ADC quantization +thermal noise

Question

ADC noise can affect the overall noise performance of a receiver. The noise is partially quantization noise and partially thermal noise and as a general rule it extends up to the Nyquist frequency = Fs/2 . A simplification or assumption in receiver overall noise performance is to consider the noise spectrum to be flat or white. Are there any general rules or situations in terms of sampling rate (or anything else) that make this assumption grossly wrong?

Answer 1

Treating ADC quantization noise as a uniform white noise source is generally valid. Please refer to this post where I further detail practical limitations on using white noise assumptions for quantization noise as well as oversampling considerations: What are advantages of having higher sampling rate of a signal?

It is typically good design practice to place the ADC quantization noise to be at least 10 dB below the amplified thermal noise of the input signal to minimize the ADC quantization impact on overall noise figure (As the waveform we wish to measure/capture typically is the input waveform including its signal and noise components, not the ADC quantization noise!).

When choosing 10 dB for example as I noted above, the ADC contribution to increasing the noise floor (and hence the noise figure given the same signal level) using the white noise assumption for quantization noise is 0.4 dB given as:

$$10 \log_{10}(1+10^{-\text{dB}/10})$$

where dB is 10 in this case. (This is simply from adding the relative powers and converting back to dB).

The trade off here is dynamic range vs noise figure degradation. Certainly you can place the quantization noise to be much lower below the input amplified noise floor to minimize overall increase in noise (by providing more gain prior to the ADC) but that would be at the expense of dynamic range. For example, if instead of placing the quantization noise 10 dB below the input amplified noise floor as we did above, we placed it 30 dB below, we would lose 20 dB of dynamic range in the process. Typically I use numbers in the range of 10 dB to 15 dB as starting parameters for input noise floor vs ADC quantization noise, but ultimately is part of an overall noise figure budget.

This is identical to a cascaded noise figure computation for those familiar with that in a receiver design. In this case the ADC has an equivalent noise figure, thus constraining the overall gain requirements prior to the ADC in order to meet an overall noise figure objective while balancing instantaneous dynamic range constraints.

Below are my slides where I walk through a typical ADC receiver design showing how this was used in terms of a "Noise Figure" for the ADC. If there is interest in the rest of this (which shows the same considerations for the maximum input signal), please ask as an additional question specific to that and I will post that there as well (since I already have the slides):

Note: The "Noise Figure" shown in the graphic below refers to the "front-end" noise figure which is the entire receiver up to the input of the ADC. This predicts the amplified noise floor level since that would be the receiver gain up to this point plus the receiver noise figure. This is not the "ADC Noise Figure" that I reference in the text and prior graphics.