Short note: Data hold circuit

A data hold circuit reconstructs a continuous signal from a sequence of samples by holding or extrapolating the last sample(s) until the next sample arrives. It is used after the D/A converter (and in S/H circuits) so the plant receives a continuous signal.

General form

Between $kT$ and $(k+1)T$ the output is a polynomial in $\tau$:

$$h(kT+\tau) = a_n\tau^n + \cdots + a_1\tau + x(kT), \quad 0 \le \tau < T$$

An $n$th-order hold uses the last $n+1$ samples.

Zero order hold (ZOH)

$h(kT+\tau) = x(kT)$; the output is a staircase.

$$G_{h0}(s) = \frac{1-e^{-Ts}}{s}$$

First order hold (FOH)

Straight-line extrapolation using the slope of the last two samples: $h(kT+\tau) = x(kT) + \frac{x(kT)-x((k-1)T)}{T}\tau$

$$G_{h1}(s) = \frac{Ts+1}{T}\left(\frac{1-e^{-Ts}}{s}\right)^2$$

 ZOH:  |‾‾|‾‾|‾‾      FOH:  / / /

Comparison

The ZOH is the standard hold in digital control because it is simple and its lag is small when $T$ is small.