In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a microdisk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a microgyroscope and show that synchronization arising from mutual coupling dramatically reduces frequency instability at the cost of increased amplitude instability. We present an alternative synchronization scheme that suppresses this drawback while still taking advantage of a passive frequency mode-match operation.

References

References
1.
Pikovsky
,
A.
,
Rosenblum
,
M.
, and
Kurths
,
J.
,
2003
,
Synchronization: A Universal Concept in Nonlinear Sciences
,
Cambridge University Press
,
Cambridge, UK
.
2.
Ronacher
,
B.
, and
Römer
,
H.
,
1985
, “
Spike Synchronization of Tympanic Receptor Fibres in a Grasshopper (Chorthippus Biguttulus L., Acrididae). A Possible Mechanism for Detection of Short Gaps in Model Songs
,”
J. Comp. Physiol., A
,
157
(
5
), pp.
631
642
.
3.
Buck
,
J.
, and
Buck
,
E.
,
1968
, “
Mechanism of Rhythmic Synchronous Flashing of Fireflies
,”
Science
,
159
(
3821
), pp.
1319
1327
.
4.
Guevara
,
M. R.
,
Glass
,
L.
, and
Shrier
,
A.
,
1981
, “
Phase Locking, Period-Doubling Bifurcations, and Irregular Dynamics in Periodically Stimulated Cardiac Cells
,”
Science
,
214
(
4527
), pp.
1350
1353
.
5.
Smith
,
D. R.
,
1985
,
Digital Transmission Systems
,
Springer
,
New York
.
6.
Antonio
,
D.
,
Czaplewski
,
D. A.
,
Guest
,
J. R.
,
López
,
D.
,
Arroyo
,
S. I.
, and
Zanette
,
D. H.
,
2015
, “
Nonlinearity-Induced Synchronization Enhancement in Micromechanical Oscillators
,”
Phys. Rev. Lett.
,
114
(
3
), p.
034103
.
7.
Matheny
,
M. H.
,
Grau
,
M.
,
Villanueva
,
L. G.
,
Karabalin
,
R. B.
,
Cross
,
M. C.
, and
Roukes
,
M. L.
,
2014
, “
Phase Synchronization of Two Anharmonic Nanomechanical Oscillators
,”
Phys. Rev. Lett.
,
112
(
1
), p.
014101
.
8.
Shoshani
,
O.
,
Heywood
,
D.
,
Yang
,
Y.
,
Kenny
,
T. W.
, and
Shaw
,
S. W.
,
2016
, “
Phase Noise Reduction in an MEMS Oscillator Using a Nonlinearly Enhanced Synchronization Domain
,”
J. Microelectromech. Syst.
,
25
(
5
), pp.
870
876
.
9.
Acar
,
C.
, and
Shkel
,
A.
,
2009
,
MEMS Vibratory Gyroscopes
,
Springer
,
New York
.
10.
Painter
,
C. C.
, and
Shkel
,
A. M.
,
2003
, “
Active Structural Error Suppression in MEMS Vibratory Rate Integrating Gyroscopes
,”
IEEE Sens. J.
,
3
(
5
), pp.
595
606
.
11.
Norouzpour-Shirazi
,
A.
,
Serrano
,
D. E.
,
Zaman
,
M. F.
,
Casinovi
,
G.
, and
Ayazi
,
F.
,
2015
, “
A Dual-Mode Gyroscope Architecture With In-Run Mode-Matching Capability and Inherent Bias Cancellation
,” 18th International Conference on Solid-State Sensors, Actuators and Microsystems (
TRANSDUCERS
), Anchorage, AK, June 21–25, pp.
23
26
.
12.
Ezekwe
,
C. D.
, and
Boser
,
B. E.
,
2008
, “
A Mode-Matching ΔΣ Closed-Loop Vibratory-Gyroscope Readout Interface With a 0.004A°/s/√Hz Noise Floor Over a 50 Hz Band
,”
IEEE International Solid-State Circuits Conference—Digest of Technical Papers
(
ISSCC
), San Francisco, CA, Feb. 3–7, pp.
580
637
.
13.
Nitzan
,
S.
,
Ahn
,
C. H.
,
Su
,
T.-H.
,
Li
,
M.
,
Ng
,
E. J.
,
Wang
,
S.
,
Yang
,
Z. M.
,
O'Brien
,
G.
,
Boser
,
B. E.
,
Kenny
,
T. W.
, and
Horsley
,
D. A.
,
2013
, “
Epitaxially-Encapsulated Polysilicon Disk Resonator Gyroscope
,”
IEEE 26th International Conference on Micro Electro Mechanical Systems
(
MEMS
), Taipei, Taiwan, Jan. 20–24, pp.
625
628
.
14.
Ahn
,
C. H.
,
Ng
,
E. J.
,
Hong
,
V. A.
,
Yang
,
Y.
,
Lee
,
B. J.
,
Ward
,
M. W.
, and
Kenny
,
T. W.
,
2013
, “
Geometric Compensation of (100) Single Crystal Silicon Disk Resonating Gyroscope for Mode-Matching
,”
17th International Conference on Solid-State Sensors, Actuators and Microsystems
(
TRANSDUCERS EUROSENSORS XXVII
), Barcelona, Spain, June 16–20, pp.
1723
1726
.
15.
Nitzan
,
S. H.
,
Taheri-Tehrani
,
P.
,
Defoort
,
M.
,
Sonmezoglu
,
S.
, and
Horsley
,
D. A.
,
2016
, “
Countering the Effects of Nonlinearity in Rate-Integrating Gyroscopes
,”
IEEE Sens. J.
,
16
(
10
), pp.
3556
3563
.
16.
Gallacher
,
B. J.
,
Hedley
,
J.
,
Burdess
,
J. S.
,
Harris
,
A. J.
,
Rickard
,
A.
, and
King
,
D. O.
,
2005
, “
Electrostatic Correction of Structural Imperfections Present in a Microring Gyroscope
,”
J. Microelectromech. Syst.
,
14
(
2
), pp.
221
234
.
17.
Lynch
,
D. D.
,
1995
, “
Vibratory Gyro Analysis by the Method of Averaging
,”
Second Saint Petersburg International Conference on Gyroscopic Technology and Navigation
, St. Petersburg, Russia, May 24–25, pp. 26–34.
18.
Kline
,
M. H.
,
Yeh
,
Y.-C.
,
Eminoglu
,
B.
,
Najar
,
H.
,
Daneman
,
M.
,
Horsley
,
D. A.
, and
Boser
,
B. E.
,
2013
, “
Quadrature FM Gyroscope
,”
IEEE 26th International Conference on Micro Electro Mechanical Systems
(
MEMS
), Taipei, Taiwan, Jan. 20–24, pp.
604
608
.
You do not currently have access to this content.