8 to 18 kHz. All four drivers have a nominal
impedance of 8 W [34].
3.3.6 Audio Amplifiers
A pair of 2-channel Crown XTi1000 audio amplifiers are used to power the drivers.
These amps are capable of outputting 275 W per channel with an operating range of 20 Hz
to 20 kHz. Additionally, they have a signal to noise ratio of 100 dB [35].
93
3.3.7 Data Acquisition Device
For data acquisition purposes, the National Instruments 6143 multifunction DAQ is
utilized. The device uses a PCI interface for connection to a PC. It has 8 analog inputs each
capable of recording 250,000 samples/sec simultaneously. LabView software is used to
collect the data. Five inputs, one from each gyro in a group, are connected to the DAQ and
read into LabView. This setup allows for the collection of five gyro?s rate output signals at
the same time [36].
3.3.8 Microphone
For measuring the high intensity sound, the onmidirectional Endevco 8510B piezore-
sistive pressure transducer is used. This transducer employs a four-active arm strain gage
bridge diffused into a sculptured silicon diaphragm providing capability for measurement
from static pressure throughout the normal audio range. The microphone can measure
sound pressure levels up to 181 dB with a 10 VDC supply source [37].
3.3.9 Equipment Setup
The first step in setting up the equipment involves arranging the testbed. The speaker
mount is positioned around the rate table as shown in Fig. 3.27. This figure also shows the
power supply for the microphone (in the foreground). Next, the drivers are positioned using
the threaded bolts and accompanying nuts. The bolts are attached to the drivers with the
nuts. The nuts additionally adjust the height of the drivers by positioning them through the
pegboard at a specified length from the rate table. This configuration is illustrated in Fig.
3.28. Notice how the two high-frequency drivers are 180 degrees from each others. This
arrangement provides an extra 3 dB of sound output as compared to a single driver which
approximately doubles the power of the high frequency range sound. The speaker cables
94
are then connected to the amplifiers and sent through the chamber port and into each driver.
After the speakers are positioned, the reference gyro (1) is attached to the rate table with
screws. The serial connector is connected to the appropriate signal lines through the table
(see Appendix C for a circuit diagram of the wiring). Fig. 3.29 shows the reference gyro in
place. Next, a gyro group such as the one seen in Fig. 3.30 is interfaced to both the table
and the reference gyro (Fig 3.31). The microphone and thermometer are fed through the
pegboard and are located as close to the gyros as possible. The thermometer ensures that
there are no wild temperature fluctuations during testing. The microphone measures the
average and peak sound pressure levels. The microphone is powered by 10 VDC with the
output lines going outside the acoustic chamber. The digital thermometer and microphone
can be seen in Figs. 3.32 and 3.33, respectively. Lastly, A ribbon cable is used to send all
the output and input signal lines through the acoustic chamber?s port. The lines are then
connected to the NI DAQ units. One unit is for the microphone and another is for the gyros.
Thus, two computers are used for collecting data. A 5 VDC supply is used to power the
gyros from outside the acoustic chamber. Fig. 3.34 shows the data collection station used
during testing. The double doors are closed prior to any testing.
The amplifiers have been programmed with the correct crossover frequencies and de-
lay for each driver. Therefore, to achieve maximum output from the speakers, match the
correct driver to the appropriate channel. The gain knobs may be turned to maximum set-
tings safely. A multimeter can be connected to any channel output to monitor voltage spikes
if necessary.
3.3.10 Data Collection and Sound Generation Software
This section provides a brief tutorial on the methods used for data collection. Once
the PC?s have booted up, the user will be presented with desktops on each. For gyro output
data collection, four programs are important: NCH Tone Generator, gyro.exe, Gyros.vi,
95
Figure 3.27: Gyro testbed
Figure 3.28: Configuration of the four drivers relative to the rate table
96
Figure 3.29: Reference gyro attached to the rate table
97
Figure 3.30: Assembled gyro group
98
Figure 3.31: Reference gyro and group on table
99
Figure 3.32: Digital thermometer
100
Figure 3.33: Microphone and thermocouple
101
Figure 3.34: Data collection station
102
and NViewHMI. Shortcuts for these applications are located on the desktop. Run all four
programs.
