Bài giảng Sensors and analytical devices - Part B: Sensors Characteristics - Nguyễn Công Phương

Nguyễn Công Phương Sensors and Analytical Devices Sensors Characteristics Contents A. Introduction B. Sensors Characteristics I. Static Characteristics II. Dynamic Characteristics C. Some Basic Measurement Methods D. Measurement Systems sites.google.com/site/ncpdhbkhn 2 Static Characteristics 1. Accuracy 2. Precision 3. Repeatability 4. Reproducibility 5. Stability 6. Error 7. Noise 8. Drift 9. Resolution 10. Minimum detectable signal 11. Calibration curve 12. Sensitivity 13. Linearity 14. Selectivity 15. Hysteresis 16. Measurement range 17. Response & recovery time sites.google.com/site/ncpdhbkhn 3 Accuracy • Accuracy: the correctness of a sensing system’s output in comparison to the actual value of a measurand. • To assess the accuracy: – The system is benchmarked against a standard measurand, or – The output is compared with a measurement system with a superior accuracy More accurate Less accurate 25_meter_precision_and_50_meter_pistol_target-svg/ sites.google.com/site/ncpdhbkhn 4 Precision • Precision: the capacity of a sensing system to give the same reading when repetively measuring the same measurand under the same condition. • It is a statistical parameter & can be assessed by the standard deviation (variance) of a set of readings of the system for similar inputs Low precision High precision High precision Low accuracy Low accuracy High accuracy sites.google.com/site/ncpdhbkhn 5 Repeatability • When all operating & environmental conditions remain constant, repeatability is the sensing system’s ability to produce the same response for successive measurements. • It is closely related to precision. Temperature The actual temperature 10:00 10:02 20:00 20:02 Time 10:01 20:01 sites.google.com/site/ncpdhbkhn 6 Reproducibility • The sensing system’s ability to produce the same responses after measurement conditions have been altered. sites.google.com/site/ncpdhbkhn 7 Stability • The sensing system’s ability to produce the same output value when measuring the same measurand over a period of time. sites.google.com/site/ncpdhbkhn 8 Static Characteristics 1. Accuracy 2. Precision 3. Repeatability 4. Reproducibility 5. Stability 6. Error 7. Noise 8. Drift 9. Resolution 10. Minimum detectable signal 11. Calibration curve 12. Sensitivity 13. Linearity 14. Selectivity 15. Hysteresis 16. Measurement range 17. Response & recovery time sites.google.com/site/ncpdhbkhn 9 Error • Error is the difference between the actual value of the measurand and the value produced by the sensing system. • It can be systematic or random. Absolute error Output  Truevalue Output Truevalue Relative error  Truevalue sites.google.com/site/ncpdhbkhn 10 Noise • Noise: the unwanted fluctuations in the output signal of the sensing system, when the measurand is not changing. • Electronic noise: thermal energy causes charge carriers to move in random motion, which results in random variations of current and/or voltage. • Shot noise: the random fluctuations, which are caused by the carriers’ random arrival time, produce shot noise. • Generation – recombination noise: it is produced from the generation & recombination of electrons & holes in semiconductors • Pink noise (or 1/f noise): in this type of noise the components of the frequency spectrum of the interesting signals are inversely proportional to the frequency. sites.google.com/site/ncpdhbkhn 11 Drift • It is observed when a gradual change in the sensing system’s output is seen, while the measurand actually remains constant. • It is the undesired change that is unrelated to the measurand. Temperature The actual temperature Time sites.google.com/site/ncpdhbkhn 12 Resolution • Resolution (sometimes discrimination): the minimal change of the measurand that can produce a detectable increment in the output signal. • It is strongly limited by any noise in the signal. sites.google.com/site/ncpdhbkhn 13 Minimum Detectable Signal • Minimum Detectable Signal (MDS) is the minimum signal increment that can be observed, when all interfering factors are taken into account. • When the increment is assessed from zero, the value is generally referred to as threshold or detection limit. • If the interferences are large relative to the input, it will be difficult to extract a clear signal & small MDS can not be obtained. sites.google.com/site/ncpdhbkhn 