Question E8A04:
What is “dither” with respect to analog-to-digital converters?  

Choices:  
A: An abnormal condition where the converter cannot settle on a value to represent the signal  
B: A small amount of noise added to the input signal to reduce quantization noise  
C: An error caused by irregular quantization step size  
D: A method of decimation by randomly skipping samples    

Correct Answer is  B: A small amount of noise added to the input signal to reduce quantization noise  

Dither is intentionally added noise at the ADC input to make quantization error behave like random noise instead of signal-correlated distortion.

Why the correct answer (B) is correct:
- Adding a small, controlled noise source “decorrelates” the quantization error from the signal, reducing spurious tones and distortion.
- The quantization error becomes more noise-like and can be reduced by averaging or filtering, improving perceived resolution for low-level signals.

Why the other choices are incorrect:
- A: That describes instability/metastability or oscillation, not dither. Dither is deliberate and beneficial, not an abnormal condition.
- C: Irregular step size is differential nonlinearity (DNL) or integral nonlinearity (INL) error, not dither.
- D: Randomly skipping samples is a sampling/decimation strategy, not the addition of input noise.

Useful formulas and rules of thumb:
- LSB size (quantization step): $$Q = \frac{V_{\text{FS}}}{2^N}$$
- Quantization noise (rms, no dither, uniform quantizer): $$V_{q,\text{rms}} = \frac{Q}{\sqrt{12}}$$
- Ideal ADC SNR: $$\text{SNR}_{\text{ideal}} \approx 6.02\,N + 1.76\ \text{dB}$$
- Averaging uncorrelated noise over $M$ samples improves SNR by: $$\Delta \text{SNR} \approx 10 \log_{10} M\ \text{dB}$$
  Equivalent ENOB improvement: $$\Delta N \approx 0.5 \log_2 M\ \text{bits}$$
- Practical dither levels:
  - White Gaussian dither rms ≈ $0.5$ to $1$ LSB often works well.
  - Triangular PDF dither with about $2$ LSB peak-to-peak can fully remove correlated distortion components.