NView HMI is used to control to spinning speed and direction of the rate table. Once
the application has started, click ?Manual? or press ?F3?. This is shown in Fig. 3.35. Next,
enter a distance and velocity and change the jog type to ?Distance.? Then, click the small
?x? in the top left corner of the window and click either the ?+? or ?-? sign to spin clockwise
or counterclockwise, resp. To stop the spinning, click the ?x? once more. A screenshot is
presented in Fig. 3.36.
Figure 3.35: NView HMI for controlling rate table startup screen
NCH Tone Generator is used to generate noise. Set all parameters prior to any testing.
These parameters include frequencies, tones, amplitudes, duration, and waveform. Once
these parameters are set, click ?Play? or press ?F9? to generate the sound specified. Fig.
3.37 is an example sound profile.
Gyros.vi is a LabView frontend for collecting data from the (up to) five gyros simul-
taneously. Simply enter in a file location in the ?Path? box and set the test duration (in
103
Figure 3.36: NView HMI for controlling rate table
Figure 3.37: NCH Tone Generator Software
104
seconds). ST1 and ST2 are used to toggle the self-test inputs of the reference gyro only.
All five gyros? outputs will be shown in real-time and saved to the file specified in an Excel
readable format. See Appendix D for a block diagram. Run the VI when ready to collect
data. Fig. 3.38 shows this interface.
Figure 3.38: Gyros.vi data collection screen
The gyro.exe program provides some keyboard hotkeys for test synchronization. For
instance, starting and stopping both sound and data collection in discrete intervals. The
application also will chart data in Excel automatically. Please see Appendix B for more
information.
The other PC is used for sound pressure level measurement via the microphone. Pres-
sureTransducerSUM.vi is a LabView application to visually monitor two key elements.
The first element is the Current Max Frequency. This displays the single frequency which
has acquired the most energy (in Hz). The other element is the Current Max dB value. The
number represents the SPL of the aforementioned frequency. This value is expressed in
105
dB. These values are crucial in determining the actual maximum output from the drivers in
real-time at a specific frequency. Fig. 3.39 shows a screenshot of the GUI. See Appendix
D for the block diagram.
Figure 3.39: PressureTransducerSUM.vi screen
3.4 Evaluation of the ADXRS300 Gyros
This section is comprised of the pertinent raw data from acoustic tests performed on
the ADI ADXRS300 gyros. This data is primarily composed of sound pressure amplitudes
across the acoustic frequency spectrum and the corresponding effects on the gyro?s rate
voltage output.
106
3.4.1 Minimum and Maximum Sound Pressure Levels
Fig. 3.40 shows the baseline sound pressure levels (SPL), in decibels (dB), versus
frequency (Hz) in the absence of sound. Note: the amplitudes for all the following SPL
charts are continuously averaged over 10s. In other words, over a period of time, the data in
the chart would eventually depict a flat line at a certain amplitude. In this case, the baseline
data indicates that the average SPL for the silent acoustic chamber is approximately 68
dB over the acoustic spectrum. This number represents the minimum SPL the Endevco
sound pressure transducer is capable of detecting. This is due to its calibration for accurate
readings at extremely high SPL?s of over 180 dB. For all tests that involve ?no sound,? Fig.
3.40 is a typical frequency response. This graphed data will be representative of all these
cases. Note the spikes in this graph. These spikes are more than likely a result of electronic
noise in the test equipment. This noise appears to be present in regular frequency intervals
and is more prominent at lower frequencies. These spikes have no bearing on the real world
ambient noise present in the tests.
Fig. 3.41 illustrates the maximum sound pressure levels experienced in the presence
of white noise. See Appendix A for more information. Here, peaks can be seen as high
as 100 dB. This level is equivalent to standing in the front row of a rock concert. White
noise is a random distribution of frequencies with equal amplitudes. Therefore, Fig. 3.41
encapsulates the speakers? ability to effectively reproduce mathematically random white
noise at a maximum power level. In general, white noise is a good model for a variety
of acoustic events. Anything from music concerts to powerful exhaust emissions can be
modeled by white noise. Overall, white noise can test the gyros? output in the presence
of a large number of random powerful frequencies. Notice how the low frequency spikes
from the test electronics is still present. All further white noise tests will use Fig. 3.41 as a
reference for typical maximum SPL?s of white noise.
