November 2009 1

Phase Noise under VibrationTheory and Test Results

Bernd NeubigAXTAL GmbH & Co. KGWasemweg 5D-74821 Mosbachwww.axtal.com

November 2009 2

Content

Theoretical BackgroundSensitivity to forces and accelerationSensitivity to vibrations

Experimental ResultsAXIOM75-16-60 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

Content

Theoretical BackgroundSensitivity to forces and accelerationSensitivity to vibrations

Experimental ResultsAXIOM75-16-60 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 4

Piezo-electrial Effect

Longitudinal PE

Transversal PE

Mechanical force (pressure) createselectrical charge (voltage)and vice versa

November 2009 5

SC cut

AT cut

ATAT cut

Most popular cuts

X cutY cut

November 2009 6

Example:Resonator 5 MHz 3rd overtone, 14 mm diameter

3 ppm/N for AT-cut resonator1.7 ppm/N for SC-cut resonator{=⎟⎠

⎞⎜⎝⎛

Maxf∆f

F

F

X’

Z’

Ψ

Influence of lateral forces

November 2009 7

AT-cut resonator

SC-cut resonator

fo = 10MHz fo = 10MHz

5g

Freq

uenc

y C

hang

e (H

z)

Freq

uenc

y C

hang

e (H

z)

30

20

10

0 240120 18060 300 360

240120 18060 300 360

+10

-10

Azimuth angle ψ (degrees)

Azimuth angle ψ (degrees)

Frequency change for symmetrical bending, SC-cut crystal.

Frequency change for symmetrical bending, AT-cut crystal.

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•••••

•••••••••••

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Influence of bending forces

November 2009 8

A1

A2

A3

A5

A6

A2

A6

A4

A4

A3

A5

A1

Crystalplate

Supports

ff∆

X’

Y’

Z’

GO

Frequency change with acceleration

Strains due to acceleration cause frequency changes.Under vibration, the time varying strains cause time dependent frequency changes, i.e. frequency modulation

November 2009 9

Axis 1 Axis 2

Axis 3

γ1γ2

γ3Γ

23

22

21

321 k̂ĵî

γγγ=Γ

γ+γ+γ=Γ

++

Acceleration Sensitivity Vector

November 2009 10

L(f)-10-20

-30

-40

-50

-60

-70

-80

-90-

100

-250

-200

-150

-100 -50 0 50 100

150

200

250f

Sine Vibration Induced Sidebands

Sinusoidal vibration with vibration frequency fv produces spectral lines at ± fv from the carrier

Example:Vibration 10 G @ 100 HzAcceleration sensitivity vector|Γ| = 1.4 x 10-9 / G

November 2009 11

0

-10

-20

-30

-40

-50

-60

-70

-80

-90

-100

-250

-200

-150

-100 -50 0 50 100

150

200

250f

L(f)

10X

1X

Each frequency multiplication by 10 increases the sidebands by 20 dB

Frequency Multiplication

)log(20 Na ⋅=∆

November 2009 12

Sinusoidal vibration produces spectral lines at ±fv from the carrier, where fv is the vibration frequency.

e.g., if |Γ| = 1 x 10-9/G and f0 = 10 MHz, then even if theoscillator is completely noise free at rest, the spectral lines due solely to a sine vibration level of 1G are:

Vibr. freq., fv [Hz]1

101001,000

10,000

-46-66-86

-106-126

L’(fv) [dBc]

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ •Γ=

v

0v f2

fAlog20f'L

Sine Vibration Induced Sidebands

November 2009 13

Random vibration’s contribution to phase noise is given by:

e.g., if |Γ| = 1 x 10-9/G and f0 = 10 MHz, then even if theoscillator 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

101001,000

10,000

L’(f) [dBc/Hz]-53

-73-93

-113-133

( ) ( )( )[ ] 210 PSD2lAlwhere,f2

fAlog20f =⎟⎟⎠

⎞⎜⎜⎝

⎛ •Γ=L

Random Vibration Induced Phase Noise

November 2009 14

-70-80-90

-100

-110

-120-130-140-150

-160

L (f)

(dB

c)

