## Calculation of signal to quantization noise ratio

#### The maximum quantization error q that can occur in the sampled output of an A/D converter is equal to half the minimum resolution of the converter which is given by q = Vmax / M, where M = 2n is the number of quantization levels for the converter.
Making the assumption that all values of quantization error within the range +q/2 to –q/2 are equally likely, the mean-squared value of the quantization error, Eq, can be calculated from:

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#### The rms error is thus q/12½.
The peak signal voltage for a sinewave input will be Vmax = Mq/2 (allowing for positive and negative excursions of the sinewave), and the rms value is thus Mq/2.2½. The signal to quantization noise power ratio can now be determined as:

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#### Thus, for an 8-bit converter, the peak signal to quantization noise ratio is approximately 3 x (28)2 x 0.5 = 98.304 or 50 dB.