107
Figure 3.40: 10 Second Average SPL Baseline(No Sound)
108
Figure 3.41: White Noise
109
Fig. 3.42 is an example of the sound pressure level of a single frequency or tone. In
this case, the tone is 13,766 Hz and reaches a SPL of nearly 140 dB. 140 dB sound levels
are equivalent to a jet engine takeoff and results in immediate hearing damage in humans.
This level is well over the threshold of pain, which begins at 125 dB. This sound pressure
level is the maximum level that the test equipment can produce. All tone and sine sweep
data will use Fig. 3.42 as a model for the maximum SPL of a single frequency tone.
Figure 3.42: Single Frequency (Tone)
3.4.2 Reference Gyro Data
This section will aim to fully characterize the reference gyro as pertains to its acoustic
responses. For example, Fig. 3.43 depicts the reference gyro?s output rate (V) versus time
(s) at various rotational speeds in degrees per second (DPS).
110
Figure 3.43: Reference gyro?s rate output at various angular rates without sound
111
Fig. 3.44 illustrates the reference gyro?s self-test function. Here, the output of ST1
and ST2 are compared to the actual angular rates they are designed to simulate. Clearly,
this function does an adequate job.
Figure 3.44: Reference gyro?s self-test rate out without sound
Fig. 3.47 and 3.48 show how the reference gyro responds to a sine sweep signal from
6000 Hz to 18000 Hz in 30 seconds. It can be seen that a clear disruption occurs at certain
frequencies near 14000 Hz which corresponds to the gyro?s natural frequency.
After a trial and error period, the reference gyro?s resonant frequency can be found.
The resonant frequency is reached when the gyro?s rate output becomes a steady-state sig-
nal as shown in Fig. 3.50. In this case, the resonant frequency occurs at 13903.77 Hz.
In addition, the gyros exhibit a noticeable harmonic frequency at roughly half the
resonant frequency. In the reference gyro?s case, this first sub-harmonic occurs at 6951.95
Hz as seen in Fig. 3.51.
112
Figure 3.45: Reference gyro with white noise
113
Figure 3.46: Reference gyro?s self-test with white noise
114
Figure 3.47: Reference gyro sine sweep
115
Figure 3.48: Reference gyro?s self-test sine sweep
116
Figure 3.49: Reference gyro sine sweep near resonant frequency (0 DPS)
117
Figure 3.50: Reference gyro?s resonant frequency (0 DPS)
118
Figure 3.51: Reference gyro?s 1st harmonic at 6951.95 Hz (0 DPS)
119
Fig. 3.52 shows the reference gyro?s output response to a linear increase in sound
pressure levels over 100 seconds.
Figure 3.52: Reference gyro output at various sound pressure levels (0 DPS)
Fig. 3.53 to Fig. 3.61 represent a two tone test. Two tones equidistant from the
resonant frequency are generated and the gyro?s output response is plotted.
3.4.3 Baseline (No Sound and 0 DPS)
Fig. 3.62 provides a baseline look at the gyros. Baseline indicates that there is no
rotation and no noise. These readings provide a default output voltage bias for each gyro
relative to each other.
120
Figure 3.53: Reference gyro two tone test (+/- 4 kHz)
121
Figure 3.54: Reference gyro two tone test (+/- 3 kHz)
122
Figure 3.55: Reference gyro two tone test (+/- 2 kHz)
123
Figure 3.56: Reference gyro two tone test (+/- 1 kHz)
124
Figure 3.57: Reference gyro two tone test (+/- 100 Hz)
125
Figure 3.58: Reference gyro two tone test (+/- 10 Hz)
126
Figure 3.59: Reference gyro two tone test (+/- 1 Hz)
127
Figure 3.60: Reference gyro two tone test (+/- 0.1 Hz)
128
Figure 3.61: Reference gyro two tone test (+/- 0.01 Hz)
129
Figure 3.62: Baseline (No Sound and 0 DPS)
130
3.4.4 White Noise
Here, each gyro is subjected to full power white noise at various angular rates from
-300 DPS to +300 DPS. The resulting rate output voltage is shown in Fig. 3.63 to Fig. 3.73.
