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I understand the formula SNR = 6.02N+1.76 for a N-bit ADC which quantizes a modulated tone sampled at twice the BW. I am trying to understand what the same equation would be for a unmodulated CW tones with Zero BW. Any pointers/explanation would be very helpful! Thanks.

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Actually, that formula is specifically for an unmodulated sine wave at full scale just prior to clipping. This SNR result provides a reference point as to what the total quantization noise power will relative to that full scale sine wave at the input to the ADC, and that noise power will be at that similar total power level relative to that full scale reference point even as the tone is lowered in power (it doesn't go down accordingly) and in the presence of modulated signals at lower power levels.

So for example if we have a perfect 8 bit ADC with a full scale sine wave at an incommensurate rate with +10 dBm just prior to clipping, the total quantization noise spread evenly over the sampling bandwidth would be close to 50 dB down or at -40 dBm. If we then removed the sine wave and applied modulated signals (or a lower power sine wave), the total quantization noise would remain about the same. Thus, this formula and what we know about the input to the ADC gives us a good reference point as to where our quantization noise floor is.

So that formula is already what the OP is looking for precisely.

I explain this formula in more detail at this post.

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  • $\begingroup$ Excellent Dan! Thank you. This is precisely what I was looking for. $\endgroup$ Jun 23 at 3:06

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