# How 10bit SAR ADC achieves 12bit resolution

#### spacejedigundam

Joined Feb 8, 2022
5
I want to do a 10bit ADC , but after run FFT , the enob result will achieve 12bit , is this possible ? how to do that ?

sorry for my poor English , your answer can help me a lots , kowtow , thanks your holy reply , Thank you so much brother

#### MrChips

Joined Oct 2, 2009
30,464
You can increase the ENOB by taking averages from many samples if you have random noise added.

#### Ian Rogers

Joined Dec 12, 2012
1,136
I do it all the time.... I sample 10 bit 24 times then divide by 6... The result is pretty good..

On most systems I don't even divide... I keep the value large then use that to map my sensors... keeping precision as best I can.

#### crutschow

Joined Mar 14, 2008
34,028
From Analog Devices:

As a general guideline, oversampling the ADC by a factor of four provides one additional bit of resolution, or a 6 dB increase in dynamic range. Increasing the oversampling ratio (OSR) results in overall reduced noise and the DR improvement due to oversampling is ΔDR = 10log10 (OSR) in dB.

On that basis, an oversample (and average) by a factor of 16 should give you two more bits of resolution.

Does your ADC have the speed to achieve a factor of 32 oversample for the highest frequency of interest?

#### drjohsmith

Joined Dec 13, 2021
850
An FFT is performing lots of multiplies
you might be confusing number of FFT bits with ENOB,

i.e if I multiply a two bit number by a 5 bit number I get a 7 bit result,
it does not mean you have more bits, just the lower bits are "not relevant" to the ENOB

Also as other have said
you can increase the dynamic range of a ADC, by over sampling and averaging,

So if you were over sampling at 4 MHz, 8 bits,
assuming the "noise" is "gaussian white noise"
then you could average the 4 samples to give you a 9 bit answer, but at 1 MHz sample rate
that gives you very slightly over a 6dB increase in SNR

https://www.silabs.com/documents/public/application-notes/an118.pdf

Some audio ADC and DAC use this to make a bit ADC or DAC into 22 bits,
but its not with simple averaging, and audio tends to have good Gaussian noise, but it does not always work