noise talk 1

8/2/2019 Noise Talk 1

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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

noise talk 1

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