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# Resolution of a sigma delta modulator

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#### nishanthpv

##### Junior Member level 2
Hi,
Can somebody help me with a procedure to find the resolution of a sigma delta adc (single bit quantizer) ?
Nishanth

the more you oversample, the higher the resolution becomes. is it a 1st order ?
assuming you are referring to a 1st order single bit quantizer, the SQNR=sqrt(9*(oversample ratio)^3/(2*pi^2))
SQNR is the signal to quantizer noise (SDM noise is typically referenced to the quantizer noise, not the component noise, or overall noise)
oversample ratio, the frequency ratio of SDM to target signal.
sooo if you had a OSR of say 128, your SQNR = 59.8dB
now use the well known equation SNR=6.02N +1.76dB, rearrange to get ENOB= (SNR-1.76)/6.02 = 9.64
in this case you would output 10 bits with the LSB being not completely reliable(its probability to be correct is greater then its probability to be incorrect)
Hope this helped
-Pb

how do you get 59.8dB for the SQNR?

SQNR ~ 978 so in db 20log(978)~59.8db

dawson

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Points: 2

### dawson

Points: 2
Don't forget a very important fact, that in making higher order modulators, you need to consider coefficient scaling within the loop filter for stability. If using a single bit internal quantization, you will never match the calculated values by the commonly used equations! It only matches for first order. If you go to multi-bit, you will match up to 3rd order, but when looking at 4th order it shifts down alittle.

JGK

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Points: 2