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

Description of vibration equipment and PM noise measurement.
Primary Measurement Effects due to Motion of an Ideal Device Under Test
(DUT):
Path fluctuation
Uniform motion
OUTLINE OF TALK
Relativity under vibration
Cable multipath instability and impedance mismatch
Calculation of Γ = 1/2 per g
Measurements of PM noise of a low-vibe-sensitivity Qz under vibration:
Sine-wave vibration, 20 – 2000 Hz
Random-noise vibration, 10 – 200 Hz
Scatter plots of phase-fluctuations vs. acceleration
Strategy for constructing ultra-low noise microwave reference oscillator with
reduced acceleration sensitivity.

Vibration phase noise test bed
Vibration controller and amplifier, actuator, adaptor, and
power converter

Vibration phase noise test bed
3-axis mounting of low-vibrationsensitivity
quartz oscillator (~5x10-11/g).

Path Fluctuations
Δν
rms 10
= Gi = Gi7.3x10 ν π i
0
8
2 10 (100)
−11
7.3x10 Γ= , @ fvibe =
100Hz
g
rms
−11

Uniform Motion
The detected frequency will be identical to the
proper frequency of the oscillator and, to first
order in the velocity, this does not depend on
the velocity.

Acceleration Effect
−17
2.4x10 / g
Δν
ν
DUT
0
=−
@ f =
100 Hz,
vibe
1
2
v
c
2
2

ρ
α =
Signal Multipath Effect from Impedance
Mismatch, Dielectric Distortion, etc.
Vt () = Acos[ ω t−α]
( C / β )cos( pt / 2)
−1
0 0
tan
1 − ( C0 / β )sin( pt0
/2)
0
1.46x10 Γ=
g
rms
−10
in the worst case.
C0 is an infinite series involving the coefficient of
reflection ρ. The quantity α represents a lagging
phase error that depends upon the modulation
index β . In the worst case, a reflected signal of
equal strength makes ρ equal to one-half the
phase lag of the reflected signal.
,

Vibration phase noise test bed
Oscillator Under Vibration
An oscillator that is vibrated generates carrier-frequency
sidebands at v 0 +f v where f v is the vibration frequency.
Usually f v is in the range 0 < f v < 5 kHz.

Sine Vibration-Induced Phase Noise
Sinusoidal vibration produces spectral lines at ±fv from the
carrier, where fv is the vibration frequency.
'
L
( ) ⎟ 0
f = 20 log ⎜
e.g., if Γ = 1 x 10 -9 /g and f 0 = 10 MHz, then even if the
oscillator is completely noise free at rest, the phase “noise”
i.e., the spectral lines, due solely to a sine vibration level of
1g will be;
Vibr. freq., f v, in Hz
1
10
100
1,000
10,000
v
4-70
⎛ Γ • Af
⎜
⎝ 2fv
⎞
⎠
L’(fv), in dBc
-46
-66
-86
-106
-126

Random Vibration-Induced Phase Noise
Random vibration’s contribution to phase noise is given by:
() [ ( )( ) ] 2
1
⎛ Γ • Af
⎞ 0 L f = 20 log
⎜ , where lAl
= 2 PSD
2f
⎟
⎝ ⎠
e.g., if Γ = 1 x 10 -9 /g and f 0 = 10 MHz, then even if the
oscillator is completely noise free at rest, the phase “noise”
i.e., the spectral lines, due solely to a vibration
PSD = 0.1 g 2 /Hz will be:
Offset freq., f, in Hz
1
10
100
1,000
10,000
R. L. Filler, "The Acceleration Sensitivity of Quartz Crystal Oscillators: A
Review," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency
Control, Vol. 35, No. 3, pp. 297-305, May 1988.
L’(f), in dBc/Hz
-53
-73
-93
-113
-133

0000

Compensation Off

Compensation On

Acceleration
70
60
50
40
30
20
10
0
-10
-20
Phase Noise and Acceleration vs. Frequency
X Axis
1 10 100 1000
-180
10000
Frequency (Hz)
Acceleration
Phase
-90
-100
-110
-120
-130
-140
-150
-160
-170
Phase Noise

X Axis

Compensation Off

Compensation On

Acceleration
70
60
50
40
30
20
10
0
-10
-20
Phase Noise and Acceleration vs. Frequency
Y Axis
1 10 100 1000
-180
10000
Frequency (Hz)
Acceleration
Phase
-90
-100
-110
-120
-130
-140
-150
-160
-170
Phase Noise

Y Axis

Compensation Off

Compensation On

Acceleration
70
60
50
40
30
20
10
0
-10
-20
Phase Noise and Acceleration vs. Frequency
Z Axis
Acceleration
Phase Noise
1 10 100 1000 10000
Frequency (Hz)
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
Phase Noise

Z Axis

Strategy for constructing ultra-low noise microwave
reference oscillator with reduced acceleration sensitivity.
While the oscillator is under vibration, an estimate of a complexconjugate
(same amplitude, opposite phase) signal will be
generated from accelerometer signals and used to modulate the
oscillator’s output phase in such a way as to suppress or cancel the
induced sidebands. One-axis cancellation is shown for simplicity.