Figure 3.63: White Noise at 0 DPS
3.4.5 Resonant Frequencies
Fig. 3.74 shows each gyro?s response to a sine wave whose frequency matches that of
its resonant frequency.
3.4.6 First Sub-Harmonics
In this section, Fig. 3.75 will show each gyro?s output response to a sine wave whose
frequency matches that of its first sub-harmonic frequency. The first sub-harmonic fre-
quency is mathematically half the resonant frequency.
131
Figure 3.64: White Noise at 60 DPS
132
Figure 3.65: White Noise at 120 DPS
133
Figure 3.66: White Noise at 180 DPS
134
Figure 3.67: White Noise at 240 DPS
135
Figure 3.68: White Noise at 300 DPS
136
Figure 3.69: White Noise at -60 DPS
137
Figure 3.70: White Noise at -120 DPS
138
Figure 3.71: White Noise at -180 DPS
139
Figure 3.72: White Noise at -240 DPS
140
Figure 3.73: White Noise at -300 DPS
141
Figure 3.74: Resonant Frequency Response
142
Figure 3.75: First Sub-Harmonics
143
3.4.7 Sine Sweeps
Fig. 3.76 illustrates each gyro?s response to a sine sweep signal. This sine wave is
swept from 0 to 20,000 Hz in 5 minutes (300 seconds) at maximum power. Harmonic and
resonant frequencies can be seen in detail in this figure.
Figure 3.76: Sine sweeps
3.5 Evaluation Data Analysis and Results
This section will provide a statistical analysis of the gyros. Of primary concern will
be mean and standard deviation values.
144
3.5.1 Bias Voltage
Fig. 3.77 describes the bias voltage for each gyro. These are the mean values of the
baseline test results. Equ. 3.1 shows the standard deviation of these mean bias voltages.
Finally, Fig. 3.78 shows the standard deviation of each gyro?s baseline rate output voltage.
Figure 3.77: Baseline mean bias voltages
BaselineBiasVoltage : s = 0:055096862 (3.1)
3.5.2 No Noise Standard Deviations
In this section, the standard deviations of the rate output voltage of each gyro at various
rotation speeds without noise will be presented in Tbl. 3.1 and 3.2.
145
Figure 3.78: Baseline standard deviations of rate output
146
Gyro -300 -240 -180 -120 -60 0 60 120
Ref 0.0264 0.0218 0.0212 0.0158 0.0106 0.0025 0.0109 0.0164
2 0.0323 0.0264 0.0252 0.0182 0.0160 0.0032 0.0155 0.0197
3 0.0283 0.0237 0.0235 0.0175 0.0155 0.0028 0.0150 0.0185
4 0.0361 0.0294 0.0285 0.0203 0.0171 0.0033 0.0164 0.0213
5 0.0365 0.0334 0.0314 0.0210 0.0174 0.0033 0.0170 0.0227
7 0.0353 0.0330 0.0286 0.0192 0.0136 0.0028 0.0131 0.0203
8 0.0428 0.0419 0.0354 0.0225 0.0152 0.0030 0.0147 0.0236
9 0.0442 0.0430 0.0393 0.0249 0.0157 0.0031 0.0153 0.0264
11 0.0363 0.0339 0.0280 0.0206 0.0154 0.0030 0.0155 0.0219
12 0.0420 0.0371 0.0332 0.0240 0.0174 0.0031 0.0173 0.0255
13 0.0445 0.0425 0.0356 0.0261 0.0185 0.0033 0.0181 0.0266
14 0.0398 0.0349 0.0327 0.0217 0.0162 0.0029 0.0168 0.0216
15 0.0352 0.0324 0.0297 0.0216 0.0161 0.0031 0.0169 0.0217
16 0.0479 0.0421 0.0391 0.0261 0.0192 0.0032 0.0201 0.0263
18 0.0042 0.0045 0.0044 0.0043 0.0041 0.0027 0.0042 0.0043
19 0.0035 0.0037 0.0035 0.0035 0.0033 0.0024 0.0035 0.0034
20 0.0042 0.0043 0.0044 0.0042 0.0038 0.0025 0.0041 0.0042
21 0.0041 0.0043 0.0043 0.0040 0.0039 0.0025 0.0040 0.0041
22 0.0039 0.0037 0.0038 0.0038 0.0038 0.0029 0.0036 0.0036
23 0.0038 0.0033 0.0036 0.0036 0.0035 0.0025 0.0034 0.0035
24 0.0041 0.0038 0.0040 0.0042 0.0038 0.0027 0.0040 0.0041
Table 3.1: No noise standard deviations
147
Gyro 180 240 300
Ref 0.0211 0.0301 0.0229
2 0.0246 - 0.0257
3 0.0232 - 0.0245
4 0.0269 - 0.0279
5 0.0291 - 0.0300
7 0.0295 0.0324 0.0305
8 0.0356 0.0390 0.0370
9 0.0380 0.0386 0.0406
11 0.0256 0.0277 0.0335
12 0.0292 0.0297 0.0366
13 0.0335 0.0352 0.0432
14 0.0294 0.0302 0.0348
15 0.0267 0.0285 0.0319
16 0.0354 0.0376 0.0439
18 0.0044 0.0042 0.0038
19 0.0037 0.0035 0.0032
20 0.0042 0.0040 0.0037
21 0.0042 0.0040 0.0038
22 0.0038 0.0036 0.0036
23 0.0033 0.0035 0.0032
24 0.0040 0.0041 0.0035
Table 3.2: No noise standard deviations (cont.)
