Phase Noise under Vibration
Theory and Test Results
Bernd Neubig
AXTAL GmbH & Co. KG
Wasemweg 5
D-74821 Mosbach
www.axtal.com
November 2009
1
Content
Theoretical Background
Sensitivity to forces and acceleration
Sensitivity to vibrations
Experimental Results
AXIOM75-16-60 MHz with AT-cut (HC-43/U)
AXIOM75-16A-60 MHz with SC-cut (HC-35/U)
AXIOM35-14A-100 MHz with SC-cut (HC-43/U)
100 MHz with SC-cut (HC-43/U) other supplier
November 2009
2
Content
Theoretical Background
Sensitivity to forces and acceleration
Sensitivity to vibrations
Experimental Results
AXIOM75-16-60 MHz with AT-cut (HC-43/U)
AXIOM75-16A-60 MHz with SC-cut (HC-35/U)
AXIOM35-14A-100 MHz with SC-cut (HC-43/U)
100 MHz with SC-cut (HC-43/U) other supplier
November 2009
3
Piezo-electrial Effect
Longitudinal PE
Mechanical force (pressure) creates
electrical charge (voltage)
and vice versa
Transversal PE
November 2009
4
Most popular cuts
SC cut
AT cut
November 2009
AT
AT cut
X cut
Y cut
5
Influence of lateral forces
Z’
F
Ψ
X’
F
Example:
Resonator 5 MHz 3rd overtone, 14 mm diameter
⎛ ∆f ⎞
⎜ ⎟ =
⎝ f ⎠Max
November 2009
{
3 ppm/N for AT-cut resonator
1.7 ppm/N for SC-cut resonator
6
Influence of bending forces
fo = 10MHz
AT-cut resonator
•
20
•
• •
• •
•
•
•
•
•
• •
•
•
•
10
•
•
•
•
•
•
••
•
•
•
5g
•
+10
•
•
• •
•
Frequency Change (Hz)
Frequency Change (Hz)
30
fo = 10MHz
SC-cut resonator
•
•
• ••
••
•
•
•
•
•
•
•
•
•
•
••• • 360
• 60 120• •180 240 • •300
• •
•
••
•
Azimuth angle ψ (degrees)
•
•
••
-10
0
60
120
180
240
300
Azimuth angle ψ (degrees)
Frequency change for symmetrical
bending, AT-cut crystal.
November 2009
360
Frequency change for symmetrical
bending, SC-cut crystal.
7
Frequency change with acceleration
∆f
f
Z’
A5
A4
A1
O
A3
X’
Supports
A6
A2
Y’
Crystal
plate
A2
A4
A3
G
A5
A6
A1
Strains due to acceleration cause frequency changes.
Under vibration, the time varying strains cause
time dependent frequency changes, i.e. frequency modulation
November 2009
8
Acceleration Sensitivity Vector
Axis 3
γ3
γ1
Axis 1
November 2009
Γ = γ1ˆi + γ2ˆj + γ3kˆ
Γ
Γ = γ12 + γ22 + γ32
γ2
Axis 2
9
Sine Vibration Induced Sidebands
-10
Example:
Vibration 10 G @ 100 Hz
Acceleration sensitivity vector
|Γ| = 1.4 x 10-9 / G
L(f)
-20
-30
-40
-50
-60
-70
f
250
200
150
100
50
-90
100
0
-50
-100
-150
-200
-250
-80
Sinusoidal vibration with vibration frequency fv
produces spectral lines at ± fv from the carrier
November 2009
10
Frequency Multiplication
L(f)0
-10
-20
-30
-40
10X
-50
-60
-70
1X
-80
f
250
200
150
100
50
-100
0
-50
-100
-150
-200
-250
-90
Each frequency multiplication by 10 increases the sidebands by 20 dB
∆a = 20 ⋅ log( N )
November 2009
11
Sine Vibration Induced Sidebands
Sinusoidal vibration produces spectral lines at ±fv from the
carrier, where fv is the vibration frequency.
⎛ Γ • Af0 ⎞
⎟⎟
L' (fv ) = 20 log ⎜⎜
2
f
v
⎝
⎠
e.g., if |Γ| = 1 x 10-9/G and f0 = 10 MHz, then even if the
oscillator is completely noise free at rest, the spectral lines due
solely to a sine vibration level of 1G are:
Vibr. freq., fv [Hz]
1
10
100
1,000
10,000
November 2009
L’(fv) [dBc]
-46
-66
-86
-106
-126
12
Random Vibration Induced Phase Noise
Random vibration’s contribution to phase noise is given by:
⎛ Γ • Af0 ⎞
⎟⎟,
L (f ) = 20 log ⎜⎜
2
f
⎝
⎠
where lAl = [(2)(PSD )]
1
2
e.g., if |Γ| = 1 x 10-9/G and f0 = 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 of power
spectral density, PSD = 0.1 g2/Hz will be:
Offset freq. f [Hz]
1
10
100
1,000
10,000
November 2009
L’(f) [dBc/Hz]
-53
-73
-93
-113
-133
13
Random Vibration Induced Phase Noise
-70
-80
f) u
nd
er
L (f) (dBc)
-90
-100
-110
-120
L(
f)
-130
-140
-150
wi
th
ou
t
the
ran
do
m
vib
rat
ion
45 dB
vib
ra
tio
Random Vibration for a Crystal
with Vibration Sensitivity of
|Γ| = 1x10-9/G
Osc frequency f0 = 10 MHz
sh
ow
n
n
-160
5
November 2009
Vibration profile (aircraft):
PSD (g2/Hz)
L(
300
1K 2K
.07
.04
5
300
1K 2K
Frequency (Hz)
14
Vibration Sensitivity Γ [/G]
Acceleration Sensitivity with Resonances
10-8
10-9
10-10
100
200
300
400
500
1000
Vibration Frequency [Hz]
In an ideal oscillator, Γ(fv) would be constant, but real oscillators exhibit
resonances which increase the Γ in the relevant frequency band
November 2009
15
Factors determining Acceleration Sensitivity
Crystal cut
Crystal holder
Mounting structure
Crystal design
symmetrical shape of crystal blank (contour),
electrodes and mounting structure
G-Sensitivity of other components
November 2009
16
Cuts with zero TC (Thickness shear)
90o
60o
AT
30o
θ
0
-30o
-60o
November 2009
Do
rot ubly
a te
d
RT
BT
Θ ≈ 35°:
IT
SC
•Y
-90o0o
gl y d
n
i
S ate
rot
FC
10o
20o
30o
φ
AT cut: TC = 0 ppm/K at ≈ 25°C
SC cut*: TC = 0 ppm/K bei ≈ 95°C
*SC = Stress Compensated
17
f(T) for doubly rotated cuts
The inflection temperature
moves up with increasing 2nd rotation
angle Φ.