14 Static Characteristics 1. Accuracy 2. Precision 3. Repeatability 4. Reproducibility 5. Stability 6. Error 7. Noise 8. Drift 9. Resolution 10. Minimum detectable signal 11. Calibration curve 12. Sensitivity 13. Linearity 14. Selectivity 15. Hysteresis 16. Measurement range 17. Response & recovery time sites.google.com/site/ncpdhbkhn 15 Calibration Curve • Calibration curve: the relationship between the measured variable x & the signal variable generated by the system y. • A sensing system has to be calibrated against a known measurand to assure that the sensing results in correct outputs. y x sites.google.com/site/ncpdhbkhn 16 Sensitivity • Sensitivity: the ratio of the incremental change in the sensor’s output (Δy) to the incremental change of the measurand in input (Δx). • An ideal sensor has a large & preferably constant sensitivity in its operating range. y y x x sites.google.com/site/ncpdhbkhn 17 Linearity • Linearity: the closeness of the calibration curve to a specified line. • The degree of resemblance to a straight line describes how linear a system is. sites.google.com/site/ncpdhbkhn 18 Selectivity • Selectivity: the sensing system’s ability to measure a target measurand in the presence of other interferences. sites.google.com/site/ncpdhbkhn 19 Hysteresis • Hysteresis: the difference between output readings for the same measurand, depending on the trajectory followed by the sensor. • It may cause false & inaccurate readings. y x sites.google.com/site/ncpdhbkhn 20 Measurement Range • Measurement range (dynamic range or span): the maximum & minimum values of the measurand that can be measured with a sensing system. • All sensing systems are designed to perform over a specified range. • Signals outside of this range may be unintelligible, cause unacceptably large inaccuracies, & may even result in irreversible damage to the sensor. sites.google.com/site/ncpdhbkhn 21 Response and Recovery Time • Response time: the time a sensing system requires to reach a stable value when it is exposed to a measurand. • Recovery time: the time a sensing system requires to reach a stable value when it is no longer exposed to a measurand. sites.google.com/site/ncpdhbkhn 22 Contents A. Introduction B. Sensors Characteristics I. Static Characteristics II. Dynamic Characteristics C. Some Basic Measurement Methods D. Measurement Systems sites.google.com/site/ncpdhbkhn 23 Dynamic Characteristics (1) • Applied to time – varying measurands. • To describe the sensing system’s transient properties. • Can be used to define how accurately the output signal is employed for the description of a time – varying measurand. • Deal with issues such as the rate at which the output changes in response to a measurand alteration, and how these changes occur. sites.google.com/site/ncpdhbkhn 24 Dynamic Characteristics (2) x() t Linear time invariant y() t (LTI) system dn y()()() t d n1 y t dy t a a ...  a  a y ( t )  ndtn n1 dt n1 1 dt 0 dm1 x()()() t d m  2 x t dx t b  b ...  b  b x ( t )  b mdtm1 m1 dt m  2 2 dt 1 0 x() t t dn y()()() t d n1 y t dy t a  a ...  a  a y ( t )  b ndtn n1 dt n1 1 dt 0 1 sites.google.com/site/ncpdhbkhn 25 Dynamic Characteristics (3) x() t Linear time invariant y() t (LTI) system b1 a0 y( t ) b 1 or y ( t )   K a0 Zero – order system sites.google.com/site/ncpdhbkhn 26 Dynamic Characteristics (4) x() t Linear time invariant y() t (LTI) system dy() t a a y() t  b (First – order system) 1dt 0 1 a1 dy() t b 1  y() t  1 a0 dt a 0 dy() t 0.8  y(), t  K 1 dt 0.6 K(1 1/ e )  0.6321 K a b y(t)  1; K  1 0.4 a0 a 0 t  0.2  y( t )  K (1  e )  0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 t (s) sites.google.com/site/ncpdhbkhn 27 Dynamic Characteristics (5) Ex. A car is equiped with altitude & temperature sensors & associated measurement systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The o o temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude sensing system is a zero – order response. The temperature sensing system has a first – order response with τ = 10s. a) What are the temperature & height measurements at 10, 20, 30, & 40s? b) What are the temperature measurements if τ = 1s? vx 3.6km/h  1m/s x( t ) vx t  1  t  t x dy() t  y()() t  x t dt dTm () t 10Tm ( t )  T x ( t ) dt T() t T() t x Linear time invariant m 20  0.1x (LTI) system y() t 20  0.1t x() t sites.google.com/site/ncpdhbkhn 28 Dynamic