---
title: "Short note: Data hold circuit"
subject: "Digital Control System"
chapter: 1
key: "semester_6/digital_control_system:short-note-data-hold"
source: https://www.bctengineer.com/q/semester_6/digital_control_system/short-note-data-hold
site: BCT Engineering
---

# Short note: Data hold circuit

Digital Control System · Chapter 1: Introduction to Discrete Time Control System

- Asked in: 2068 Jestha, 4 marks
- Video: [Discrete control #3: Designing for the zero-order hold](https://www.youtube.com/watch?v=yetLPW9sQaI) — Brian Douglas
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/digital_control_system/short-note-data-hold
- Whole chapter: https://www.bctengineer.com/md/semester_6/digital_control_system/chapter-1

## Question

Write a short note on data hold circuit.

## Short answer

A data hold circuit reconstructs a continuous signal from samples by holding or extrapolating past values. An nth-order hold uses the last n+1 samples to form a polynomial between sampling instants. Zero-order hold (ZOH) outputs a staircase with transfer function (1-e^{-Ts})/s. First-order hold (FOH) uses linear extrapolation with transfer function (Ts+1)/T((1-e^{-Ts})/s)². ZOH is standard due to simplicity and small phase lag at high sampling rates.

## Answer

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:
$h(kT+\tau) = x(kT) + \frac{x(kT)-x((k-1)T)}{T}\tau$

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

```text
 ZOH:  |‾‾|‾‾|‾‾      FOH:  / / /
```

#### Comparison

| ZOH | FOH |
|---|---|
| Uses one sample | Uses two samples |
| Staircase output | Piecewise-linear output |
| Phase lag $\omega T/2$ | Larger phase lag at high frequency |
| Simple, most used | More memory and hardware |

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A data hold circuit:
   A. Samples a continuous signal
   B. Reconstructs a continuous signal by holding or extrapolating samples
   C. Quantizes a signal
   D. Multiplexes channels
   Answer: B. It is used after the D/A so the plant gets a continuous signal. (Key point: Purpose)

2. How many samples does FOH use?
   A. One
   B. Three
   C. Two
   D. None
   Answer: C. FOH uses the slope of the last two samples; ZOH uses one. (Key point: ZOH vs FOH)

3. The FOH transfer function is:
   A. (1 - e^(-Ts))/s
   B. (1/T)(1 - e^(-Ts))
   C. (Ts+1)/s
   D. ((Ts+1)/T)((1 - e^(-Ts))/s)^2
   Answer: D. A straight-line extrapolation. (Key point: FOH transfer function)

4. ZOH is standard because:
   A. It is simple and its lag is small when T is small
   B. It has zero lag always
   C. It uses two samples
   D. It gives piecewise-linear output
   Answer: A. FOH has more lag at high frequency and needs more memory. (Key point: Preferred hold)

## Related in Digital Control System

- [Data hold circuit and ZOH derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adata-hold-zoh-derivation) — Digital Control System, chapter 1
- [Short note: Sample and hold circuit](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Ashort-note-sample-hold) — Digital Control System, chapter 1
- [Data acquisition system and tracking/hold modes](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adata-acquisition-tracking-hold) — Digital Control System, chapter 1
- [Transfer function of zero order hold](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Azoh-transfer-function) — Digital Control System, chapter 1, asked 7×
- [Transfer function of first order hold](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Afoh-transfer-function) — Digital Control System, chapter 1, asked 7×
- [Sample and hold: tracking and hold modes](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Asample-hold-tracking-hold) — Digital Control System, chapter 1, asked 3×

## Related in other subjects

- [Sample and hold circuit](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Asample-and-hold-circuit) — Instrumentation I, chapter 6
- [Short circuit at load B (ohmic data)](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Ashort-circuit-load-b-ohmic) — Power System Analysis II, chapter 3