# Noise vs Signal

All, I have created a photo-diode amplifier(2 stage) which allows me to set a gain from 2 to 551 (v/v) [4.6 to ~55dB] in 64 steps.

The gain is achieved using pre-calculated resistance to provide non-linear gain (as per the application).

The gain's theoretical chart is provided below:

Now when I read Signal and plot it with respect to Noise (Noise: when no light it exposed to the detector), I get the following data (12 bit adc)

I think that I am happy with this as the noise is pretty much low and signal rises as expected!

Whats concerns me is the analysis of noise in absence of signal. In this case, noise seems to be bouncing around for higher gains. Note that ADC, OPAMP all have decouplings caps right next to the chips (.1 uF, 1 uF, 10 uF).

I may live with the noise and do digital averaging to get a nice curve and use it, but is this noise behavior OK and expected?

To explain better, I am concerned that why is the noise not like this?

• How can you expect noise to be as you said? Have you calculated what the noise will be given the op-amps, resistors and photodiode? May 21, 2015 at 7:24
• @Andyaka I did not calculate the noise but should not it grow in increasing order with gain? Why does the noise have a smooth uphill in less gain and changes dramatically in higher gains? May 21, 2015 at 7:32
• I do not see what you see maybe. I don't see what issue you have with the noises? May 21, 2015 at 8:04
• @Andyaka I am not sure if the noise chart is OK. It might be OK in all sense but I dont know if I need to work on it to make it "smoother"! P.S. Offtopic : I did learn and implemented bits from "Digital filter design for Analogue engineers.pdf" . Its great work! May 21, 2015 at 8:08
• Ha ha that was a surprise! What I'm saying is that I don't see what is wrong with the noise you are seeing. Maybe you can spell it out a bit more - maybe I'm just being blind or stupid (it has been known) May 21, 2015 at 8:35

The signal at the output of the amplifier is proportional to the feedback resistor. However, the feedback resistor also contributes its own thermal noise, which scales with the square-root of the feedback resistance. Therefore, $$Signal \propto R_F$$ $$Noise \propto \sqrt{R_F}$$ So for the regime where the resistor's thermal noise dominates the amplifier noise, $$SNR \propto \sqrt{R_F}$$ So even though the noise increases, the signal-to-noise ratio still improves (as your data shows).
In the case of the transimpedance amplifier, the SNR will continue to improve as $R_F$ increases, until the point when the noise is dominated by the op-amp's input bias current. At that point, increasing $R_F$ any further won't improve the SNR. This is why low-$I_B$ op-amps are popular.