digital processing of digital output of a sigma delta ADC

Hello everyone !!!!

My question is regarding the method to process the digital output of sigma delta ADCs.

For example:
Lets take the example of 3-bit flash ADC. Assume that it outputs a binary 010 for an analog input of 2V. Another flash ADC of the same kind outputs a binary 011 for an analog input of 3V. Now if we wish to find the product of the two analog inputs, we can perform the binary multiplication of 010 and 011 to obtain a binary 110 as the result. Binary 110 is equivalent to analog 6V, which is exactly what we expected( 2V*3V=6V). Hence the binary result is a direct representation of the analog output.

Now, lets take the case of sigma delta ADC. Assume that the following is the output of this ADC.
Result for 20 samples
Input volts Sequence of output bits
0.2 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1
Now if we try to find the product of analog 0.2V with itself, i.e. 0.2*0.2. If we try to find the normal binary product of the the output provided by the sigma delta ADC, we see that the binary result does not directly represent the expected 0.04 analog voltage.


Hence, can anyone tell me how is the processing done in the case of delta sigma ADC, and how is the result obtained post processing is analysed.

---------- Post added at 05:50 ---------- Previous post was at 05:48 ----------

digital processing of digital output of a sigma delta ADC

Hello everyone !!!!

My question is regarding the method to process the digital output of sigma delta ADCs.

For example:
Lets take the example of 3-bit flash ADC. Assume that it outputs a binary 010 for an analog input of 2V. Another flash ADC of the same kind outputs a binary 011 for an analog input of 3V. Now if we wish to find the product of the two analog inputs, we can perform the binary multiplication of 010 and 011 to obtain a binary 110 as the result. Binary 110 is equivalent to analog 6V, which is exactly what we expected( 2V*3V=6V). Hence the binary result is a direct representation of the analog output.

Now, lets take the case of sigma delta ADC. Assume that the following is the output of this ADC.
Result for 20 samples
Input volts------->Sequence of output bits
0.2V--------------> 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1
Now if we try to find the product of analog 0.2V with itself, i.e. 0.2*0.2. If we try to find the normal binary product of the the output provided by the sigma delta ADC, we see that the binary result does not directly represent the expected 0.04 analog voltage.


Hence, can anyone tell me how is the processing done in the case of delta sigma ADC, and how is the result obtained post processing is analysed.

You're discussing the bitstream output of a sigma delta modulator. A SD modulator isn't a complete ADC. It's comprised of the modulator and a decimation filter, that removes the off-band noise. The output of the filter is a data word with a bit width according to the intended ADC resolution

Dear FvM,
u are correct regarding the output data stream.... but my question is how is the processing done with the data stream, and how the obtained result obtained post processing co-realtes to the corresponding analog data....

So you are asking "how to build a Sigma Delta ADC"? The most simple decimation filter is a simple averager, counting the "ones" over a fixed number of clock cycles. A second or third order CIC decimator (Cascaded integrator-comb filter - Wikipedia, the free encyclopedia) gives acceptable filtering and has been used in many low speed industry standard SD ADCs. For a sharper filter frequency, as needed e.g. in audio ADC, other decimator designs are in use.

Dear FvM,

Thanks for your prompt replies.
But, u didnt get my question correctly.
Assume u have two output data streams corresponding to two analog signals from the sigma delta ADC. Now u want to find the product of the two signals. My question is, how will u process the digital datastream to get the product of the two signals....

As I said, it's not correct to name the modulator bitstream "output of a sigma delta ADC". Assuming the bitstreams outputs of two SD modulators would be uncorrelated, an AND operation is corresponding to a multiplication of the ADC output words.

Unfortunately, the bitstreams aren't uncorrelated for deterministic signals, e.g. constant DC voltages.