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Message ID: 1974     Entry time: Wed Jul 15 13:40:38 2015
 Author: Arjun Type: Misc Category: PD noise Subject: Intensity stabilization servo

I was able to deduce the answers for a few questions I was working on. The factor that will limit how well we ca subtract two signals is limited by the amplifier we use and it Common Mode Reduction Ratio(CMRR). Some calculations to support my point:

Output of any amplifier is given as : $V_o=A_d(V_+-V_-)+\frac{1}{2}A_{cm}(V_++V_-)$, where $A_d$ is the differential gain and $A_{cm}$ is the common mode gain. CMRR is defined as $20\log(\frac{A_d}{A_{cm}})$ in dB.

Consider a generic differential amplifier(like AD620) it has a CMRR of 100dB($10^5$) for a gain of 100. The common mode noise is at $\sim 10^{-5}V/\sqrt{Hz}$ and the noise we wish to detect is at $\sim 10^{-8}V/\sqrt{Hz}$ ie around the shot noise limit. Lets say the gain of this differential amplifier is 100, then that would mean that the gain associated with the common mode noise would be $10^{-3}$ as CMRR is 100dB. So the final output of the amplifier would be $\sim10^{-3}\times 10^{-5} + 100\times 10^{-8}$ that is the common mode would be 1% of the total output and this is not very good, by doing a intensity suppression we can improve our ability to subtract by another order or two depending on our servo design. This is the idea behind doing a intensity supression, so that at  our output we have negligible common mode component, which comes from our readout amplifier which has finite CMRR.

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