Vibration-induced PM Noise in Oscillators and Studies of Correlation ...
Vibration-induced PM Noise in Oscillators and Studies of Correlation ... Vibration-induced PM Noise in Oscillators and Studies of Correlation ...
“Vibration Vibration-induced induced PM Noise in Oscillators and Studies of Correlation with Vibration Sensors” Sensors D. A. Howe, J. L. Lanfranchi, Lanfranchi, N. Ashby, L. Cutsinger, Cutsinger, C. W. Nelson, A. Hati National Institute of Standards & Technology (NIST), Boulder, CO, CO, USA
- Page 2 and 3: Description of vibration equipment
- Page 4 and 5: Vibration phase noise test bed 3-a
- Page 6 and 7: Uniform Motion The detected frequen
- Page 8 and 9: ρ α = Signal Multipath Effect fro
- Page 10 and 11: Sine Vibration-Induced Phase Noise
- Page 12: 0000
- Page 15 and 16: Compensation On
- Page 17: X Axis
- Page 21 and 22: Compensation On
- Page 23: Y Axis
- Page 27 and 28: Compensation On
- Page 29 and 30: Z Axis
- Page 31 and 32: Conclusion State-of-art phase nois
- Page 33 and 34: Conclusion State-of-art phase nois
- Page 35 and 36: Low-noise Oscillator w/ Active Vibr
- Page 37 and 38: Vibration-induced PM Noise in Oscil
- Page 39 and 40: L(f) dBc/Hz 0 -10 -20 -30 -40 -50 -
- Page 41 and 42: Phase noise under vibration is for
- Page 43: Acceleration 70 60 50 40 30 20 10 0
- Page 46: Qz Osc w/ Vibration Suppression: Ph
“<strong>Vibration</strong> <strong>Vibration</strong>-<strong><strong>in</strong>duced</strong> <strong><strong>in</strong>duced</strong> <strong>PM</strong> <strong>Noise</strong> <strong>in</strong><br />
<strong>Oscillators</strong> <strong>and</strong> <strong>Studies</strong> <strong>of</strong> <strong>Correlation</strong><br />
with <strong>Vibration</strong> Sensors” Sensors<br />
D. A. Howe, J. L. Lanfranchi, Lanfranchi,<br />
N. Ashby, L. Cuts<strong>in</strong>ger, Cuts<strong>in</strong>ger,<br />
C. W.<br />
Nelson, A. Hati<br />
National Institute <strong>of</strong> St<strong>and</strong>ards & Technology (NIST), Boulder, CO, CO,<br />
USA
Description <strong>of</strong> vibration equipment <strong>and</strong> <strong>PM</strong> noise measurement.<br />
Primary Measurement Effects due to Motion <strong>of</strong> an Ideal Device Under Test<br />
(DUT):<br />
Path fluctuation<br />
Uniform motion<br />
OUTLINE OF TALK<br />
Relativity under vibration<br />
Cable multipath <strong>in</strong>stability <strong>and</strong> impedance mismatch<br />
Calculation <strong>of</strong> Γ = 1/2 per g<br />
Measurements <strong>of</strong> <strong>PM</strong> noise <strong>of</strong> a low-vibe-sensitivity Qz under vibration:<br />
S<strong>in</strong>e-wave vibration, 20 – 2000 Hz<br />
R<strong>and</strong>om-noise vibration, 10 – 200 Hz<br />
Scatter plots <strong>of</strong> phase-fluctuations vs. acceleration<br />
Strategy for construct<strong>in</strong>g ultra-low noise microwave reference oscillator with<br />
reduced acceleration sensitivity.
<strong>Vibration</strong> phase noise test bed<br />
<strong>Vibration</strong> controller <strong>and</strong> amplifier, actuator, adaptor, <strong>and</strong><br />
power converter
<strong>Vibration</strong> phase noise test bed<br />
3-axis mount<strong>in</strong>g <strong>of</strong> low-vibrationsensitivity<br />
quartz oscillator (~5x10-11/g).
