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:

The rms error is thus q/12½.

The peak signal voltage for a sinewave input will be VmaxMq/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:

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.