Conclusion
State-of-art phase noise measurements plus vibration test facility.
“Acceleration, Vibration and Shock Effects-IEEE Standards Project P1193” by Vig, Audoin, Cutler,
Driscoll, EerNisse, Filler, Garvey, Riley, Smythe and Weglein, Proc. Of the 46 rd Ann.
Symp. On Frequency Control, pp. 763-781, 1992.
“The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review,” by Filler, IEEE
Transactions on Ultrasonics, Ferroelectrics and Frequency Control, pp. 297-305, 1988.
“A Measurement Technique for Determination of Frequency vs. Acceleration Characteristics of
Quartz Crystal Units,” by Healy, Hahn, and Powell, Proc. Of the 37 th Ann. Symp. On Frequency
Control, pp.284-289, 1983, AD-A136673.
“Improved Vibration Performance in Passive Atomic Frequency Standards by Servo-Loop
Control,” by Kwon and Hahn, Proc. Of the 37 th Ann. Symp. On Frequency Control, pp.28-20,
1983, AD-A136673.
“Mechanical and Acoustic Effects in Low Phase Noise Piezoelectric Oscillators,” by Renoult,
Girardet and Bidart, Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 439-446, 1989, IEEE
Catalog No. 89CH2690-6.
“The Physics of the Environmental Sensitivity of Rubidium Gas Cell Atomic Frequency
Standards,” by Riley, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,
vol. 39, pp. 232-240, 1992.
Vibration Analysis for Electronic Equipment, by Steinberg, John Wiley & Sons, 1988.
“Technique for Measuring the Acceleration Sensitivity of SC-cut Quartz Resonators,” by Watts,
EerNisse, Ward, and Wiggins, Proc. Of the 42 rd Ann.
Symp. On Frequency Control, pp. 442-446, 1988, AD-A217275.
“The Vibration-Induced Phase Noise of a Visco-Elastically Supported Crystal Resonator,” by
Weglein, Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 433-438, 1989. IEEE Catalog
No. 89CH2690-6.

The End
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

Conclusion
State-of-art phase noise measurements plus vibration test facility.
J.R. Vig, C. Audoin, L.S. Cutler, M.M. Driscoll, E.P. EerNisse, R.L. Filler, R.M. Garvey, W.L. Riley,
R.C. Smythe, R.D. Weglein, “Acceleration, Vibration and Shock Effects-IEEE Standards Project
P1193” Proc. Of the 46 rd Ann.
Symp. On Frequency Control, pp. 763-781, 1992
R.L. Filler, “The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review,” IEEE
Transactions on Ultrasonics, Ferroelectrics and Frequency Control, pp. 297-305, 1988.
D.J. Healy, H. Hahn, S. Powell, “A Measurement Technique for Determination of Frequency vs.
Acceleration Characteristics of Quartz Crystal Units,” Proc. Of the 37 th Ann. Symp. On Frequency
Control, pp.284-289, 1983, AD-A136673.
T.M. Kwon, T. Hahn, “Improved Vibration Performance in Passive Atomic Frequency Standards
by Servo-Loop Control,” Proc. Of the 37 th Ann. Symp. On Frequency Control, pp.28-20, 1983, AD-
A136673.
P. Renoult, E. Girardet, L. Bidart, “Mechanical and Acoustic Effects in Low Phase Noise
Piezoelectric Oscillators,” Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 439-446, 1989,
IEEE Catalog No. 89CH2690-6.
W. Riley,“ The Physics of the Environmental Sensitivity of Rubidium Gas Cell Atomic Frequency
Standards,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 39, pp.
232-240, 1992.
D. Steinberg, Vibration Analysis for Electronic Equipment, John Wiley & Sons, 1988.
M.H. Watts, E.P. EerNisse, R.W. Ward, R.B. Wiggins, “Technique for Measuring the Acceleration
Sensitivity of SC-cut Quartz Resonators,” Proc. Of the 42 rd Ann.
Symp. On Frequency Control, pp. 442-446, 1988, AD-A217275.
R.D. Weglein, “The Vibration-Induced Phase Noise of a Visco-Elastically Supported Crystal
Resonator,” Proc. Of the 43 rd Ann. Symp. On Frequency Control, pp. 433-438, 1989. IEEE
Catalog No. 89CH2690-6.