Path Fluctuations<br />
Δν<br />
rms 10<br />
= Gi = Gi7.3x10 ν π i<br />
0<br />
8<br />
2 10 (100)<br />
−11<br />
7.3x10 Γ= , @ fvibe =<br />
100Hz<br />
g<br />
rms<br />
−11
Uniform Motion<br />
The detected frequency will be identical to the<br />
proper frequency <strong>of</strong> the oscillator <strong>and</strong>, to first<br />
order <strong>in</strong> the velocity, this does not depend on<br />
the velocity.
Acceleration Effect<br />
−17<br />
2.4x10 / g<br />
Δν<br />
ν<br />
DUT<br />
0<br />
=−<br />
@ f =<br />
100 Hz,<br />
vibe<br />
1<br />
2<br />
v<br />
c<br />
2<br />
2
ρ<br />
α =<br />
Signal Multipath Effect from Impedance<br />
Mismatch, Dielectric Distortion, etc.<br />
Vt () = Acos[ ω t−α]<br />
( C / β )cos( pt / 2)<br />
−1<br />
0 0<br />
tan<br />
1 − ( C0 / β )s<strong>in</strong>( pt0<br />
/2)<br />
0<br />
1.46x10 Γ=<br />
g<br />
rms<br />
−10<br />
<strong>in</strong> the worst case.<br />
C0 is an <strong>in</strong>f<strong>in</strong>ite series <strong>in</strong>volv<strong>in</strong>g the coefficient <strong>of</strong><br />
reflection ρ. The quantity α represents a lagg<strong>in</strong>g<br />
phase error that depends upon the modulation<br />
<strong>in</strong>dex β . In the worst case, a reflected signal <strong>of</strong><br />
equal strength makes ρ equal to one-half the<br />
phase lag <strong>of</strong> the reflected signal.<br />
,
<strong>Vibration</strong> phase noise test bed<br />
Oscillator Under <strong>Vibration</strong><br />
An oscillator that is vibrated generates carrier-frequency<br />
sideb<strong>and</strong>s at v 0 +f v where f v is the vibration frequency.<br />
Usually f v is <strong>in</strong> the range 0 < f v < 5 kHz.
S<strong>in</strong>e <strong>Vibration</strong>-Induced Phase <strong>Noise</strong><br />
S<strong>in</strong>usoidal vibration produces spectral l<strong>in</strong>es at ±fv from the<br />
carrier, where fv is the vibration frequency.<br />
'<br />
L<br />
( ) ⎟ 0<br />
f = 20 log ⎜<br />
e.g., if Γ = 1 x 10 -9 /g <strong>and</strong> f 0 = 10 MHz, then even if the<br />
oscillator is completely noise free at rest, the phase “noise”<br />
i.e., the spectral l<strong>in</strong>es, due solely to a s<strong>in</strong>e vibration level <strong>of</strong><br />
1g will be;<br />
Vibr. freq., f v, <strong>in</strong> Hz<br />
1<br />
10<br />
100<br />
1,000<br />
10,000<br />
v<br />
4-70<br />
⎛ Γ • Af<br />
⎜<br />
⎝ 2fv<br />
⎞<br />
⎠<br />
L’(fv), <strong>in</strong> dBc<br />
-46<br />
-66<br />
-86<br />
-106<br />
-126
R<strong>and</strong>om <strong>Vibration</strong>-Induced Phase <strong>Noise</strong><br />
R<strong>and</strong>om vibration’s contribution to phase noise is given by:<br />
() [ ( )( ) ] 2<br />
1<br />
⎛ Γ • Af<br />
⎞ 0 L f = 20 log<br />
⎜ , where lAl<br />
= 2 PSD<br />
2f<br />
⎟<br />
⎝ ⎠<br />
e.g., if Γ = 1 x 10 -9 /g <strong>and</strong> f 0 = 10 MHz, then even if the<br />
oscillator is completely noise free at rest, the phase “noise”<br />
i.e., the spectral l<strong>in</strong>es, due solely to a vibration<br />
PSD = 0.1 g 2 /Hz will be:<br />
Offset freq., f, <strong>in</strong> Hz<br />
1<br />
10<br />
100<br />
1,000<br />
10,000<br />
R. L. Filler, "The Acceleration Sensitivity <strong>of</strong> Quartz Crystal <strong>Oscillators</strong>: A<br />
Review," IEEE Transactions on Ultrasonics, Ferroelectrics, <strong>and</strong> Frequency<br />
Control, Vol. 35, No. 3, pp. 297-305, May 1988.<br />
L’(f), <strong>in</strong> dBc/Hz<br />
-53<br />
-73<br />
-93<br />
-113<br />
-133