148
3.5.3 White Noise
In this section, the standard deviations of the rate output voltage of each gyro while
being subjected to white noise at various rotation speeds will be presented in Tbl. 3.3 and
3.4.
Gyro -300 -240 -180 -120 -60 0 60 120
Ref 0.0413 0.0442 0.0439 0.0367 0.0424 0.0111 0.0397 0.0450
2 0.0571 0.0610 0.0600 0.0549 0.0518 0.0418 0.0495 0.0534
3 0.0455 0.0458 0.0422 0.0404 0.0390 0.0641 0.0378 0.0427
4 0.0400 0.0373 0.0329 0.0270 0.0266 0.0108 0.0230 0.0285
5 0.0446 0.0422 0.0385 0.0307 0.0313 0.0261 0.0296 0.0312
7 0.0743 0.0681 0.0724 0.0676 0.0702 0.0481 0.0663 0.0677
8 0.0973 0.0899 0.0905 0.0872 0.0722 0.0748 0.0720 0.0805
9 0.1242 0.1304 0.1166 0.1046 0.1166 0.1376 0.1078 0.1116
11 0.0499 0.0505 0.0445 0.0429 0.0421 0.0126 0.0406 0.0374
12 0.0522 0.0512 0.0444 0.0408 0.0385 0.0231 0.0316 0.0382
13 0.0959 0.0885 0.0838 0.0758 0.0749 0.0260 0.0792 0.0716
14 0.0579 0.0577 0.0502 0.0428 0.0455 0.0569 0.0427 0.0459
15 0.0481 0.0449 0.0368 0.0366 0.0292 0.0174 0.0315 0.0354
16 0.0735 0.0683 0.0634 0.0541 0.0511 0.0554 0.0566 0.0608
18 0.0712 0.0678 0.0721 0.0731 0.0727 0.1227 0.0711 0.0763
19 0.0114 0.0116 0.0113 0.0121 0.0111 0.0098 0.0108 0.0131
20 0.0558 0.0548 0.0514 0.0594 0.0568 0.0988 0.0589 0.0491
21 0.0193 0.0204 0.0187 0.0197 0.0217 0.0215 0.0191 0.0207
22 0.0556 0.0535 0.0571 0.0607 0.0554 0.0396 0.0537 0.0545
23 0.0202 0.0218 0.0208 0.0206 0.0205 0.0124 0.0215 0.0187
24 0.0547 0.0548 0.0546 0.0508 0.0602 0.0470 0.0561 0.0529
Table 3.3: White noise standard deviations
3.5.4 Resonant Frequencies
Fig. 3.79 lists the resonant frequencies of each gyro. Equ. 3.2 shows the standard
deviation of those frequencies.
