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Transcript
PERFORMANCE CHARECTERISTICS OF AN INSTRUMENT / MEASURING DEVICE Understanding what is instrument and Measurement system. An Instrument is a device used to determine the value or magnitude of quantity or a variable A measurement system is a combination of functional units namely primary sensing element, secondary element for signal conditioning and final element of display to measure the value or magnitude of a quantity or a variable FUNCTIONAL ELEMENTS OF A MEASUREMENT SYSTEM Secondary Sensing Element (Signal Conditioning) Primary Sensing Element (Sensor) Final Element (Display) Performance Characteristics of an Instrument We need to understand the performance characteristics of an instrument in order to obtain a measured value which is closest to the True value of the measurement TRUE VALUE of an Instrument may be defined as the exact error free value of the measuring variable at an ideal state. No Instrument can actually measure the True Value of a measuring variable as an effect of presence of Performance characteristics of that particular instrument. The performance characteristics of an Instrument can be classified into two types 1. Static Characteristics 2. Dynamic Characteristics Performance Characteristics of an Instrument Static Charecterstics Dynamic Characteristics Static Characteristics of an Instrument may be defined as the characteristics of an Instrument whose measuring variable doesn’t vary with time. Dynamic Characteristics of an Instrument may be defined as the characteristics of an Instrument whose measuring variable varies with time Static Characteristics of an Instrument Accuracy It is the closeness with which an instrument reading approaches the true value of the quantity being measured. Thus accuracy of a measurement means conformity of truth. Accuracy may be specified in terms of inaccuracy or limits of error can be expressed in following ways 1. Point Accuracy: This is the accuracy of the instrument only at one point on its scale. The specification of this accuracy doesn’t give any information about the general accuracy of the instrument. However range of instrument can be obtained by drawing up a table which specifies the accuracy at number of points throughout the range of the scale. * see Annexure I for definitions of Scale Range and Scale Span 2. Accuracy as a Percentage of Scale Range: When a instrument has a uniform scale its accuracy may be expressed in terms of scale range. For example, the accuracy of a thermometer having a range 500₀C may be expressed as ± 0.5% of the scale range. This means that the accuracy of the thermometer when the reading is 500₀C is ±0.5% which is negligible but when the reading is 25₀C that is 20% of scale range the error is as high as (500/25) x (±0.5) = 10% and therefore specification of accuracy in this manner is highly misleading. 3. Accuracy as a Percentage of a True value: The best way to conceive the idea of accuracy is to specify it in terms of the true value of the quantity being measured that is within ±0.5 percent of true value. This statement means thus as the reading get smaller so do the errors. Thus at 5% of Full scale the accuracy of the instrument would be 20% better than that of an Instrument which is accurate to ±0.5 % of scale range. Precision It is a measure of the reproducibility of the measurements. That is, given fixed value of a quantity, Precision is a measure of the degree or an agreement within a group of measurements. Precision is composed of two characteristics namely conformity and the number of significant figures. i.e. Conformity and Significant figures Conformity is nothing but a group of measurements that lie within the range of true value. If an instrument is precise and reproducing values close to true value, but if instrument has a zero adjustment error or parallax error then the groups of measurements are precise but don’t confirm the accuracy of the instrument. Thus precision is a necessary but not sufficient condition for accuracy. Perfect set precise values indicate no drift in the instrument. *see Annexure I for definition and categories of Drift Significant figures indicate the error created by the limitation of the scale. Suppose a resistor of 139890Ώ is being read as 1.4 M Ώ and the same reading is observed throughout the group of measurements because the scale of the instrument is confined to that value. Thus it indicates that conformity is a necessary but not sufficient condition for Significant figures. Sensitivity The static sensitivity of an Instrument or a measurement system is the ratio of the magnitude of the output signal to that of the magnitude of the input signal or quantity being measured. To understand the sensitivity at a point of measurement See the figures Sensitivity (a) when the curve is linear and (b) when the curve is non linear of drawings as specified in ANNEXURE II 𝑆𝑡𝑎𝑡𝑖𝑐 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 ∆𝑞𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑖𝑛𝑝𝑢𝑡 ∆𝑞 𝑖𝑛𝑝𝑢𝑡 Linearity One of the best characteristics of an instrument is considered to be linearity which is nothing but output being linearly proportional to the input. Most of the systems require a linear behavior as it is desirable. This is because the conversion from the scale reading to the corresponding measurement value of input quality is the most convenient if one merely has to multiply by a fixed constant rather than consulting a non linear calibration curve or compute from non linear calibration equations There are many definitions of linearity that exist. However, linearity defined in terms of Independent Linearity is most preferable in many cases. The computation of independent linearity