Sampling, holding, quantizing, coding and decoding

An analog-to-digital converter changes a continuous signal into binary numbers in several steps, and a decoder (D/A) changes them back.

 x(t) -> Sampler -> Hold -> Quantizer -> Encoder -> binary
                                                    word

Terms

• Sampling: taking the value of the continuous signal only at discrete instants $t = kT$ ($T$ = sampling period). The output is a discrete-time signal $x(kT)$ of continuous amplitude.
• Holding: keeping the sampled value constant for the conversion time (or until the next sample) by a sample-and-hold or zero order hold circuit, so the converter sees a steady input.
• Quantizing: rounding (or truncating) the held amplitude to the nearest of a finite set of levels. For an n-bit ADC with full-scale range $FSR$, there are $2^n$ levels and the step size is $Q = FSR/2^n$. The difference between true and quantized value is the quantization error, at most $\pm Q/2$.
• Coding (encoding): assigning a binary code (straight binary, BCD, two's complement, Gray) to each quantized level, giving an n-bit word. Example: 3-bit ADC, $FSR = 8$ V, input 5.3 V is quantized to level 5, coded as 101.
• Decoding: the reverse process in a D/A converter: converting the binary word back into an analog voltage, $V = Q \times (\text{decimal value of code})$. With a hold circuit this gives a staircase signal.

Advantages of digital control system over analog

• Flexible: control law changed by reprogramming, not rewiring.
• Accurate and drift-free: no change with temperature or ageing of components.
• Better noise immunity of digital signals.
• Complex/adaptive/nonlinear control is easy to implement in software.
• One computer serves many loops (time sharing), so cost per loop is low.
• Easy data storage, display, alarms and networking.
• Smaller, cheaper, more reliable hardware.