0000
Compensation Off
Compensation On
Acceleration<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
Phase <strong>Noise</strong> <strong>and</strong> Acceleration vs. Frequency<br />
X Axis<br />
1 10 100 1000<br />
-180<br />
10000<br />
Frequency (Hz)<br />
Acceleration<br />
Phase<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
Phase <strong>Noise</strong>
X Axis
Compensation Off
Compensation On
Acceleration<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
Phase <strong>Noise</strong> <strong>and</strong> Acceleration vs. Frequency<br />
Y Axis<br />
1 10 100 1000<br />
-180<br />
10000<br />
Frequency (Hz)<br />
Acceleration<br />
Phase<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
Phase <strong>Noise</strong>
Y Axis
Compensation Off
Compensation On
Acceleration<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
Phase <strong>Noise</strong> <strong>and</strong> Acceleration vs. Frequency<br />
Z Axis<br />
Acceleration<br />
Phase <strong>Noise</strong><br />
1 10 100 1000 10000<br />
Frequency (Hz)<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
-180<br />
Phase <strong>Noise</strong>
Z Axis
Strategy for construct<strong>in</strong>g ultra-low noise microwave<br />
reference oscillator with reduced acceleration sensitivity.<br />
While the oscillator is under vibration, an estimate <strong>of</strong> a complexconjugate<br />
(same amplitude, opposite phase) signal will be<br />
generated from accelerometer signals <strong>and</strong> used to modulate the<br />
oscillator’s output phase <strong>in</strong> such a way as to suppress or cancel the<br />
<strong><strong>in</strong>duced</strong> sideb<strong>and</strong>s. One-axis cancellation is shown for simplicity.
Conclusion<br />
State-<strong>of</strong>-art phase noise measurements plus vibration test facility.<br />
“Acceleration, <strong>Vibration</strong> <strong>and</strong> Shock Effects-IEEE St<strong>and</strong>ards Project P1193” by Vig, Audo<strong>in</strong>, Cutler,<br />
Driscoll, EerNisse, Filler, Garvey, Riley, Smythe <strong>and</strong> Wegle<strong>in</strong>, Proc. Of the 46 rd Ann.<br />
Symp. On Frequency Control, pp. 763-781, 1992.<br />
“The Acceleration Sensitivity <strong>of</strong> Quartz Crystal <strong>Oscillators</strong>: A Review,” by Filler, IEEE<br />
Transactions on Ultrasonics, Ferroelectrics <strong>and</strong> Frequency Control, pp. 297-305, 1988.<br />
“A Measurement Technique for Determ<strong>in</strong>ation <strong>of</strong> Frequency vs. Acceleration Characteristics <strong>of</strong><br />
Quartz Crystal Units,” by Healy, Hahn, <strong>and</strong> Powell, Proc. Of the 37 th Ann. Symp. On Frequency<br />
Control, pp.284-289, 1983, AD-A136673.<br />
“Improved <strong>Vibration</strong> Performance <strong>in</strong> Passive Atomic Frequency St<strong>and</strong>ards by Servo-Loop<br />
Control,” by Kwon <strong>and</strong> Hahn, Proc. Of the 37 th Ann. Symp. On Frequency Control, pp.28-20,<br />
1983, AD-A136673.<br />
“Mechanical <strong>and</strong> Acoustic Effects <strong>in</strong> Low Phase <strong>Noise</strong> Piezoelectric <strong>Oscillators</strong>,” by Renoult,<br />
Girardet <strong>and</strong> Bidart, Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 439-446, 1989, IEEE<br />
Catalog No. 89CH2690-6.<br />
“The Physics <strong>of</strong> the Environmental Sensitivity <strong>of</strong> Rubidium Gas Cell Atomic Frequency<br />
St<strong>and</strong>ards,” by Riley, IEEE Transactions on Ultrasonics, Ferroelectrics <strong>and</strong> Frequency Control,<br />