0000

Low-noise Oscillator w/ Active Vibration
L(f)
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150
Vibration-Induced Phase Noise
Nominally 5 x 10^(-10)/g and f0 = 100 MHz
1 10 100 1000 10000 100000 1000000 10000000
Frequency

Low-noise Oscillator w/Vibration
L(f) dBc/Hz
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
-190
aPROPOS Performance Goals at 10 GHz
Nominal 1g random vibration with uniform PSD, 0.05 g2/Hz
1 10 100 1000 10000 100000 1000000 10000000
Frequency (Hz)
NIST 100 MHz mult. to 10 GHz w/
Vibration
Phase I w/ Vibration

Vibration-induced PM Noise in
Oscillators and Studies of Correlation
with Vibration Sensors
D. A. Howe, J. L. Lanfranchi, N. Ashby, L. Cutsinger, C. W.
Nelson, A. Hati
National Institute of Standards & Technology (NIST), Boulder, CO, USA

Low-noise Oscillator w/Vibration
Milestones, accomplishments, experiences:
Motivation for DSP using Wavelet Decomposition
The functions from accelerometers are time-domain, asymmetric signals that contain
phase information in a distribution of frequencies that do not necessarily have harmonic
relationships.
Swept-sine tests of g-sensitivity are informative, but not completely satisfactory,
because harmonics of f_v have phases that need to be suppressed. The g-sensitivity
vs. N x f_v must include the phase of harmonics, so a superior test is swept-triangle at
low f_v to account for harmonic phase-matching.
Ideally, random noise should be used to characterize all harmonic and anharmonic
phases in the suppression.
We must resort to adaptive transfer functions in the feed-forward suppression (FFS).

L(f) dBc/Hz
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
-190
Phase II Goal for Low-noise
Oscillator w/Vibration
aPROPOS Performance Goals at 10 GHz
Nominal 1g random vibration with uniform PSD, 0.05 g2/Hz
1 10 100 1000 10000 100000 1000000 10000000
Frequency (Hz)
Phase II NIST Active w/ Vibration, Goal
Phase I
Phase II & III
Phase I w/ Vibration
Phase II w/ Vibration
Phase III w/ Vibration

L(f) dBc/Hz
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
-190
Phase II Goal for Low-noise
Oscillator w/Vibration
aPROPOS Performance Goals at 10 GHz
Nominal 1g random vibration with uniform PSD, 0.05 g2/Hz
1 10 100 1000 10000 100000 1000000 10000000
Frequency (Hz)
Phase II w/ Vibration
Phase II NIST Active w/ Vibration, Goal
Phase II & III
Phase I w/ Vibration
NIST 100 MHz mult. to 10 GHz w/
Vibration
SLCO 10 GHz
Phase I
NIST Power CSO
Phase III w/ Vibration

Phase noise under vibration is for Γ = 1 x 10-9 Random Vibration-Induced Phase Noise
per g and f = 10 MHz
L (f) (dBc)
-70
-80
-90
-100
-110
-120
-130
-140
-150
-160
5
L(f) under the random vibration shown
L(f) without vibration
45 dB
300
4-72
1K 2K
PSD (g 2 /Hz)
.04
.07
5 300 1K 2K
Frequency (Hz)
Typical aircraft
random vibration
envelope

While the oscillator is under vibration, an estimate of a
complex-conjugate (same amplitude, opposite phase)
signal will be generated from accelerometer signals and
used to modulate the oscillator’s output phase in such a
way as to suppress or cancel the induced sidebands.
One-axis cancellation is shown for simplicity.

Acceleration
70
60
50
40
30
20
10
0
-10
Phase Noise and Acceleration vs. Frequency
Y Axis
-20
-180
1 10 100 1000 10000
Frequency (Hz)
Acceleration
Phase
-90
-100
-110
-120
-130
-140
-150
-160
-170
Phase Noise
Acceleration
70
60
50
40
30
20
10
0
-10
Phase Noise and Acceleration vs. Frequency
Z Axis
-20
-180
1 10 100 1000 10000
Frequency (Hz)
Acceleration
Phase Noise
-90
-100
-110
-120
-130
-140
-150
-160
-170
Phase Noise

Qz Osc w/ Vibration Suppression: Phase Dev. vs. Z-accel.

Qz Osc w/ Vibration Suppression: Phase Dev. vs. Y-accel.