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1. Today • General transducer model • How to read a datasheet • Least Square Method

2. General Transducer Model Physical property information Numerical data Measurement system Measurement chain TRANSDUCER Data Acquisition system - ADC - Filters Conditioning and Amplification MEASURAND DATA PRESENTATION SENSOR PROBE Electrical signal Measuring Instrument

3. Terminology pinpoint • “probe”:external part of sensor or transducer, usually handheld • “sensor”:element of the transducer directly affected by the measurand • “transducer”:device that provides an output quantity having a relationship with the quantity of the measurand • “measurement instrument”:device intended to be used to make measurements, standalone or in conjunction with any other device • “measurement system”:complete set of measuring instruments and any other equipment needed to carry out specified measurement • “measurement chain”:series of element of measuring systems that constitutes the path from the input to the output

4. General Transducer Model • Probe: optional, external, part of the sensor or of the transducer directly in connection with the measurand or immersed in it, usually handheld or detachable. • Example:moisture content probes are a couple of electrodes inserted in the material whose humidity is to be measured. • Note:in some fields the term probe and the term sensor are used as synonyms, due to the fact that some common sensor (such as thermocouples) are mostly defined by their probe part. probes

5. General Transducer Model • Sensor: primary part of the transducer, directly affected by the measurand and by the measuring principle • Example:Rotor of turbine flow meters, sensing coil of a PT100. In piezo-accelerometers the sensor is actually a block of quartz excited by the compression of a small mass inside the transducer. In this case the transducer is composed by the sensor and the circuitry needed to transfer out the charges information.

6. General Transducer Model • Transducer:device that provides an output quantity having a relationship with the quantity of the measurand. Usually the relation is linear, although others are possible. • Example:in potentiometers the transducer is the composition of running cursor on a fixed resistance (the sensor) and of the supply and measurement circuitry.

7. General Transducer Model MEASURING SYSTEM MEASURING INSTRUMENT CONDITIONING TRANSDUCER DATA ACQUISITION SENSOR PROBE* *not external

8. General transducer model influencing parameters qin qout TRANSDUCER INPUT OUTPUT measurand data display Unlike a physical model it does not account for the internal assembly of the transducer but only for the relation between input and output of the transducer, where the input is the measurand and the output is the measurement display.

9. General Transducer Model • Suitable for every transducer regardless of the physical principles used for measuring • Allows for composition of elementary transducer into a complex one • Relies on input and output for a definition incapsulating every internal aspect in an input/output relation affected by uncertainty Measure=f(Reading) This relation can be found in the calibration chart as a calibration curve

10. Static calibration: Calibration Diagram ConfidenceIntervals Calibration Curve TRANSDUCER Full Scale Input Measure Range Full Scale Output Reading Range

11. Static calibration: Calibration Diagram Calibration Curve TRANSDUCER ConfidenceIntervals

12. Static calibration: Calibration Diagram TRANSDUCER ks: static sensibility at a given point [output/input] Offset: value of output when input is null [output]

13. General Transducer Model • Static sensitivity:prime derivative of the output of a transducer on the input, when both output and input are not function of time. • Offset:Constant value of reading whereas input is null. If not corrected leads to systematic error or bias. • Resolution:smallest change in the input that leads to a detectable change in the output

14. General Transducer Model • <Influencing effect> sensitivity:prime derivative of the output of a transducer on the interfering or influencing effect, in static condition. • Linearity:Deviation of the input/output relation from a linear model assumed, usually the first uncertainty contributor. • Hysteresis:Deviation of the input/output relation in its upward phase with respect to its downward phase. • Accuracy:Uncertainty associated with a transducer only, usually a composition of linearity effect, hysteresis and repeatability.

15. General transducer model influencing parameters qin qout TRANSDUCER INPUT OUTPUT measurand data display How can I identify the relation between input and output without knowing the inside of my black box model?

16. Static calibration: transducer model influencing parameters qin qout TRANSDUCER INPUT OUTPUT CALIBRATION: the procedure used to assess the relation between the output and the input of a transducer if all influencing parameters are controlled within working range measurand data display BY COMPARISON AGAINST A STANDARD SAMPLE BY COMPARISON AGAINST A REFERENCE TRANSDUCER

17. Static calibration: Calibration Diagram ConfidenceIntervals Calibration Curve TRANSDUCER Full Scale Input Measure Range Full Scale Output Reading Range

18. Static calibration: Calibration Diagram Calibration Curve TRANSDUCER ConfidenceIntervals

19. Static calibration: Calibration Diagram TRANSDUCER ks: static sensibility at a given point [output/input] Offset: value of output when input is null [output]

20. Static calibration: transducer model BY COMPARISON AGAINST A STANDARD SAMPLE BY COMPARISON AGAINST A REFERENCE TRANSDUCER The uncertainty of the standard sample or of the reference transducer SHOULD BE less than a tenth of the uncertainty desired to be associated with the forecast… standard sample reference transducer reading reading measurement result CALIBRATION DIAGRAM CALIBRATION

21. International System of Units (SI) BIPM prototypes (implementation of SI definitions) National Metrology Institute(INRIM in Italy) International standards National standards Accredited calibration laboratory (SIT laboratories in Italy) company calibration centre Company reference standards Reference standards in-house calibration section Working factory standards company measuring equipment