Quantisation Noise and Oversampling in Low-Resolution ADCs: A Numerical Study

The resolution of an analogue-to-digital converter (ADC) sets a theoretical limit to the signal-to-noise ratio, but real measurements also contain analogue noise. This paper uses numerical simulation to verify the quantisation limit and to quantify the benefit of oversampling and averaging. For a full-scale sine wave, the simulated signal-to-quantisation-noise ratio agreed with the 6.02N + 1.76 dB rule within 0.5 dB for 10 bits and above, with larger deviations of up to 2.2 dB at 4 bits. For a 10-bit converter with 1 LSB rms input noise, averaging 4 samples raised the effective number of bits from 8.0 to 9.0, and each further factor of four in oversampling ratio added about one bit, reaching 13.0 bits at an oversampling ratio of 1024. Without noise on the input, oversampling helped only because the slowly varying signal crossed many quantisation levels. This is a simulation study; all results are outputs of the deposited Python code with assumed parameters. Source code is attached.