Problem with missing code in Pipe-line ADC

[neoflash]

In a lecture on ADC converter, lecturer stated that in pipeline ADC, if previous stage’s non-ideality induces significant extra quantization noise, next stage suffer missing code issue.

Below graph illustrated this problem, Y-axis is the residue of 1st stage ADC, as we see, the extra residue (red curve) will overload next stage, such that induced more error.

Lecturer stated that this will incur missing code issue. She ascribed the reason to the extra residue overload 2nd stage, so she suggested a kind of cure to lower the gain between 1st and 2nd stage, so that the "long" residue will be shorter.

However, I understand it differently. The missing code is induced not by the extra quantization noise. It is not coming from the “long” residue, instead, it is caused by the “short” residue curve. The short residue might not be able to cover all codes in 2nd stage, thus induce the missing code.

If my understanding is right, thus lowering the gain will not cure the problem, instead, it will make things worse since it make the short residue shorter, am I right?

 

[manissri]

hi neo ,,
what i think if the residue error is less than 1/2 lsb then there will be no problem.
this amount of error will be corrected by digital error correction logic ckt of adc.
correct if i am wrong ..
manish

 

[neoflash]

1st stage's residue should cover all 2nd stage's code range.
If residue is too long, it will have huge DNL, while no missing code.
If it is too short, 2nd stage's code will not be fully covered. Thus will have missing code.

That's my idea.

 

[rfsystem]

You be absolute correct! Error correction radix converter today using an code overlap of 5-10*sigma of the estimated gain or mismatch error. In the early times, 15-20 years ago, radix 1.5 instead of 1.98 today where popular.

 

[neoflash]

You be absolute correct! Error correction radix converter today using an code overlap of 5-10*sigma of the estimated gain or mismatch error. In the early times, 15-20 years ago, radix 1.5 instead of 1.98 today where popular.

Thanks for the information.

But I did not catch all. What do you mean by saying "In the early times, 15-20 years ago, radix 1.5 instead of 1.98 today where popular."?

thanks,
Neoflash

Added after 9 minutes:

You be absolute correct! Error correction radix converter today using an code overlap of 5-10*sigma of the estimated gain or mismatch error. In the early times, 15-20 years ago, radix 1.5 instead of 1.98 today where popular.

By the way. can i understand it in this way that:

code overlap make normal residue "longer" enough so that any "mismatch" will not make it too short to cause missing code in next stage?

 

[rfsystem]

I have trouble to use your plot. I understand the pipeline or algorithmic converter from the operating equations and parameters.

If the input range is -1...1 the first stage decide the amount of substraction from the input to feed to the next stage.

For the case of radix 1.5 and input range -1...1 the substraction is either -1/3 or +1/3. For the radix2 case the substraction is -1/2 or +1/2. If that is not exact there is code missing or overlap.

 

[neoflash]

I found we are speaking different language, thanks anyway... ^_*