The accuracy of a sensor Introduction 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: Linearity Repeatability Resolution Hysteresis 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. Repeatability 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. Resolution 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. Hysteresis 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 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. CALIBRATION ERRORS 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 process: (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 Visit their comprehensive website at www.rdpe.com

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