149
Gyro 180 240 300
Ref 0.0447 0.0678 0.0397
2 0.0513 - 0.0594
3 0.0467 - 0.0460
4 0.0341 - 0.0373
5 0.0366 - 0.0404
7 0.0692 0.0746 0.0727
8 0.0916 0.0822 0.0878
9 0.1177 0.1224 0.1004
11 0.0466 0.0476 0.0503
12 0.0450 0.0467 0.0500
13 0.0786 0.0867 0.0882
14 0.0525 0.0544 0.0489
15 0.0422 0.0430 0.0452
16 0.0651 0.0668 0.0674
18 0.0690 0.0641 0.0707
19 0.0111 0.0101 0.0114
20 0.0576 0.0539 0.0488
21 0.0216 0.0203 0.0208
22 0.0523 0.0549 0.0577
23 0.0224 0.0197 0.0191
24 0.0594 0.0520 0.0542
Table 3.4: White noise standard deviations (cont.)
150
Figure 3.79: Resonant frequencies of each gyro
151
ResonantFrequencies : s = 934:0686737 (3.2)
3.5.5 First Sub-Harmonics
Fig. 3.80 lists the first sub-harmonic frequencies of each gyro. Equ. 3.3 shows the
standard deviation of those frequencies.
Figure 3.80: First sub-harmonic frequencies of each gyro
FirstSubHarmonicFrequencies : s = 467:0496657 (3.3)
152
CHAPTER 4
CONCLUSIONS
In this section, the following questions, first stated in Section 3.2, will addressed:
1. Is the frequency or amplitude of the sine wave in the output signal sound level de-
pendent?
2. How close above and below the resonant frequency of the sensor does this occur?
3. Does it occur at the two other minor resonant frequencies?
4. What happens if a two-tone signal is applied, where one tone is above and one below
the resonant frequency?
5. Does a single tone far away from the resonant frequencies have any effect on the gyro
output at any realistic sound power level?
6. What is the probability distribution of the natural frequency for the gyros tested?
7. Does the standard deviation of the output rate increase in proportion to the applied
angular rate?
Fig. 3.52 provides the answer to Question 1. Based on the data acquired from the
reference gyro, a gyro?s output will be sinusoidal when subjected to a single tone near its
resonant frequency. It is seen that as the SPL?s increase, the amplitude of the gyro?s output
increases linearly. In fact, the rate at which it increases is 0.0026 V/dB (0.0052 Vpp/dB).
153
The output frequency, on the other hand, is not affected at all. The reference gyro?s gathered
data shows that the output frequency is a function of the frequency of the ambient noise.
Question 2 can be answered by referring to Fig. 3.76. In this figure, it can be seen
exactly when each gyro?s output starts to become affected by a single high-pressure tone.
As the tone frequency nears the resonant frequency, the gyros? output become increasingly
erratic at an exponential rate. In general, the gyros are dramatically affected within 1 kHz
of its resonant frequency. Slight sinusoidal tendencies can be seen as far away as 3 kHz.
The answer to Question 3 is ?yes.? Examining the first sub-harmonic plots will reveal
that the other minor frequencies are indeed affected by noise near this frequency. Please
refer to Figs. 3.76 and 3.75.
Question 4 is answered by examining the reference gyro output. As two tones equidis-
tant from its resonant frequency become closer, the gyro?s output begins to behave as in
Figs. 3.53 to Fig. 3.61.
Once again, the Question 5 can be illuminated by Fig. 3.76. Even at maximum
SPL?s there are certain frequencies which have no discernible impact on the gyros? out-
put. Namely, these frequencies exist well outside their resonant and harmonic frequencies.
In order to answer Question 6, we examine Fig. 4.1 which shows, Fig. 4.1 shows the
normal distribution (Gaussian) of the natural frequencies of the tested gyros. The graph
concisely shows the probabilities of the various natural frequencies centered around 15.3
kHz, the mean natural frequency of the gyros. This typical range of frequency values fluc-
tuates significantly from the manufacturer?s stated nominal 14 kHz resonating frequency of
each ADXRS300 MEMS gyro [28].
Question 7 is answered by examining the data in Fig. 4.2. The graph shows the output
rate standard deviation of each gyro as the angular rate increases from 0 to 300 degrees
per second. Curiously, there seems to be two trends amongst the gyros. Groups A through
D experience relatively linear increases in standard deviation as the angular rate increases.
154
However, Groups E and F show little change in their standard deviations by comparison.