Characteristics (6) Ex. A car is equiped with altitude & temperature sensors & associated measurement systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The o o temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude sensing system is a zero – order response. The temperature sensing system has a first – order response with τ = 10s. a) What are the temperature & height measurements at 10, 20, 30, & 40s? b) What are the temperature measurements if τ = 1s? dT() t dT() t 10m T ( t )  20  0.1 t m 0.1T ( t )  2  0.01 t dt m dt m 0.1dt ()t e  e0.1t e0.1t (2 0.01 t ) dt  C 2e0.1t dt 0.01 te 0.1 t dt  C T() t      m e0.1t e0.1t 20e0.1t 0.1 tde 0.1 t  C 20e0.1t 0.1 te 0.1 t  e 0.1 t dt  C     e0.1t e0.1t sites.google.com/site/ncpdhbkhn 29 Dynamic Characteristics (7) Ex. A car is equiped with altitude & temperature sensors & associated measurement systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The o o temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude sensing system is a zero – order response. The temperature sensing system has a first – order response with τ = 10s. a) What are the temperature & height measurements at 10, 20, 30, & 40s? b) What are the temperature measurements if τ = 1s? 20e0.1t 0.1 te 0.1 t  e 0.1 t dt  C 20e0.1t 0.1 te 0.1 t  10 e 0.1 t   C T() t    m e0.1t e0.1t 21  0.1t  Ce0.1t 21  0.1  0 Ce0.1  0  20 o Tm (0) 20 C C  1 0.1t Tm ( t )  21  0.1 t  e sites.google.com/site/ncpdhbkhn 30 Dynamic Characteristics (8) Ex. A car is equiped with altitude & temperature sensors & associated measurement systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The o o temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude sensing system is a zero – order response. The temperature sensing system has a first – order response with τ = 10s. a) What are the temperature & height measurements at 10, 20, 30, & 40s? b) What are the temperature measurements if τ = 1s? o o 0.1t Tx( x ) 20 C  0.1 t ; T m ( t )  21 C  0.1 t  e Time (s) Altitude (m) Real temp (oC) Measured temp (oC) Temp error (oC) 0 0 20 20 0 10 10 19 19.6321 0.6321 20 20 18 18.8647 0.8647 30 30 17 17.9502 0.9502 40 40 16 16.9817 0.9817 sites.google.com/site/ncpdhbkhn 31 Dynamic Characteristics (9) Ex. o o 0.1t Tx( x ) 20 C  0.1 t ; T m ( t )  21 C  0.1 t  e 20 Actual temperature Measured temperature C) o 19 18 Temperature ( 17 16 0 5 10 15 20 25 30 35 40 Time (s)/Altitude (m) 1 C) o 0.8 0.6 0.4 0.2 Temperature error ( 0 0 5 10 15 20 25 30 35 40 Time (s)/Altitude (m) sites.google.com/site/ncpdhbkhn 32 Dynamic Characteristics (10) Ex. A car is equiped with altitude & temperature sensors & associated measurement systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The o o temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude sensing system is a zero – order response. The temperature sensing system has a first – order response with τ = 10s. a) What are the temperature & height measurements at 10, 20, 30, & 40s? b) What are the temperature measurements if τ = 1s? o o 0.1t Tx( x ) 20 C  0.1 t ;  10  T m ( t )  21 C  0.1 t  e o o t Tx( x ) 20 C  0.1 t ;  1  T m ( t )  20.1 C  0.1 t  0.1 e Time (s) Altitude (m) Real temp (oC) Measured temp (oC) Temp error (oC) 0 0 20 20 0 10 10 19 19.1 0.1 20 20 18 18.1 0.1 30 30 17 17.1 0.1 40 40 16 16.1 0.1 sites.google.com/site/ncpdhbkhn 33 Dynamic Characteristics (11)  = 10  = 1 20 Actual temperature 20 Actual temperature Measured temperature Measured temperature C) C) o 19 o 19 18 18 Temperature ( 17 Temperature ( 17 16 16 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Time (s)/Altitude (m) Time (s)/Altitude (m) C) 1 C) 1 o o 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 Temperature error ( Temperature error ( 0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Time (s)/Altitude (m) Time (s)/Altitude (m) sites.google.com/site/ncpdhbkhn 34 Dynamic Characteristics (12) x() t Linear time invariant y() t (LTI) system d2 y()() t dy t a a  a y() t  b (Second – order system) 2dt2 1 dt 0 1 1d2 y ( t ) 2 dy ( t )   y() t  K 2dt 2  dt a 2  0 : the undamped naturalfrequency a2 a   1 a a : thedampening ratio 2 0 2 b K  1 a0 sites.google.com/site/ncpdhbkhn 35 Dynamic Characteristics (13) 1d2 y ( t ) 2 dy ( t )  y() t  K 2dt 2  dt 2 1.8 1.6 1.4 1.2 1 y(t)/K 0.8  = 0 0.6  = 0.1  = 0.2 0.4  = 0.4  = 1.0 0.2  = 2.0  = 0.707 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) sites.google.com/site/ncpdhbkhn 36