Hysteresis, dead space and linearity

(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.

 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.

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