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sigma delta adc concept (Read 475 times)
saralandry
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sigma delta adc concept
Nov 13th, 2020, 12:58pm
 
Hi,

I have a couple of question and I hope someone can help me to understand a few concepts.


Letís assume that we have a second order sigma delta modulator similar to the block diagram below. In Richard Schreier books it is mentioned that ďThe c2 coefficient is unimportant since the quantizer is singlebit.Ē.

Now my question is that how to implement the coefficient C2? Shall we simply remove C2 coefficient from the calculation and remove it from the following block diagram? If so, I think it is going to impact the STF of the modulator. Is that correct?



My second question is that letís say we synthesize NTF such that the modulator is stale for 0.9 of the full scale (for example if the reference voltage is 3-V then the input can swing from 0.15V to 2.85V. Now letís assume that we want to input goes from 0 to 3V. There is a footnote in Schreierís book but I do not understand it. I am quoting it here

ďA simple transformation u' =0.9u + 0.15 would allow input voltages u in [0,3V] while ensuring that the modulator receives an input u' which is within the stable input range. Such a transformation could be implemented by changing the input-sampling/reference-feedback network.
My question is how to change the reference voltage to be able to support 0to3 V.

thanks
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bernd2700
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Re: sigma delta adc concept
Reply #1 - Jan 15th, 2021, 3:01am
 
Dear "saralandry",

I am new to this forum since today (15.1.2021) and I have seen your question below. Did you solve the topic already?

Coefficient "c2" is for single-bit, what you have, usually also named as "quantizer" gain (more precisely the "quantizer-dac" gain since "gain" is unit-less", often referred as to "kq" or "k", check Schreier). And this also has to be modelled if you want a correct model e.g. in Simulink. How to calculate it: Check Schreier, Yellow Book, p. 144.

Of course a different kq will shift the STF, too. Make a simple Matlab feedback model, so do a la:

STF = Forward / ( 1 + Forward * Return )

whereas the "Forward" includes the multiplication of "kq".

The full-scale, input referred, is also what is the full-scale of the DAC multiplied by any gain blocks. E.g. if the gain blocks from the feedback (=DAC) are 1 and also the input gain blocks are 1, and the DAC Full-Scale (FS) is e.g. 3V, then also your input-referred FS is _in the average_ also 3V. If there is an additional gain block from the feedback, e.g. factor 2, then your input-referred FS is 6V.

Got it?

Nice greetings,
bernd2700
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