#### Characteristics of Instruments - Terminology

Accuracy is how close is the measurement to the true value.  It is more easily quantified by percentage error where:

##### Percentage error = ( indicated value – true value) / true value x 100%

It can also be related to the percentage error of the full measuring range:

= ( indicated value – true value  ) / Maximum scale value x 100%

Therefore, if a thermometer is defined as having an accuracy of ±2.5% with a range of 0 to 50°C, then the maximum error is 1.25°C.  This error may not be a problem when measuring in the 40 to 50°C range but at the lower end, 0 to 10°C, an error of ±1.25°C is quite large if defined using the true value.  It is important to select an instrument so that it is not normally operating at the extremes of its measuring range.

Bandwidth = Working frequency range.  Every system has a limited ability to respond to fast moving stimuli.  This may be due to mechanical inertia of components within the system or perhaps electrical inductance and capacitance.  The effect of this is to alter the performance of the system depending upon the frequency of the stimulus.  For example, a hi-fi system has a limited bandwidth as a result of its electronic components and the mechanical inertia of the speakers.  The hi-fi’s output for a range of fixed amplitude but varying frequency inputs could be plotted as follows:

Bandwidth is the range of frequencies for which the gain is within 1/Ö2 (70.7%) of its peak value.  It is generally limited to specifying the frequency response of amplifiers where the output is measured in dB and the bandwidth is then the range of frequencies for which the gain is within 3dB of its peak value.

Full Scale Deflection: A term that has its origins in the deflection of a needle on a meter such as a voltmeter or ammeter.  It is equivalent to the range (see below) of an instrument and is sometimes used instead of this term.

Hysteresis.  This refers to the situation where different readings (outputs) are sometimes observed for the same input because the input was approached from different directions.  For example a thermometer exposed to an increasing temperature input (i.e. going from 0 to 100°C) may show a slightly different profile to that for the decreasing input (i.e. decreasing from 100 to 0°C).

Hysteresis is often noticeable in mechanical systems where degradation of parts due to wear create slightly different results when the direction of the input is reversed.  Imagine two cogs that have small gaps between the teeth due to wear.  This will create hysteresis.

Linearity.  This is usually referred to as non-linearity.  It is the difference between actual and ideal straight line behaviour.  One way to define non linearity is to divide the maximum non linearity value by the full scale deflection.

Linear:                                                                               Non-linear

Loading effects.  Sensors (and hence instruments) work by removing energy from the system they are connected to.  As a result of this they change the state of the system.  This is known as a loading effect.  In other words, the parameter that is being measured is changed in some way by the method of measurement.  Flow measurement is often implemented by introducing a restriction in a pipe which changes the flowrate.  Another example is the electrical loading effect where an electrical meter which has an internal resistance affects the voltage it is measuring.

Offset, Drift : a measurement must be made with respect to a known datum or base line.  It is very common and convenient to adjust the output of the instrument to zero at the datum.  For example, a thermometer is set up to display zero at the freezing point of water.  A pressure gauge is adjusted to read zero when open to atmosphere.

However, the output signal may be offset from zero by some amount.  It is often possible to adjust the instrument to remove this offset.  For example, a bathroom weighing scales can be adjusted to display zero when no one is standing on it.

A common problem with instruments is that the output at the datum drifts and introduces an error to the measurement.  All sensors are affected by drift to some extent whether it be short term or long term.  Short term drift is usually associated with changes in temperature or electronics stablising.  Long term drift is usually associated with aging of the transducer.

Precision: the reproducibility with which repeated measurements of the same variable can be made under identical conditions.  An instrument can be precise but inaccurate and, likewise, it is possible to have an accurate but imprecise instrument.  See below:

Which is preferable - precise but inaccurate or accurate but not precise?

Range: The total range of values an instrument is capable of measuring.  For a standard thermometer this is 0 to 100°C.  This is the same as the full scale.

Repeatable: An instrument is repeatable if it produces a particular output when a certain input is applied in spite of the passage of time.

Resolution : smallest change in input signal needed to produce a change in the output signal

Sensitivity is defined as the output over the input (this is also called the gain of the instrument).  Static sensitivity is the sensitivity exhibited during steady state conditions.  Sensitivity has units which depend on the measuring system.  For example, a temperature measuring system that uses a platinum resistance temperature device (RTD) produces a change in resistance as the temperature changes.  The input is temperature and the output is resistance.  The output over the input is therefore,

### Sensitivity = DR/DTUnits = W/°C

Overall sensitivity – a measurement system consists of a number of devices.  If the sensitivities of these devices are K1, K2, K3, etc., then the overall sensitivity is the product of the individual sensitivities, K1xK2xK3xetc.

Span : range of input signals corresponding to range of output signal (i.e. largest input signal which can be displayed/indicated – smallest input signal which can be displayed/indicated).  For a standard thermometer this is 100 - 0 = 100°C.  If the thermometers range is -30 to 220°C, then the span is equal to 250°C.

Stability: Output is constant when the input is constant.

Tolerance is the maximum error.  A 1000W resistor with a tolerance of ±5% has an actual resistance between 950 and 1050W.