The accuracy of a sensor

We will begin our analysis of 'Accuracy' by first setting out the factors that
must be taken into account.

Fundamentally, 'Accuracy' simply describes how closely the indicated value
represents the actual measurand being monitored, whilst taking into account
all possible sources of error that are relevant to the application.

It is our experience that accuracy is very often confused with linearity, which
is of course only one source of potential error, albeit quite a significant one.
In fact in the practical world the quoted accuracy of a measurement should
include at least some and possibly all of the following sources of error:

Zero temperature coefficient
Gain temperature coefficient
Long term stability
Calibration equipment errors and the calibration standard

Clearly then, accuracy can be closely defined for a given set of operating
conditions but it is vitally important to take into account all contributing
factors if the very best results are required.

Furthermore, it must be remembered that not all manufacturers will define
these parameters in exactly the same way, so choosing the best device for
your job can become quite a challenge.

Let us examine the issues of Repeatability, Resolution and Hysteresis.

It should be appreciated that there are two main aspects to these potential
sources of error. Firstly there is the inherent performance of the transducer
and secondly the quality of the means of measurement of that performance
i.e. the calibration equipment. It is generally accepted that the test equipment
must be at least five times more accurate than the device being tested in
order to be confident that the claims for the transducer are correct.

This is simply the ability of a transducer to consistently reproduce the same
output signal for repeated application of the same value of the measurand.
It is a clear factor and one that varies with different methods of sensing the
measurand. For instance an inductive or capacitive method will be potentially
better than a strain gauged device, typically 0.001% and 0.05% respectively.

This parameter represents the smallest increment of the measurand that can
be determined by the transducer. The resolution of most modern transducers
is good and mainly limited by the noise levels ~of the associated electronic
circuits. In general the resolution of most analogue sensing techniques,
e.g. strain gauge, inductive, capacitive would be well within 10 parts per
million, but potentiometers, incremental digital and absolute digital devices
have resolutions determined directly by design and mainly limited by the
number of bits.

So, resolution is possibly the least worrying of these sources of error because
it is either clearly defined or not very relevant.

This represents the difference in output from a transducer when any particular
value of the measurand is approached from the low and the high side.

In general, hysteresis occurs when a sensing technique relies on the stressing
of a particular material such as strain gauged metals, and would have a worst
case value of 0.2% for a low-cost device. Some transducers such as inductive
or capacitive-based displacement transducers do not exhibit this error at all
because they do not involve the stressing of any material to convert the
measurand into an electrical signal.

In summary then, these three error factors together could contribute up to
0.26% FS error in a transducer such as a strain gauged load cell and pressure
transducer, or up to 0.010% FS error in a device such as an LVDT or capacitive
based transducer as these do not display any significant hysteresis effects.
These errors are fixed physical characteristics of a particular device and are
generally independent of temperature.

Temperature Coefficients
All types of transducers exhibit two sources of temperature error due to:

(a) Zero coefficient

(b) Gain coefficient

Sometimes these two elements can be taken as a combined coefficient but
this will not necessarily be equal to the simple addition of the zero and gain
coefficients, but rather the sum of the two, bearing in mind that the value of
these coefficients can be either positive or negative.

The zero coefficient is simply the change of output of the transducer when
set at its zero output condition as the temperature is changed and is expressed
as a percentage of F.S. per degree centigrade (F.S. / °C), or sometimes in parts
per million.

It can be affected by several elements of the device. For instance expansion
or contraction of any mechanical parts, changes of resistance, capacitance or
inductance in the overall electrical circuit, or even changes in magnetic
properties in some devices.

Furthermore, if the device includes complex electronic components then it is
certain that changes in these will also affect the overall output of the device
as the ambient temperature changes.

This error would typically be ± 0.001% to ±0.01% F.S. / °C for non-electronic,
to 0.01% to 0.02% F.S. / °C for transducers having 'built-in' electronic circuits.

Gain changes with temperature are caused by many of the same basic constituent
parts as zero changes, but in this case they have a direct effect on the sensitivity
or the output per unit measurand.

The errors from this source would be typically in the same ranges as that for the
zero coefficient. We could find that a simple addition of these errors would result
in a total error for an electronic device that could yield a coefficient of the order
of 0.04%/°C. In practice, the combined error of zero and gain coefficients would
give a typical error of say 0.02 to 0.03%/°C. This can be sometimes improved by
using special compensation techniques.

Long-term stability is a factor that is rarely quoted by manufacturers, but of
considerable interest in some applications.

Clearly, it can only really be determined by very long term monitoring in
controlled conditions which for small and relatively inexpensive components
is not practical. It is therefore more likely that initially, at least, a figure will be
quoted based on the long experience of the manufacturer and the knowledge
of the components and techniques incorporated in the design. Obviously the
degree of difficulty is increased by the variation in the conditions under which
the transducer is intended to operate. Depending on the complexity of the
device a typical figure for this would be 0.05% per annum to 1.0% per annum
for fairly benign conditions but may be significantly higher in rugged conditions,
hence the importance of regular calibration checks of the device.

Calibrations are usually canled out in ambient conditions with a temperature
of around 20°C. Generally, there are just two sources of error in the calibration

(a) Human error. Obviously it is important to ensure far as possible that the
minimum amount of human determination is involved in this process. Today
much of it is computerised so that all calculations are accurate and consistent.

(b) Equipment error. The ultimate accuracy of the calibration will of course
be very dependent upon the calibration standard used to input the measurand
to the device under test. It is generally accepted that this should be at least
5 times more accurate than that claimed for the finished transducer and regularly
checked against equipment closely traceable to National Standards. For instance,
a purely mechanical device such as a linear vernier gauge will need more
frequent checking than say a dead weight load or pressure tester.

In concluding our Accuracy in Transducers series, we can say that taking into
account Unearity, Repeatability, Hysteresis, Resolution, temperature coefficients,
long term drift and calibration errors, a device which offers an overall accuracy
of say 1% over a temperature excursion of 100°C is excellent and one that can
offer 0.5% is absolutely exceptional.

In practice for most industrial applications we would see a maximum temperature
range of say 50°C and we would not generally expect to achieve much better
than around 1% overall accuracy under these conditions.

Article supplied by RPD Electronics Ltd
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