# Noise and SNR calculation with a Lock-in Amp

Discussion in 'Electronic Design' started by Hüseyin Rahmi Seren, Jun 21, 2007.

1. ### Hüseyin Rahmi SerenGuest

I am trying to make low noise optical measurements using a Lock-in
after getting the signal with a PD circuit (one of the Hobbs'
circuits). However, I have trouble on calculating my SNR and noise in
units of 1/sqrt(Hz).

1- First (without the Lock-in) I am taking the data using a Tectronix
oscilloscope. Using 128 sample averaging, I detect a noise level
around 800uV. Should I divide it by the sqrt(bandwidth) of the PD
circuit to have the noise in 1/sqrt(Hz)?

2- Again without Lock-in, looking at FFT of the oscilloscope, can I
make a SNR calculation? (There is approximately 60 dB difference
between the white noise and my frequency in FFT screen)

3- Later, in order to make some improvement on the noise performance,
I use a Lock-in. For Lock-in output (which is a DC for a sine input),
what should I do for SNR calculation and how should I calculate the
noise? Should I use the BW of the Lock-in instead of the PD circuit?

Any help is appreciated. Thanks a lot.

Huseyin.

2. ### Phil HobbsGuest

In order to calculate the noise voltage spectral density, you have to
know the bandwidth accurately, and it has to be the right bandwidth. If
your noise canceller circuit has a noise bandwidth of, say, 5 MHz, then
you want to use that. You won't be able to do good noise measurements
with a scope.

I'd recommend just using a quiet light source (e.g. a flashlight) to
make the noise canceller generate really really pure shot noise, and use
that as your noise standard. That's actually the best way to measure
the noise bandwidth of the whole system.

Cheers,

Phil Hobbs

3. ### MooseFETGuest

That only works if the noise is uniform with frequency. The 1/F part
of the noise doesn't work like that.

Does the scope have an anti-alias filter and how many bits is its
digitizer good to? Are you using all the bits? You will usually see
an RMS noise that is 1/sqrt(12)RMS times the LSB of the digitizer.
Most lockins have a narrower bandwidth than most PDs. The bandwidth
of the lockin sets the system bandwidth.

All sorts of nonsense measurements can be made when you use a lockin.
Beware of the bandwidth of the lockin vs the bandwidth over which you
measure. Also read the manual carefully if the source frequency is
changing.

4. ### MooseFETGuest

Also be careful about getting the system gain.

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