For Φ ≈ 22° (Tinv ≈ 95°C), the so-called
SC cut („Stress Compensated)
the impact of mechanical stresses on the
Resonance frequency compensate
November 2009
18
Comparison of Crystal packages
Two-point Mount Package
e.g. HC-43/U or HC-45/U
November 2009
Three- and Four-point Mount Package
e.g. HC-35/U or HC-37/U
19
Testing of Vibration Sensitivity
Test Setup
PN Test Systems:
- Phase Quadrature Method
- Cross Correlation
November 2009
20
Phase Noise Test
Phase Quadrature Method
The signal under test and a signal of same
frequency from a reference oscillator are
combined in a phase detector. The frequency of
oscillator #2 is locked to oscillator #1 by a PLL
The DC output signal of the phase detector is
proportional to the phase difference of the two
signals. All noise spectral components, which are
„faster“ than the loop filter will be measured by the
spectrum analyzer or FFT.
If the reference oscillator has very low phase
noise, the measured noise is dominated by the
noise of the oscillator under test.
Φ det = K ⋅ (Φ (t ) − Φ ref (t ) )
If both oscillators have the same noise, the noise
of one oscillator is -3 dB lower than the noise
measured with the spectrum analyzer.
Example: Aeroflex PN9000
November 2009
21
Phase Noise Test
Cross Correlation Method
© Agilent
The signal is fed into two phase detectors and both channels are mixed with an internal lownoise reference signal. Both channels are locked to the test signal through a PLL. The
noise content of the identical channels is evaluated by mathematical cross-correlation
technique. Examples: Agilent Signal Source Analyzer E5052B, Rohde & Schwarz FSUP
November 2009
22
Testing of Vibration Sensitivity
Cables and mounting
November 2009
23
Content
Theoretical Background
Sensitivity to forces and acceleration
Sensitivity to vibrations
Experimental Results
AXIOM75-16-60 MHz with AT-cut (HC-43/U)
AXIOM75-16A-60 MHz with SC-cut (HC-35/U)
AXIOM35-14A-100 MHz with SC-cut (HC-43/U)
60 MHz with SC-cut (HC-43/U) other vendor
November 2009
24
Vibration Spectrum
W1=0.01g2/Hz, W2=0.06g2/Hz
f1=500Hz, f2=1500Hz
Customer spec
November 2009
Tested profile
25
AXIOM75-16-60 MHz AT-cut (HC-43/U)
Output Spectrum
November 2009
26
AXIOM75-16-60 MHz AT-cut (HC-43/U)
Phase Noise
November 2009
27
AXIOM75-16-60 MHz AT-cut (HC-43/U)
G - Sensitivity
November 2009
28
AXIOM75-16A-60 MHz SC-cut (HC-35/U)
Test fixture
Z
Y
Orientation
November 2009
29
AXIOM75-16A-60 MHz SC-cut (HC-35/U)
Output Spectrum
November 2009
30
AXIOM75-16A-60 MHz SC-cut (HC-35/U)
Phase Noise
November 2009
31
AXIOM75-16A-60 MHz SC-cut (HC-35/U)
G - Sensitivity
November 2009
32
AXIOM35-14A-100 MHz SC-cut (HC-43/U)
Test fixture
Z
Y
Orientation
November 2009
33
AXIOM35-14A-100 MHz SC-cut (HC-43/U)
Output Spectrum
November 2009
34
AXIOM35-14A-100 MHz SC-cut (HC-43/U)
Phase noise
November 2009
35
AXIOM35-14A-100 MHz SC-cut (HC-43/U)
G-Sensitivity
November 2009
36
60 MHz SC-cut (HC-43/U) other vendor
Test fixture
Z
Y
Orientation
November 2009
37
60 MHz SC-cut (HC-43/U) other vendor
Output Spectrum
November 2009
38
60 MHz SC-cut (HC-43/U) other vendor
Phase noise
November 2009
39
60 MHz SC-cut (HC-43/U) other vendor
G-Sensitivity
November 2009
40