1K 2K3005

45 dBL(f) without vibration

L(f) under the random vibration shown

Random Vibration for a Crystalwith Vibration Sensitivity of|Γ| = 1x10-9/GOsc frequency f0 = 10 MHz

Vibration profile (aircraft):

5 300 1K 2K

PS

D (g

2 /Hz)

.04

.07

Frequency (Hz)

Random Vibration Induced Phase Noise

November 2009 15

Vibr

atio

n Se

nsiti

vity

Γ[/G

]

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

Acceleration Sensitivity with Resonances

November 2009 16

Crystal cutCrystal holderMounting structureCrystal design

symmetrical shape of crystal blank (contour),electrodes and mounting structure

G-Sensitivity of other components

Factors determining Acceleration Sensitivity

November 2009 17

Singly

rotated

Doublyrotated

Θ ≈ 35°: AT cut: TC = 0 ppm/K at ≈ 25°CSC cut*: TC = 0 ppm/K bei ≈ 95°C

*SC = Stress Compensated

φ

90o

60o

30o

0-30o

-60o

-90o0o 10o 20o 30o

AT FC ITSC

RTBT

θ Y•

Cuts with zero TC (Thickness shear)

November 2009 18

f(T) for doubly rotated cuts

The inflection temperaturemoves up with increasing 2nd rotationangle Φ.

For Φ ≈ 22° (Tinv ≈ 95°C), the so-calledSC cut („Stress Compensated)the impact of mechanical stresses on theResonance frequency compensate

November 2009 19

Two-point Mount Packagee.g. HC-43/U or HC-45/U

Three- and Four-point Mount Packagee.g. HC-35/U or HC-37/U

Comparison of Crystal packages

November 2009 20

Test Setup

Testing of Vibration Sensitivity

PN Test Systems:- Phase Quadrature Method- Cross Correlation

November 2009 21

Phase Noise Test

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.

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

Phase Quadrature Method

( ))()(det ttK refΦ−Φ⋅=Φ

November 2009 22

Phase Noise Test

Cross Correlation MethodThe signal is fed into two phase detectors and both channels are mixed with an internal low-noise 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

© Agilent

November 2009 23

Cables and mounting

Testing of Vibration Sensitivity

November 2009 24

Content

Theoretical BackgroundSensitivity to forces and accelerationSensitivity to vibrations

Experimental ResultsAXIOM75-16-60 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 25

Vibration Spectrum

W1=0.01g2/Hz, W2=0.06g2/Hz

f1=500Hz, f2=1500Hz

Customer spec Tested profile

November 2009 26

AXIOM75-16-60 MHz AT-cut (HC-43/U)Output Spectrum

November 2009 27

AXIOM75-16-60 MHz AT-cut (HC-43/U)Phase Noise

November 2009 28

AXIOM75-16-60 MHz AT-cut (HC-43/U)G - Sensitivity

November 2009 29

AXIOM75-16A-60 MHz SC-cut (HC-35/U)Test fixture

Orientation

Y

Z

November 2009 30

AXIOM75-16A-60 MHz SC-cut (HC-35/U)Output Spectrum

November 2009 31

AXIOM75-16A-60 MHz SC-cut (HC-35/U) Phase Noise

November 2009 32

AXIOM75-16A-60 MHz SC-cut (HC-35/U) G - Sensitivity

November 2009 33

AXIOM35-14A-100 MHz SC-cut (HC-43/U)Test fixture

Orientation

Y

Z

November 2009 34

AXIOM35-14A-100 MHz SC-cut (HC-43/U)Output Spectrum

November 2009 35

AXIOM35-14A-100 MHz SC-cut (HC-43/U)Phase noise

November 2009 36

AXIOM35-14A-100 MHz SC-cut (HC-43/U)G-Sensitivity

November 2009 37

Orientation

Y

Z

60 MHz SC-cut (HC-43/U) other vendorTest fixture

November 2009 38

60 MHz SC-cut (HC-43/U) other vendorOutput Spectrum

November 2009 39

60 MHz SC-cut (HC-43/U) other vendorPhase noise

November 2009 40

60 MHz SC-cut (HC-43/U) other vendorG-Sensitivity