is done with reference to the straight line showing the relation between output and input. *See the figure of Linearity deviation in Annexure II The non linearity in the curve may be defined as With respect to actual reading 𝑁𝑜𝑛 𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦 = 𝑀𝑎𝑥 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑠𝑡 𝑙𝑖𝑛𝑒 X 100 𝐴𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 With respect to full scale deflection 𝑁𝑜𝑛 𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦 = 𝑀𝑎𝑥 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑠𝑡 𝑙𝑖𝑛𝑒 X 100 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 Resolution The smallest increment in the input (quantity being measured) which can be detected with certainty by an instrument is its Resolution or Discrimination. So Resolution is the smallest input change while the Threshold is defined as smallest measurable input Hysteresis Hysteresis is a phenomenon which depicts different output effects when loading and unloading whether it is a mechanical system or a electrical system and for that matter any system. Hysteresis is a non coincidence of loading and unloading curves. Hysteresis in a system arises due to the fact that all the energy put into the stressed parts when loading is not recoverable upon unloading. *See Annexure I for Second law of thermodynamics and Annexure II for the drawing on Hysteresis curve. Dead Zone It is defined as the largest change of input quantity for which there is no output of the instrument. For Example the input applied to the instrument may not be sufficient to overcome the friction and will, in that case, not move at all. It will only move when the input is such that it produces a driving force which can overcome friction forces. Other factors which produce dead zone are backlash and high hysteresis in the instrument. The term Dead zone is sometimes used interchangeably with terms of Hysteresis. However it may defined as a total range of input values possible for a given output and may thus be numerically twice the Hysteresis. Loading Effect The incapability of the system to faithfully measure, record or control the input signals (measurand) in an undistorted form is called Loading Effect Input Impedance **The figure Input Impedance circuit in Annexure II shows a voltage signal resource and input device connected across it. The magnitude of the impedance of element connected across the signal source is called Input Impedance The magnitude of the input impedance is given by Zi = ei /ii The instantaneous power extracted by the input device from the signal source is given by P = ei ii = ei2 / zi Thus it is clear from the above equations a low input impedance device connected across the voltage signal resource draws more current and drains more power from signal resource than a high input impedance device. In other words a low input impedance device connected across a voltage signal resource loads the source more heavily than a high input impedance device Output Impedance The output impedance of a device is defined as its equivalent impedance as seen by the load. The definition of output device is only meaningful for an active device at a pair of terminals considered as source. ** See the figure output impedance circuit (a) and (b) in Annexure II The term equivalent impedance implies the device can be represented by a Thevenin’s Equivalent circuit. As in Fig (b) Let eo = voltage appearing across the output terminals of the device when the load is not connected, and eL = voltage appearing across the across the output terminals of the device when the load is connected The output impedance of an active device is defined as zo = eo – eL / iL The above equation conveys the idea that the drop in the output voltage (eo – eL) = il . zo is determined by the output impedance as system is loaded. It is clear from the expression derived the lower the output impedance the lesser is the effect of load on the output voltage. Power loss in voltage source P = (eo – eL) iL = il2 zo Thus, for voltage sources, the lower the output impedance the lower is voltage drop and also lower is the power consumption. Ideally there should not be any loading effect and this requires the output impedance zo of the voltage source be equal to Zero. ANNEXURE I SCALE RANGE AND SCALE SPAN The Scale range of an Instrument is defined as the difference between the largest and smallest reading of the instrument supposing that the highest point of calibration as Xmax while the lowest is Xmin now we can say the range of the instrument is between Xmin and Xmax The scale span of the instrument is given by Xmax – Xmin REPRODUCIBILITY AND DRIFT Reproducibility is the degree of closeness with which a given value may be repeatedly measured. It may be specified in terms of units for a given period of time. Perfect Reproducibility means that the instrument has no drift. No drift means that with given input the measured values don’t vary with time. Drift may be classified into three categories 1. Zero Drift: if the whole calibration gradually shifts due to slippage, permanent set, or due to undue warming up of electronic tube circuits, zero drift sets in. This can be prevented by zero setting. The input output characteristics with zero drift are shown in Fig (a) 2. Span Drift: If there is proportional change in the indication all along the upward scale, the drift is called span drift or sensitivity drift. The characteristics with span drift is shown in fig (b) and the characteristics with both span drift and zero drift are shown in fig (c) 3. Zonal Drift: in case the drift occurs only over a portion of span of an instrument, it is called as zonal drift. See Figures in attached sheet Second Law of Thermo dyanamics: