Quantisation SNR

This relation gives the maximum signal-to-noise ratio an ideal b-bit analogue-to-digital converter can achieve when the only error source is quantisation. It comes from modelling the rounding error as a uniformly distributed noise of size one least significant bit, then comparing the full-scale sine-wave power to that noise power; the 6.02 term is 20 log10(2), and the 1.76 dB constant comes from the RMS-to-peak factor for a sine wave. In practice, real converters often perform worse because of thermal noise, nonlinearity, jitter, and reference imperfections.

Use this when estimating the theoretical dynamic range of an ADC or DAC from its bit depth, or when checking whether a required SNR is even possible with a given resolution. It is especially useful in data acquisition, audio, instrumentation, and any sampling system where quantisation noise is a key limit.

• Using the formula for a real converter without checking whether other noise sources reduce the SNR
• Forgetting that the result is in dB, not a linear power ratio
• Applying it to non-uniform or dithered quantisation schemes without adjusting the assumptions