Choosing parameters for requirements for OS A/Ds.

Just a short post adding on to the OS converter thoughts. There are four basic sections of an OS A/D. The modulator and its noise shaping, the low pass filter, and the decimation filter. The first two can be folded into one section -- which can be called the "sigma - delta modulator". The task of this modulator is to generate, ( in the usual case) a one bit output stream, which is a very high frequency and dense bit stream. Since the converter is a one bit converter, in the absence of the noise shaping, the quantization noise would be horrendous, and the output would be useless.
However, the noise shaper causes the noise spectrum to become a high pass spectrum. The net result is that the in-band quantization noise is significantly lowered. As the oversampling rate increases, the in band noise comes down. As a result the SNR increases. ( e.g. a 96 dB SNR can be said to be the equivalent of 16 bits. Note that this is not an exact equivalence). The following parameters provide an indication for a fast assessment of modulator performace. The highest order of the modulator considered is 3. Third order and higher order modulators have instability issues.

For a second order modulator: The SNR is 100dB for an OSR of 192; 80dB for an OSR of 64; 60dB for an OSR of 14.
For a third order modulator, the numbers are: 100dB at OSR of 56; 80dB for an of OSR of 32; 60dB for an OSR of 14.
Note as order increases SNR increases for lower OSR.