vol. 39, pp. 232-240, 1992.<br />
<strong>Vibration</strong> Analysis for Electronic Equipment, by Ste<strong>in</strong>berg, John Wiley & Sons, 1988.<br />
“Technique for Measur<strong>in</strong>g the Acceleration Sensitivity <strong>of</strong> SC-cut Quartz Resonators,” by Watts,<br />
EerNisse, Ward, <strong>and</strong> Wigg<strong>in</strong>s, Proc. Of the 42 rd Ann.<br />
Symp. On Frequency Control, pp. 442-446, 1988, AD-A217275.<br />
“The <strong>Vibration</strong>-Induced Phase <strong>Noise</strong> <strong>of</strong> a Visco-Elastically Supported Crystal Resonator,” by<br />
Wegle<strong>in</strong>, Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 433-438, 1989. IEEE Catalog<br />
No. 89CH2690-6.
The End<br />
D. A. Howe, J. L. Lanfranchi, Lanfranchi,<br />
N. Ashby, L. Cuts<strong>in</strong>ger, Cuts<strong>in</strong>ger,<br />
C. W.<br />
Nelson, A. Hati<br />
National Institute <strong>of</strong> St<strong>and</strong>ards & Technology (NIST), Boulder, CO, CO,<br />
USA
Conclusion<br />
State-<strong>of</strong>-art phase noise measurements plus vibration test facility.<br />
J.R. Vig, C. Audo<strong>in</strong>, L.S. Cutler, M.M. Driscoll, E.P. EerNisse, R.L. Filler, R.M. Garvey, W.L. Riley,<br />
R.C. Smythe, R.D. Wegle<strong>in</strong>, “Acceleration, <strong>Vibration</strong> <strong>and</strong> Shock Effects-IEEE St<strong>and</strong>ards Project<br />
P1193” Proc. Of the 46 rd Ann.<br />
Symp. On Frequency Control, pp. 763-781, 1992<br />
R.L. Filler, “The Acceleration Sensitivity <strong>of</strong> Quartz Crystal <strong>Oscillators</strong>: A Review,” IEEE<br />
Transactions on Ultrasonics, Ferroelectrics <strong>and</strong> Frequency Control, pp. 297-305, 1988.<br />
D.J. Healy, H. Hahn, S. Powell, “A Measurement Technique for Determ<strong>in</strong>ation <strong>of</strong> Frequency vs.<br />
Acceleration Characteristics <strong>of</strong> Quartz Crystal Units,” Proc. Of the 37 th Ann. Symp. On Frequency<br />
Control, pp.284-289, 1983, AD-A136673.<br />
T.M. Kwon, T. Hahn, “Improved <strong>Vibration</strong> Performance <strong>in</strong> Passive Atomic Frequency St<strong>and</strong>ards<br />
by Servo-Loop Control,” Proc. Of the 37 th Ann. Symp. On Frequency Control, pp.28-20, 1983, AD-<br />
A136673.<br />
P. Renoult, E. Girardet, L. Bidart, “Mechanical <strong>and</strong> Acoustic Effects <strong>in</strong> Low Phase <strong>Noise</strong><br />
Piezoelectric <strong>Oscillators</strong>,” Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 439-446, 1989,<br />
IEEE Catalog No. 89CH2690-6.<br />
W. Riley,“ The Physics <strong>of</strong> the Environmental Sensitivity <strong>of</strong> Rubidium Gas Cell Atomic Frequency<br />
St<strong>and</strong>ards,” IEEE Transactions on Ultrasonics, Ferroelectrics <strong>and</strong> Frequency Control, vol. 39, pp.<br />
232-240, 1992.<br />
D. Ste<strong>in</strong>berg, <strong>Vibration</strong> Analysis for Electronic Equipment, John Wiley & Sons, 1988.<br />
M.H. Watts, E.P. EerNisse, R.W. Ward, R.B. Wigg<strong>in</strong>s, “Technique for Measur<strong>in</strong>g the Acceleration<br />
Sensitivity <strong>of</strong> SC-cut Quartz Resonators,” Proc. Of the 42 rd Ann.<br />
Symp. On Frequency Control, pp. 442-446, 1988, AD-A217275.<br />
R.D. Wegle<strong>in</strong>, “The <strong>Vibration</strong>-Induced Phase <strong>Noise</strong> <strong>of</strong> a Visco-Elastically Supported Crystal<br />
Resonator,” Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 433-438, 1989. IEEE<br />
Catalog No. 89CH2690-6.
