Chungming,

  My understanding is silghtly different:

1) To calculate dynamic range, you need to use SINAD not SNR.
   Distortion also limits dynamic range.

2) Dynamic range is the ratio of Signal Power to (Noise+Distortion
   Power).  

3) SINAD and Dynamic Range are pretty much directly related.

4) SINAD and Dynamic Range are a function of input level. Usually
   you sweep the input level and find the maximum SINAD.

So if the SNR is 88dB. Then the dynamic range will be less than 88dB,
due to distortion. However, for audio applications the SNR is usually
calculated using some "perceptual" filtering applied. Since our ears are
not perfect, SNR is often specified with an filtering function, typically the
A-weighted filter function. The A-weighting filter reduces the effect of
high and low frequency noise on SNR.  

                                                             Best Regards,

                                                                Sheldon

Chungming,

  SNDR is Signal to Noise + Distortion Ration and SNDR is just another
name for SINAD. The plot illustrates item #4 from the list in the previous
e-mail. The noise floor is fixed and as the signal level increases, the
SNDR[SINAD] increases. At large signal levels, distortion starts to limit
the SNDR[SINAD] and the SNDR[SINAD] starts to decrease. Hope the  
transfer function of your ADC is more linear than this example!

                                                           Best Regards,

                                                             Sheldon

Hi All,

     when I was working with sigma delta modulator I had the feeling that dynamic range was never a well defined concept. This happens because of the special phenomena typical of delta sigma known as saturation to the input power signal. I refer to the fact that, as you can see in the typical graph of SNDR  (versus the input signal power referred to the references) attached to this thread, the SNDR drops when the signal power get close to the reference power(or to its full scale input).
This behaviour creates some confusion for the quite straight Dynamic Range definition of converters that you report in the starting (there are several, but all should say the same thing):

(maximum detectable signal power) / (minimum detectable signal power)

While the maximum detectable signal power should coincide with the converter full scale, the minimum one should be limited by the idle power noise. it is intended the noise measured when no signal is applied at the converter input. What I meant before is that the SNDR (or SNR) saturation phenomena disturbs a bit the way this definition fits with classical converter (not that sigma delta are not classical today, but the dynamic range is even an elder concept). With a converter where the SNR increases monotonically with the signal power until full scale of the input, the dynamic range definition works fine without creating much problem (i.e. knowing the full scale tells us the amount of circuit noise limiting the converter accuracy, or the converter equivalent number of bits). Even true that if the considered converter is limited by circuit noise until its full scale the dynamic range should coincide with the maximum SNR reached at full scale (let us neglect possible slewing phenomena). In realistic case where for higher input signal power the SNDR is affected by growing harmonic distortion the dynamic range is always bigger than the maximum SNDR.

Now let us consider sigma delta converter, my opinion is that a fair definition of dynamic range should be the range from the signal power where SNR=0dB (here the signal power equals the circuit channel noise, that defines the power of the smallest detectable signal) to the amplitude of maximum SNR, just before saturation (after saturation the quantization noise increases overcoming the circuit noise contribution, dramatically decreasing the SNR). That is because, in my knowledge, this is the range where the converter can be used in a realistic way. With this assumption the dynamic range is, in real application, always >= than SNR (SNDR), depending by SNR (SNDR) degradation independent by idle noise power value. I must say I found in literature several example where as dynamic range was intended the range where the SNR (or SNDR) remain >=0 (as, by the way in the reported graph).
Of course, at the end of the day, is matter to agree on a definition.

Coming back to your original question my opinion is that higher the SNR higher will be the dynamic range as well. And, as said above, dynamic range is >= than SNR (SNDR).

Regards,

Ettore