# Sensitivity of lock-in amplifier

1. Apr 20, 2013

### freddyfish

Hey

I have a quick question whose answer is well-hidden on google since the key word of the search attempts is sensitivity, which of course returns results about phase-sensitive detection, and seemingly phase-sensitive detection only... My question is what the exact definition of the sensitivity of a lock-in amplifier is.

cheers

2. Apr 20, 2013

### jim hardy

No offers yet ?

A question well phrased is half answered.
And i'm not sure I know either what would be meant by "sensitivity" of a lock-in amplifier.

They have an ability to recover a weak signal out of strong noise. Probably a practical definition would be an approximate ratio of the minimum useable signal to noise ratio, but i'm kinda guessing.

Since a lock-in amplifier is effectively multiplying two signals, and how well that works depends on the phase between them, they employ "Phase Locking" to optimize.
And that's not a straightforward subject.

Try searching on terms"PLL capture ratio"

and peruse this practical article:
http://www.bentham.co.uk/pdf/F225.pdf

maybe you'll elaborate on where you ran across the term.

3. Apr 21, 2013

### freddyfish

There is plenty (and very good) information about lock-in amplifiers, so I have read my fair share. Therefore I have got an intuition what the sensitivity of the lock-in amplifier would specify, but this wasn't enough for a reliable conclusion.

Your guess makes sense, but the ratio mentioned is actually the traditional definition of dynamical reserve, which is the ratio of the largest tolerable noise signal to the full-scale signal.

Back to the question. I found an "extended" manual where the following were presented:

Vout = 10A_e(A_vV_icosØ+Vos) {if the output is X}

where...
A_e= 1 or 10 per the Expand
A_v= 1/Sensitivity
V_i= magnitude of the signal
Ø = phase between signal & reference
V_os = offset (fraction of FS < 1.024)

4. Apr 21, 2013

### jim hardy

Intuition usually gets one close -- even if pointed in wrong direction !

Where there's not a universally accepted term for something, authors will often use what is intuitive to them. Is this an old reference, perhaps from 60's ?

Looking at your equation, my intuition tells me the author uses A_v for "Amplification(of) Voltage"

which is a term I used to run across way back when... it meant simply Voltage Gain.
The product of V_i and reference is product of their magnitudes X cos(angle)
i'll guess V_i is multiplied by A_v before arrival at the multiplier
and magnitude of reference is accounted for by A_e

So, 'sensitivity' to that author is simply: 1/(gain applied to input signal)

but that's just what feels intuitive to me.

I'm not well versed in lock-in amps as you have doubtless discerned.
My 'Rock of Ages' for this subject is the AD630 datasheet. It provides precise A_v of 1, 2, 3 or 4 before presentation to multiplier..