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Design >> Analog Design >> quantization noise of ADC
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Message started by sugar on Mar 26^th, 2008, 11:29pm

Title: quantization noise of ADC
Post by sugar on Mar 26^th, 2008, 11:29pm

Hi,

As we know, an ADC's total quantization noise power VQ^2 = VLSB^2/12

Power spectral density of this quantization noise = VQ^2/Fs
where Fs is sampling frequency.

My question is why quantization noise power is distributed only in bandwidth 0~Fs.

Title: Re: quantization noise of ADC
Post by thechopper on Mar 27^th, 2008, 6:10am

Hello sugar,

The quantization noise PSD you mentioned is correct but it has some implicit assumptions:

1) The ADC incoming signal is supposed to be a "busy" signal, meaning that variations are fast enough
in order not to give the same digital code for two consecutive outputs of the ADC.
2) The ADC incoming signal never overcomes the input dynamic range.
3) The ADC LSB is much lower than the signal amplitude.

If these criteria are met then the Q noise rms value is the one you mentioned (and assumed to be white).

As for PSD there is an extra assumption to be made. Although ideally the noise PSD should be integrated from 0 to infinity, it is actually integrated from 0 to fs/2 since fs/2 is the Nyquist frequency for your ADC,
and your input signal should NEVER have any frequency content above fs/2. Therefore the only USEFUL frequency band is fs/2.
Therefore, it is assumed the noise is totally contained in the band 0-fs/2 (keep in mind quantization noise is not aliased since quantization occurs after sampling, therefore the assumption makes sense).

If this is assumed the obtained PSD is the one you mentioned.

Regards
Tosei

Title: Re: quantization noise of ADC
Post by Berti on Mar 27^th, 2008, 6:11am

An ADC does usually sample the signal (e.g. with sampling frequency fs). The resulting spectrum
is therefore periodic around -fs/2 ... +fs/2.

Cheers

Title: Re: quantization noise of ADC
Post by sugar on Mar 30^th, 2008, 12:51am

Tosei,

Thank you for your explanation. I still cannot understand.

If noise band is from 0 to maximum signal frequency, then over-sampling ADC won't be able to reduce noise floor, since that noise distributes only from 0 to maximum signal frequency, although we can increase sampling frequency, the noise band is not changed, thus noise PSD is not changed. This conclusion is inconsistent with our knowledge.

Maybe I didn’t catch your point, could you explain more?

Title: Re: quantization noise of ADC
Post by thechopper on Mar 30^th, 2008, 5:35am

Hi,

An oversampling ADC will not reduce the noise floor if the oversampling factor is 1 --> this would be the case when your signal BW for an oversampling ADC is considered 0--> fs/2. This is the signal BW considered for a general case.
For oversampling ADC the signal BW needs to be way less than fs/2, just in order to get high OSR. Otherwise the noise will not get reduced as you stated.

Bottom line: 0-->fs/2 is the signal BW for a general ADC case (never higher than this one). For an oversampling ADC signal BW will be 0--> (fs/2) / OSR; where OSR is the oversampling ratio. For this BW then you should consider then quantization noise in you oversampling ADC.

Tosei

Title: Re: quantization noise of ADC
Post by Monkeybad on Apr 1^st, 2008, 11:47pm

Hello, this is an interesting question.
Don't think it too complicate,but think it more intuitively and without any math.
As Tosei says, quantization occurs after sampling. It is the point.
Any signal's BW after sampling can't exceed the half of the sampling frequency.
The quantization noise is also a signal, of course it can't have higher frequency component than fs/2.
For example, if you describe a signal in every one second, but your ADC's precision is limited so the error will occur in every one second.
Can the error changing occur in a smaller time interval such like 1.5s? Of course not!
The fastest changing is in the situation of going up, and down, which cost 2 second.
So the maximum frequency of the error signal (quantization noise) is 1/2s=0.5Hz.