Post on 05-Apr-2018
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Noise and Interference,
the Lock-In Amplifier,(and the IV-meetkast)
Caspar van der WalFND group talk, modified to web-tutorial - 4 November 2004
( )
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Why look into this?You measure much faster if you use the lock-in
amplifier and the IV-meetkast options in theoptimal way.
It takes very little time to do a critical evaluationof actual noise levels that show up.
It is more subtle than we like to admit, but worthspending some time on.
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Outline
N a t u r e o f u n w a n t e d c o n t r i b u t i o n s t o m e a s u r e d s i g n a l s .
W h y u s e a l o c k - i n a m p l i f i e r ?
C o n c e p t s a n d g u i d e l i n e s f o r o p t i m a l u s e o f l o c k - i n a m p l i f i e r s .
E v a l u a t i o n o f o b s e r v e d n o i s e l e v e l s .
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Noise, drift:Setup-made, intrinsic
Often non-periodicShielding and isolation does not help
Interference:Environment-madeOften periodic
Shielding and isolation helps
.distinction sometimes artificial.
Unwanted contributions to measured signals
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Ideal worldWorld with some reality
R Ib i a s
Voltmeter
G
intrinsic noise,drifting offset
Johnson-Nyquist noise
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time
V
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T a k e n f r o m d a t a s h e e t O P A 6 2 7 ( p a r t o f I V - m e e t k a s t )
Spectrum of amplifier noise
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Vin
Vout
00
Drifting offset
Stable gain
For amplifiers in practice, this gives:
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Ideal worldWorld with some more reality
R Ib i a s
Voltmeter
G
Q
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time
V
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Sprectrum of interference from environment
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time
V
What to do about
Simple averaging = low-pass filtering works!
.but is inefficient and not always effectivebecause of the 1/f character of the unwanted
signals.
?
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So, what about measuring at higher frequencies,
and then band-pass filtering?
0
1Filter
transmission
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In practice it is not possible to realize ultra-narrowband-pass filters that are
-stable
-flexible
(this can work in software though lock-in amplifier)
Good idea, but..
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What does work real-time:
A lock-in amplifier
Idea:
Control or bias at some high frequency.
Amplify the measured signal (full spectrum) up to a levelwhere noise does not hurt it anymore.
Mix (multiply) it with a high-level reference signal at
exactly the same frequency as the wanted signal.
Low-pass filter the mixed signal (can be realized ultra
narrow).
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Oscillator
Experiment
control
signalG
A C
LPF
Lock-in amplifyer
mix
DC output
VR
VS
VM
VR
= AR
sin(R
t)
VS
(S
) = AS
(S
) sin( S
t + ((((S
)))) )
VM
= VS
VR
= AR AS cos( (S -R )+ ) - AR AS cos( (S +R )+ )
After LPF, only for S
= R
VD C X
= AR
AS
cos(), also VD C Y
= AR
AS
sin()
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Non-linearities
I
b i a s
V
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Time constant and repetition time
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Slope of LPF filter
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Low-pass filtering: frequency domain
0 Hz f- 3 d B
50 Hz
AL P F
0 dB
-120 dB
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Low-pass filtering: time domain
Here data taken with TR e p
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Filter slope ENBW T Rep-1%
(dB/oct)6 1/(4 T
C
) 5 TC
12 1/(8 T C
) 7 TC
18 3/(32 T C
) 9 TC
24 5/(64 T C
) 10 T C
For 6 dB case, LPF is simple RC filter.
TC
= RC-time = RC (always defined for single filter!)
f- 3 d B
= 1/(2RC)
ENBW = 1/(4RC) (for white Gaussian noise!)
E m l 6 dB 24 dB filt l
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Example 6 dB vs 24 dB filter slope
Say fR E F
= 1 kHzAssume narrow-band noise contribution at 1.05 kHzAssume noise = 104 times the signal (80 dB)Like to see signal 1% accurate (-40 dB)
Need to LPF 50 Hz by 120 dB
0 Hz f- 3 d B
50 Hz
AL P F
0 dB
-120 dB
S l o p e f
- 3 d B
T
C
T
R e p
6 d B 5 0 H z 3 0 0 0 s 1 5 0 0 0 s
2 4 d B
1 . 6 H z
1 0 0 m s
1 s
Q ; H o w d o e s t h i s w o r k o u t f o r w h i t e n o i s e ?
24 dB case is 15000 times faster than 6 dB!
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LINE and SYNC filters
Look it up. In general, use it below 200 Hz!
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Dynamic reserve
Lock-in amplifyer
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Oscillator
Experiment
control
signalG
A C
LPF
Lock-in amplifyer
mix
DC output
VR
VS
VM
Dynamic reserve:ratio between peak-peak voltage of total signal and
peak-peakof wanted signal.
Dynamic range:ratio between peak-peak voltage of total signal and
resolutionof wanted signal.
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VS
VS
VS
time
Use Low noise (0-124 dB)
Use Normal (0-154 dB)
Use High reserve (0-174 dB)
N o t e : L o c k - i n p e o p l e u s e x 1 0 = 2 0 d B
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Offset and Expand
Use OFFSET and EXPAND (x10 or x100) if you havea small signal on top of a constant background.
Without OFFSET and EXPAND you see the AD conversion
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B (mT)
V (mV)
58.1
58.2
Without OFFSET and EXPAND you see the AD conversion.
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Observed Gaussian white noise with f = 20 Hz
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Specified amplifier noise
VD C X
time
G u n w n w fR E F
z
V R M S V P - P /6
ENBW=1/4TC
Observed VN S D at sample:
VN S D
= V4TC
VR M S
Gain
N o t e u n i t s :
V
D C X
, V
R M S
, V
P - P
V
E N B W H z
G a i n 1
V
N S D
V / V H z
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What if you find 100 instead of 10 nV/VHz ?
a) Try to fix the problem
b) Just average longer
4 days instead of 1 hour for some sweep!
VR M S
= GainV
N S D
V4TC
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Conclusions
The Lock-in is an effective averaging tool to beat1/f part of the unwanted components in measuredsignals.
Improving your signal:noise ratio (in terms of
amplitudes) x 10, means 100 times faster datataking: The difference between results and noresults.
IV tk t
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IV-meetkast
Next time:Why use the IV-meetkast?Shielding
Ground loopsClean groundInductive interferenceCapacitive interference