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Published equation contexts

q=Vref2Nq = \frac{V_{ref}}{2^{N}}

Why this formula appears here

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 VrefV_{ref} , the size of one quantization step is q=Vref2Nq = \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 / 12\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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VrefV_{ref}

Symbol V_ref

VrV_ref occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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NN

Symbol N

N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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q=Vref2Nq = \frac{V_{ref}}{2^{N}}

Equation 3 · Edge AI & Electronics

How Edge AI Electronics and Sensor Systems Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 VrefV_{ref} , the size of one quantization step is q=Vref2Nq = \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 / 12\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…

Meanings in this article

  • qq: the size of one quantization step.
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