By examining Figs. 3.63 through 3.68, the ?no sound? output levels of groups E and F at the
various angular rates remain somewhat constant throughout. The other groups, however,
show a trend of increasing standard deviations. Evidently, there is some variation in the
output rate standard deviations between each gyro grouping. As to the question, Fig. 4.2
and 4.3 seem to affirm that indeed the standard deviation of the output rate of each gyro
increases in proportion to the applied angular rate, however, by varying amounts.
Finally, Table 4.1 shows the typical response of the gyros as they are subjected to
acoustic noise. The ?baseline? value represents the standard deviation of the gyros? rate
output voltages while stationary and without noise. The ?white noise 0 DPS? value rep-
resents the the gyros? standard deviations while stationary but in the presence of white
noise. Therefore, the ?factor? value illustrates how the presence of high power white noise
can affect the rate output voltage by various magnitudes. The table shows that standard
deviations can increase by a factor of 3 to 44 by applying high power white noise to a
working ADXRS300 MEMS gyro. This noise level could make the device unusable in this
environment. The effects are even more dramatic for frequencies near each gyro?s natu-
ral frequency. In fact, for these frequencies the gyros become quite useless as the output
voltages begin to swing wildly rendering the typical response of each gyro?s reported rate
value to be inaccurate and unstable. So, in summary, a MEMS gyro?s rate output voltage
is adversely affected by high-frequency acoustic noise and responds typically as shown
throughout the data presented in this thesis.
155
Gyro Baseline White Noise 0 DPS Factor
Ref 0.002379967 0.011107925 4.667260644
2 0.003124012 0.041399207 13.25193704
3 0.002703461 0.063574897 23.51611362
4 0.003218614 0.010999183 3.417366751
5 0.003263474 0.025725922 7.882986219
7 0.002936534 0.047046402 16.02106444
8 0.003041109 0.076378647 25.11539056
9 0.003133744 0.139176035 44.4120594
11 0.002866653 0.01266741 4.41888532
12 0.002801369 0.023007011 8.212774079
13 0.00287733 0.025415162 8.832898624
14 0.002836466 0.055376522 19.52306744
15 0.003031624 0.017602752 5.806376995
16 0.003121054 0.055384876 17.74556995
18 0.002611003 0.123223407 47.19389924
19 0.002357345 0.009739161 4.131411633
20 0.00239834 0.097153155 40.50849104
21 0.002496666 0.021466124 8.597914718
22 0.002798252 0.038315134 13.69252357
23 0.002443066 0.012001517 4.91248101
24 0.00261693 0.045410077 17.35242405
Table 4.1: Comparison of standard deviations between baseline and white noise
156
Figure 4.1: Natural frequency normal distribution
157
Figure 4.2: Standard deviation of gyros at increasing angular rates
158
Figure 4.3: Standard deviation of groups E and F at increasing angular rates
159
CHAPTER 5
FUTURE WORK
In the future, the main goal of this research is to develop and understand methods
for negating the affects of acoustic noise on MEMS gyros. This may be done through
packaging or design. Sufficiently high natural frequencies designed well above the acoustic
spectrum or high frequency shielding could both potentially be used to achieve this.
160
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for Micro Electrical Machined Based Inertial Measurement Units,? Honeywell Int.:
Minneapolis, Minnesota.
[30] M. S. Weinberg and A. Kourepenis, ?Error Sources in In-Plane Silicon Tuning-Fork
MEMS Gyroscopes,? Journal of Microelectromechanical Systems, Vol. 15, No. 3,
June 2006.
[31] J. Green and D. Krakauer, ?New iMEMS Angular-Rate-Sensing Gyroscope,? ADI
Micromachined Products Division.
[32] M. Weber, M. Bellrichard, and C. Kennedy, ?High Angular Rate and High G Effects
in the MEMS Gyro,? Honeywell: Minneapolis, Minnesota. Coventor: Cary, North
Carolina.
162
[33] http://www.aerotech.com/.
[34] http://www.loudspeakers.net/.
[35] http://www.crownaudio.com/.
[36] http://www.ni.com/.
[37] http://www.endevco.com/.
