Hello guys. I am a student and I have started to design a delta sigma adc for medical application. In some reference books I see that OSR = f sampling / 2 fB (fB is the highest frequency of the input signal), but in a video of texas instrument, I see that OSR = modulator clock / data rate. I don't understand the second formula completely. Please explain ...

 

 

:Bump:

 

One formula says what you need for a specific applications frequency acquisition and the other says how to get it.

You will need the correct background information to understand completely but here is a short intro with a simple modulator first.
https://www.dspguide.com/ch3/7.htm

Now, consider the characteristics of the delta modulated output signal. If the analog input is increasing in value, the output signal will consist of more ones than zeros. Likewise, if the analog input is decreasing in value, the output will consist of more zeros than ones. If the analog input is constant, the digital output will alternate between zero and one with an equal number of each. Put in more general terms, the relative number of ones versus zeros is directly proportional to the slope (derivative) of the analog input.

So we take that delta modulated output signal and chop it into timed (number of) bit slices (samples) and use that to find the slope of the analog input.

Now to the delta-sigma converter.

The relative number of ones and zeros in the output is now related to the level of the input voltage, not the slope as in the previous circuit. This is much simpler. For instance, you could form a 12 bit ADC by feeding the digital output into a counter, and counting the number of ones over 4096 clock cycles. A digital number of 4095 would correspond to the maximum positive input voltage. Likewise, digital number 0 would correspond to the maximum negative input voltage, and 2048 would correspond to an input voltage of zero. This also shows the origin of the name, delta-sigma: delta modulation followed by summation (sigma).

It's a complex subject.

 

I did not watch those videos, but I did read the explanation a few times, and the result of that being more confusing that before reading them.
Fortunately I do not have to deal with these converters presently.

 

I did not watch those videos, but I did read the explanation a few times, and the result of that being more confusing that before reading them.
Fortunately I do not have to deal with these converters presently.

It's easier if you've had lots of experience and training in symbolic digital encoding starting from simple Morse, TTY and on up the ladder to various modern digital modulation techniques. You don't need to understand how it works to reduce noise in great detail to use them.
https://forum.allaboutcircuits.com/threads/50nv-resolution.130468/post-1073894