0000
Low-noise Oscillator w/ Active <strong>Vibration</strong><br />
L(f)<br />
-50<br />
-60<br />
-70<br />
-80<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
<strong>Vibration</strong>-Induced Phase <strong>Noise</strong><br />
Nom<strong>in</strong>ally 5 x 10^(-10)/g <strong>and</strong> f0 = 100 MHz<br />
1 10 100 1000 10000 100000 1000000 10000000<br />
Frequency
Low-noise Oscillator w/<strong>Vibration</strong><br />
L(f) dBc/Hz<br />
0<br />
-10<br />
-20<br />
-30<br />
-40<br />
-50<br />
-60<br />
-70<br />
-80<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
-180<br />
-190<br />
aPROPOS Performance Goals at 10 GHz<br />
Nom<strong>in</strong>al 1g r<strong>and</strong>om vibration with uniform PSD, 0.05 g2/Hz<br />
1 10 100 1000 10000 100000 1000000 10000000<br />
Frequency (Hz)<br />
NIST 100 MHz mult. to 10 GHz w/<br />
<strong>Vibration</strong><br />
Phase I w/ <strong>Vibration</strong>
<strong>Vibration</strong>-<strong><strong>in</strong>duced</strong> <strong>PM</strong> <strong>Noise</strong> <strong>in</strong><br />
<strong>Oscillators</strong> <strong>and</strong> <strong>Studies</strong> <strong>of</strong> <strong>Correlation</strong><br />
with <strong>Vibration</strong> Sensors<br />
D. A. Howe, J. L. Lanfranchi, N. Ashby, L. Cuts<strong>in</strong>ger, C. W.<br />
Nelson, A. Hati<br />
National Institute <strong>of</strong> St<strong>and</strong>ards & Technology (NIST), Boulder, CO, USA
Low-noise Oscillator w/<strong>Vibration</strong><br />
Milestones, accomplishments, experiences:<br />
Motivation for DSP us<strong>in</strong>g Wavelet Decomposition<br />
The functions from accelerometers are time-doma<strong>in</strong>, asymmetric signals that conta<strong>in</strong><br />
phase <strong>in</strong>formation <strong>in</strong> a distribution <strong>of</strong> frequencies that do not necessarily have harmonic<br />
relationships.<br />
Swept-s<strong>in</strong>e tests <strong>of</strong> g-sensitivity are <strong>in</strong>formative, but not completely satisfactory,<br />
because harmonics <strong>of</strong> f_v have phases that need to be suppressed. The g-sensitivity<br />
vs. N x f_v must <strong>in</strong>clude the phase <strong>of</strong> harmonics, so a superior test is swept-triangle at<br />
low f_v to account for harmonic phase-match<strong>in</strong>g.<br />
Ideally, r<strong>and</strong>om noise should be used to characterize all harmonic <strong>and</strong> anharmonic<br />
phases <strong>in</strong> the suppression.<br />
We must resort to adaptive transfer functions <strong>in</strong> the feed-forward suppression (FFS).
