Quantization problems and improvement

Quantization is the rounding of a sampled amplitude to one of a finite number of levels in an A/D converter. For an n-bit ADC with full-scale range $FSR$, the step (quantum) is $Q = FSR/2^n$.

Problems caused by quantization

1. Quantization error: the difference between true and quantized value; with rounding it lies between $-Q/2$ and $+Q/2$.
2. Quantization noise: the error behaves like random noise of variance $Q^2/12$, which reduces signal-to-noise ratio.
3. Loss of small signals: changes smaller than $Q$ are not detected (dead zone).
4. Limit cycles: in a feedback loop the nonlinearity can cause small sustained oscillations of the output.
5. Steady-state error: the output can settle anywhere within one step of the set point.
6. Coefficient and arithmetic round-off in the controller with short word length.

Ways to improve

• Increase the number of bits (e.g. 8 to 12 bits): $Q$ falls by 16 times; SNR rises about 6 dB per bit.
• Match signal range to ADC range by proper amplification so all levels are used.
• Use rounding instead of truncation to make the error zero-mean.
• Oversampling and averaging/filtering to reduce noise.
• Dithering: add small noise before quantizing to break limit cycles.
• Longer word length and careful scaling in the controller software.