# How does negative feedback reduce noise?

It is a well established fact that negative feedback improves a lot of parameters related to amplification.

Effect of negative feedback on some of the factors such as gain, input and output impedances etc. can be found by mathematically solving some practical circuits, but I could not find a suitable explanation for the noise reduction caused by the negative feedback.

Can anyone give me an intuitive (or mathematical) idea as to how the negative feedback helps in reducing noise?

Edit: Excerpt from Boylested's book on Electronic Devices • What made you think -ve FB reduces noise? what noise? Dec 25, 2019 at 17:21
• Noise feed into input of differential amplifier is canceled or rather reduced due to the fact that some of amplified noise seen at the output is fed back into input where two noise signals are subtracted.
– Keno
Dec 25, 2019 at 17:23
• The noise is not actually amplified and fed back for subtraction, the input stage is differential so it does not even see common mode noise so it is not amplified. Dec 25, 2019 at 17:59
• @Tony Stewart Sunnyskyguy EE75 ; I have edited the question Dec 25, 2019 at 18:04
• en.wikipedia.org/wiki/Noise_(electronics) Dec 25, 2019 at 19:10 Feedback reduces all types of errors introduced by block "G" in the schematic above, including noise.

However, all feedback does is minimize $$\ \theta_e \$$ which does not reduce noise or other kinds of errors (offset...) from the input stage (represented as a substractor on the schematic).

This has practical applications in opamps for example, if you want to pay more for low-noise transistors, they have to go in the input stage. 1/f noise in the rest of the circuit will be reduced by feedback.

So when saying "feedback improves characteristic X" it is important to keep in mind what is "characteristic X" and to what part of the circuit it applies.

• Show why/where the noise is reduced. Dec 25, 2019 at 18:46

## THD & IMD

All single stage amplifiers have some non-linear large signal effects which produces distortion or a harmonic noise or a mix of input frequencies called intermodulation noise with the aliasing or sum and difference products of non-linear gain usually near the tip of one polarity decreasing gain.

Would you like to see a simulation of negative feedback, NFB for a high gain single stage NPN amp? Input =10mVpp, Output =604mVpp Gain= 60.4 depends on collector current
To see the asymmetry in small signal gain distortion the AC coupled compare the peaks Vpk+ + Vpk-
- subtract and divide by Vpp *100% = asymmetric distortion
- which is similar to and proportional to THD (which takes the ratio of rms of harmonics to fundamental)
- using the positive difference 302.1mV-301.6mV = 0.5mV/301 = 0.17% distortion

This is excellent, but if Rfb is increased to get a gain =100 then distortion increases to 1% and with no NFB 10%. Collector Q DC bias point also changes with NFB.

## SNR

If the noise is in the signal input, unless the noise and signal occupy a different spectrum or can be limited by the GBW of an amplifier, -ve FB (neg. feedback) cannot affect the Signal to Noise Ratio.

They can be improved by filtering by suppressing the spectrum of unwanted noise using active filters with neg. FB.