---
title: "Hysteresis, dead space and linearity"
subject: "Instrumentation and Measurement"
chapter: 3
key: "semester_4/instrumentation_and_measurement:hysteresis-dead-space-linearity"
source: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/hysteresis-dead-space-linearity
site: BCT Engineering
---

# Hysteresis, dead space and linearity

Instrumentation and Measurement · Chapter 3: Static Characteristics of Measurement System

- Asked in: year not given, 6 marks
- Video: [Hysteresis,Deadzone & Drift(हिन्दी )](https://www.youtube.com/watch?v=8LEdyeCc8rc) — LEARN AND GROW
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/hysteresis-dead-space-linearity
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_and_measurement/chapter-3

## Question

Write short notes on (a) hysteresis, (b) dead space, and (c) linearity of a measuring instrument. Explain the terms independent, terminal and least-squares linearity with a sketch.

## Answer

#### (a) Hysteresis
Hysteresis is the difference in output for the same input, depending on whether the input is increasing or decreasing. It is caused by friction, backlash, elastic after-effect and magnetic hysteresis. It is quoted as the maximum difference between the up-scale and down-scale outputs, as a percentage of full-scale output.

```text
 Output |           ___--- up
        |       _--/ _--- down
        |    _-/ _--/   <- hysteresis band
        |  _/ _-/
        | /_-/
        +------------------ Input
```

#### (b) Dead space
Dead space (dead band) is the range of input over which the output does not change even though the input changes, usually because of backlash, friction or a preload. The instrument responds only after the input leaves this band. Dead space is not the same as hysteresis: hysteresis is a difference between up-scale and down-scale readings across the whole range, while dead space is a flat zone with no response.

#### (c) Linearity
Linearity is the closeness of the calibration curve to a straight line. Nonlinearity is the maximum deviation from the reference line, expressed as a percentage of full-scale output. The reference line can be defined in three ways.

- **Terminal (end-point) linearity:** the line joins the zero and full-scale points. It is simple but gives large deviations.
- **Independent linearity:** two parallel lines enclose the curve with minimum spacing, and the line midway between them is the reference. Nonlinearity is half the spacing.
- **Least-squares linearity:** the line that minimizes $\sum (y_i - mx_i - c)^2$. It gives the smallest overall error and is the most used.

```text
 Output |        . . .  actual curve
        |     .  /  <- reference straight line (terminal,
        |   . /        independent or least-squares)
        | ./
        +----------------- Input
```

## Check yourself

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

1. Hysteresis is best described as
   A. A flat input range with no output change
   B. Different output for the same input depending on whether the input is rising or falling
   C. Deviation of the curve from a straight line
   D. Change in output due to temperature
   Answer: B. It is caused by friction, backlash and elastic after-effect, and is quoted as max up/down difference as % of full scale. (Key point: Hysteresis definition)

2. How does dead space differ from hysteresis?
   A. Dead space exists at all points; hysteresis is a flat zone
   B. Dead space is a band of input with no output change; hysteresis exists at all points
   C. They are the same effect
   D. Dead space depends only on temperature
   Answer: B. Dead space is a flat zone where output does not respond; hysteresis occurs across the range. (Key point: Dead space)

3. In independent linearity, the reference line is
   A. The line joining zero and full-scale points
   B. The line minimizing the sum of squared deviations
   C. The line midway between two parallel lines enclosing the curve with minimum spacing
   D. The tangent at zero
   Answer: C. Nonlinearity is half the spacing between the two enclosing parallel lines. (Key point: Independent linearity)

4. Why is least-squares linearity most used?
   A. It is the simplest to draw
   B. It minimizes the sum of squared deviations and gives the smallest overall error
   C. It always passes through the end points
   D. It ignores the full-scale output
   Answer: B. It minimizes sum (yi - m xi - c)^2, whereas terminal linearity is simple but gives large deviations. (Key point: Least-squares line)

## Related in Instrumentation and Measurement

- [Spring-mass-damper instrument parameters](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aspring-mass-damper-instrument-numerical) — Instrumentation and Measurement, chapter 4
- [Calibration line and nonlinearity of transducer](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Acalibration-least-squares-nonlinearity) — Instrumentation and Measurement, chapter 3

## Related in other subjects

- [Least squares: y = ax + b + c/x](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aleast-squares-ax-b-c-over-x) — Numerical Method, chapter 4
- [Least squares significance, normal equations](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aleast-squares-significance-normal) — Numerical Method, chapter 4
- [Least squares fit for calibration data](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aleast-squares-calibration-line) — Metrology, chapter 2
- [Quadratic least squares fit](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aquadratic-fit-least-squares) — Numerical Method, chapter 4