It is nice to meet you. As you look for articles about SNR and A/D converters you will find a formula that looks something like this:
SNR(ideal) = 6.02N + 1.76 dB + 10 log K
(where N is the number of converter bits and K is the number of outputs that are averaged).
This formula basically calculates the quantization noise of the converter (6.02 N + 1.76dB) and the affects from the digital filter (10 log K). With converters that do not have digital filters, K =1. You can see an improvement in SNR to equal a 1.5 bits increase with every doubling of K. But, with this said, the real power behind the reduction of noise with the DS converter is with the modulator. You will find more information at this sight. Look at the video.
http://e2e.ti.com/media/p/17339.aspx#
In terms of calculating the ideal DS converter noise you need take a close look at the modulator noise and the reduction in noise caused by the digital filter. If you want to calculate the noise reduction characteristics of the modulator you may want to study the topics discussed in R. Jacob Baker’s book, CMOS: MIXED-SIGNAL CIRCUIT DESIGN.
Since there is more noise inside the converter that is beyond the ideal calculations, the following formula is used in production when we test and characterize our parts.
SNR = 20 log (single input / converter noise)
This formula works for all converters, but it is done at the bench.
Best Regards, Bonnie Baker Sr. Applications Engineer Data Acquisition Products Texas Instruments, Tucson
Subject: Question about Delta-Sigma Converter Dear Ms. Bonnie,
First of all let me introduce my self. My name is Tommy, I am currently living in Germany. I have read your articles about Delta Sigma Converters including explanation about SNR. I do really want to understand about this matter, at the moment I am simulating delta-sigma converters first and second order to get more feeling how it works. But what really bother me at the moment is the question about the SNR and the resolution of the converter. I have read many articles about this but normally if you want to calculate the SNR of the converters, we need to know the bit-resolution and vice versa. But for my case I simulate the delta-sigma converter in a simulation program, which all the components are ideal and I don't know how to measure or to look how much the bit-resolution of my converter and the SNR as well, since the output is a bit-stream.
Could you please help me about this matter or maybe you could give me a hint about my problem?
I know you are a really busy person and I do really appreciate your time. Thank you very much in advance and hope to receive a reply from you.
Regards,
Tommy