163
APPENDICES
164
APPENDIX A
MATLAB NOISE GENERATION CODE
%--------------------------------------------------------
clear
clc
%--------------------------------------------------------
%--------------------------------------------------------
F1=13000; %Low Limit Frequency
F2=18000; %High Limit Frequncy
time=10; %Duration Of Signal
%--------------------------------------------------------
%--------------------------------------------------------
rate=44100;
rate_adj = time*rate;
white = randn(1,rate_adj);
W1 = 2*F1/rate;
W2 = 2*F2/rate;
Wn = [W1 W2];
[B,A] = butter(19, Wn);
wideband = filter(B,A,white);
sound(white,rate_adj/time);
%--------------------------------------------------------
165
APPENDIX B
DATA COLLECTION CODE
; AutoHotkey Version: 1.x
; Language: English
; Platform: Win9x/NT
; Authors: S. T. Castro & G. Roth
;
; Script Function:
; Template script (you can customize this template by editing
; "ShellNew\Template.ahk" in your Windows folder)
#NoEnv
; Recommended for performance and compatibility
; with future AutoHotkey releases.
SendMode Input
; Recommended for new scripts due to its
; superior speed and reliability.
SetWorkingDir %A_ScriptDir%
; Ensures a consistent starting directory.
?!g::
WinWait, Microsoft Excel,
IfWinNotActive, Microsoft Excel, , WinActivate, Microsoft Excel,
WinWaitActive, Microsoft Excel,
Send, ?{HOME}{SHIFTDOWN}{DOWN 20}{CTRLDOWN}{RIGHT}{CTRLUP}{SHIFTUP}
Send, !ed
Send, {RIGHT 6}{SHIFTDOWN}?{DOWN}{SHIFTUP}
Send, !ed
Send, {HOME}{SHIFTDOWN}{CTRLDOWN}{DOWN}{RIGHT}{SHIFTUP}{CTRLUP}
Send, {ALTDOWN}i{ALTUP}h
WinWait, Chart Wizard - Step 1 of 4 - Chart Type,
IfWinNotActive, Chart Wizard - Step 1 of 4 - Chart Type, ,
WinActivate, Chart Wizard - Step 1 of 4 - Chart Type,
166
WinWaitActive, Chart Wizard - Step 1 of 4 - Chart Type,
Send, {DOWN 4}{TAB}{DOWN}{RIGHT}{ENTER 4}
return
?!1::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !t{DOWN 5}{ENTER}
Sleep 100
Send, {DOWN 3}{ENTER}10000{ENTER}
WinActivate, Gyros.vi
Send, ?r
Sleep 10000
WinActivate, NCH Tone Generator
Send, {F9}
Return
?!2::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !t{DOWN 5}{ENTER}
Sleep 100
Send, {DOWN 5}{ENTER}10000{ENTER}
WinActivate, Gyros.vi
Send, ?r
Sleep 10000
WinActivate, NCH Tone Generator
Send, {F9}
Return
?!l::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !t{DOWN 6}{ENTER}
Sleep 100
Send, {DOWN 4}{ENTER}300000{ENTER}
167
WinActivate, Gyros.vi
Send, ?r
WinActivate, NCH Tone Generator
Send, {F9}
Return
?!s::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !t{DOWN 6}{ENTER}{DOWN 4}{ENTER}30000{ENTER}
WinActivate, Gyros.vi
Send, ?r
WinActivate, NCH Tone Generator
Send, {F9}
Return
?!w::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !tw{DOWN}{ENTER}10000{ENTER}
WinActivate, Gyros.vi
Send, ?r
Sleep 10000
WinActivate, NCH Tone Generator
Send, {F9}
Return
?!p::
WinWait, NCH Tone Generator
WinActivate, NCH Tone Generator
WinWaitActive, NCH Tone Generator
Send, !t{DOWN 5}{ENTER}
Send, {F9}
SoundSet, 0, MASTER
WinActivate, Gyros.vi
Send, ?r
168
Loop, 100
{
Sleep, 1000
SoundSet, +1, MASTER
}
SoundSet, 100, MASTER
Return
169
APPENDIX C
GYROS TO NI DAQ SCHEMATIC
Figure C.1: Wiring diagram for gyros to NI BNC-2110
170
APPENDIX D
LABVIEW BLOCK DIAGRAMS
Figure D.1: Gyros.vi block diagram
171
Figure D.2: Gyros.vi block diagram
172