L(f) dBc/Hz<br />
0<br />
-10<br />
-20<br />
-30<br />
-40<br />
-50<br />
-60<br />
-70<br />
-80<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
-180<br />
-190<br />
Phase II Goal for Low-noise<br />
Oscillator w/<strong>Vibration</strong><br />
aPROPOS Performance Goals at 10 GHz<br />
Nom<strong>in</strong>al 1g r<strong>and</strong>om vibration with uniform PSD, 0.05 g2/Hz<br />
1 10 100 1000 10000 100000 1000000 10000000<br />
Frequency (Hz)<br />
Phase II NIST Active w/ <strong>Vibration</strong>, Goal<br />
Phase I<br />
Phase II & III<br />
Phase I w/ <strong>Vibration</strong><br />
Phase II w/ <strong>Vibration</strong><br />
Phase III w/ <strong>Vibration</strong>
L(f) dBc/Hz<br />
0<br />
-10<br />
-20<br />
-30<br />
-40<br />
-50<br />
-60<br />
-70<br />
-80<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
-180<br />
-190<br />
Phase II Goal for Low-noise<br />
Oscillator w/<strong>Vibration</strong><br />
aPROPOS Performance Goals at 10 GHz<br />
Nom<strong>in</strong>al 1g r<strong>and</strong>om vibration with uniform PSD, 0.05 g2/Hz<br />
1 10 100 1000 10000 100000 1000000 10000000<br />
Frequency (Hz)<br />
Phase II w/ <strong>Vibration</strong><br />
Phase II NIST Active w/ <strong>Vibration</strong>, Goal<br />
Phase II & III<br />
Phase I w/ <strong>Vibration</strong><br />
NIST 100 MHz mult. to 10 GHz w/<br />
<strong>Vibration</strong><br />
SLCO 10 GHz<br />
Phase I<br />
NIST Power CSO<br />
Phase III w/ <strong>Vibration</strong>
Phase noise under vibration is for Γ = 1 x 10-9 R<strong>and</strong>om <strong>Vibration</strong>-Induced Phase <strong>Noise</strong><br />
per g <strong>and</strong> f = 10 MHz<br />
L (f) (dBc)<br />
-70<br />
-80<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
5<br />
L(f) under the r<strong>and</strong>om vibration shown<br />
L(f) without vibration<br />
45 dB<br />
300<br />
4-72<br />
1K 2K<br />
PSD (g 2 /Hz)<br />
.04<br />
.07<br />
5 300 1K 2K<br />
Frequency (Hz)<br />
Typical aircraft<br />
r<strong>and</strong>om vibration<br />
envelope
While the oscillator is under vibration, an estimate <strong>of</strong> a<br />
complex-conjugate (same amplitude, opposite phase)<br />
signal will be generated from accelerometer signals <strong>and</strong><br />
used to modulate the oscillator’s output phase <strong>in</strong> such a<br />
way as to suppress or cancel the <strong><strong>in</strong>duced</strong> sideb<strong>and</strong>s.<br />
One-axis cancellation is shown for simplicity.
Acceleration<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
Phase <strong>Noise</strong> <strong>and</strong> Acceleration vs. Frequency<br />
Y Axis<br />
-20<br />
-180<br />
1 10 100 1000 10000<br />
Frequency (Hz)<br />
Acceleration<br />
Phase<br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
Phase <strong>Noise</strong><br />
Acceleration<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
Phase <strong>Noise</strong> <strong>and</strong> Acceleration vs. Frequency<br />
Z Axis<br />
-20<br />
-180<br />
1 10 100 1000 10000<br />
Frequency (Hz)<br />
Acceleration<br />
Phase <strong>Noise</strong><br />
-90<br />
-100<br />
-110<br />
-120<br />
-130<br />
-140<br />
-150<br />
-160<br />
-170<br />
Phase <strong>Noise</strong>
Qz Osc w/ <strong>Vibration</strong> Suppression: Phase Dev. vs. Z-accel.
Qz Osc w/ <strong>Vibration</strong> Suppression: Phase Dev. vs. Y-accel.