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How to calculate a resolution of a delta-sigma ADC? (Read 2291 times)
CHL
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How to calculate a resolution of a delta-sigma ADC?
Mar 12th, 2015, 3:12pm
 
Hello

I'm confused how to calculate the resolution.

2^N clock cycles must be counted in order to achieve N-bit effective resolution.

For example, averaging 4 samples gives 2 bits of resolution, while averaging 8 samples yields 3 bits.

If the output is 00110011...., the 3bit signal is (0+0+1+1+0+0+1+1)/(2^3) = 4/8 = 1/2, whose binary code is '100'.

However, I cannot understand the required frequency.

If the input frequency is 10kHz and the ADC provides 16bit output, the sampling frequency should be 2*10k*2^16 = 1,310,720,000 Hz

This looks like reasonable, but weird.

What is wrong with my calculation?
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sheldon
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Re: How to calculate a resolution of a delta-sigma ADC?
Reply #1 - Mar 12th, 2015, 5:22pm
 
CHL,

  You are averaging the results. This is equivalent to oversampling
with a Nyquist rate converter and the rate of improvement from
oversampling is 1/2 bit for 2x sampling rate increase. Delta Sigma
modulator performance is more complex. Getting access to a good
textbook would be useful. I like Scheier & Temes "Understanding
Delta-Sigma Data Converters"*. It is well written and easy to
understand. The equation you are looking for is (1.10), the in-band
noise quantization power is

  (qrms)^2 = (pi^(2 *  L) * (erms)^2) / ( 2 * L + 1) * (OSR)^(2*L+1)

where
     L is the order of the loop filter
     OSR is the oversampling ratio

the chart in 1.7 shows the in band power vs order of the
modulator for oversampling ratios up to 2^10, you can
extrapolate from there.

This equation is only accounts for the effect of oversampling
and filter order on quantization noise. You will still need to
account for the effect of  integrator saturation, integrator
leakage, jitter, etc. on dynamic range.

                                                                     Sheldon

* You can find more info by clicking on the books link.
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CHL
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Re: How to calculate a resolution of a delta-sigma ADC?
Reply #2 - Mar 16th, 2015, 9:09pm
 
Thank you

I will take a look at the book
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