fraction

The passage around this formula

The quantization step itself has a clean expression once gain and reference voltage are fixed. For an ADC with N effective bits resolving a full-scale reference voltage $V_{ref}$ , the size of one quantization step is $q = \frac{V_{ref}}{2^{N}}$. and, treating quantization error as uniformly distributed over one step, the resulting quantization noise power has a root-mean-square value of q / $\sqrt{12}$ . This is the textbook derivation behind every “effective number of bits” figure a converter data sheet reports, and it is the reason oversampling helps: spreading the same quantization noise power across a wider sampled bandwidth before filtering it back down effectively lowers the in-band noise floor…

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