Analog to Digital Converters

An $N$-bit ADC with reference $V_{ref}$:

$\text{code} = \left\lfloor \frac{V_{in}}{V_{ref}} \times 2^N \right\rfloor \qquad \text{LSB} = \frac{V_{ref}}{2^N}$

A 12-bit ADC with 3.3 V reference resolves 3.3/4096 ≈ 0.8 mV. The quantisation noise limits the ideal SNR to:

$\text{SNR} \approx 6.02N + 1.76\ \text{dB}$

Architectures:

• SAR — moderate speed and resolution (most microcontrollers).
• Sigma-delta — high resolution (16–24 bit), slower (scales, audio).
• Flash — fastest, low resolution (oscilloscopes).
• Pipeline — high speed with good resolution.

Sample at more than twice the highest signal frequency (see Signals → Sampling Theorem) and add an anti-aliasing filter.