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https://designers-guide.org/forum/YaBB.pl Design >> Mixed-Signal Design >> How to calculate a resolution of a delta-sigma ADC? https://designers-guide.org/forum/YaBB.pl?num=1426198366 Message started by CHL on Mar 12th, 2015, 3:12pm |
Title: How to calculate a resolution of a delta-sigma ADC? Post by CHL on 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? |
Title: Re: How to calculate a resolution of a delta-sigma ADC? Post by sheldon on 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. |
Title: Re: How to calculate a resolution of a delta-sigma ADC? Post by CHL on Mar 16th, 2015, 9:09pm Thank you I will take a look at the book |
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