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Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 v

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    GENERALIZED PERFORMANCECHARACTERISTICS OF

    INSTRUMENTS

    Lecture 6Instructor : Dr Alivelu M Parimi

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    Previously discussed

    Concept of understanding function of any instrument in terms

    of functional elements has been discussed.

    Classification of instruments as Null/deflection, contact/non-

    contact, manual/automated, intelligent/dumb, analog/digitalhas also been discussed with help of many examples.

    Identification of various inputs affecting output and methods

    to remove effect of spurious inputs has also been discussed.

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    Outline in this chapter

    Static calibration

    Static characteristics

    Dynamic characteristics

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    Introduction

    Detailed specifications of the functional characteristics of an

    instrument are termed as performance.

    Instrument performance has been divided into two sub areas:

    Static Characteristics and Dynamic characteristics.

    Both these types of performance is based on the response ofan instrument to a particular input.

    For Static characteristics it is assumed that instrument is not

    subjected to time varying inputs like acceleration, vibration,

    shock and the measurand is changing slowly. The dynamic performance parameters specify how the output

    changes with time in response to time-varying inputs.

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    Static CALIBRATIONS

    Static calibration refers to a situation in which all inputs(desired, interfering and modifying) except one are kept atsome constant values.

    Then the input under study is varied over some range ofconstant values, which causes the output to vary over somerange of constant values.

    The input-output relations developed in this way comprise a

    static calibration valid under the stated constant conditions ofall the other inputs.

    If overall rather than individual effects were desired, thecalibration procedure would specify the variation of several

    inputs simultaneously.

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    Static Characteristics

    Accuracy,

    Precision,

    Range and Span,

    Resolution and Threshold,

    Sensitivity,

    Linearity,

    Drift and Hysteresis.

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    Static Characteristics:

    Accuracy, The accuracy is defined as the closeness of the agreement

    between the result of a measurement and the true value of

    the measurand

    Accuracy is measured by the absolute and relative errors.

    Absolute error is the difference between a measurement and itstrue value.

    Relative error is the ratio of an absolute error to the

    true/specified /theoretically correct value of the quantity.

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    Accuracy Accuracy is expressed in the following ways:

    Point accuracy: This is the accuracy of the instrument only at onepoint on its scale. The specification of this does not give anyinformation about the accuracy at other points on the scale and itdoes not give any information about the general accuracy of thesystem.

    Accuracy as a percentage of Full Scale range: when an instrument

    has uniform scale, its accuracy may be expressed in terms of scalerange. The accuracy of thermometer having a range of 500oC may beexpressed as 0.5% of scale range meaning reading may be in errorby + 2.5oC.

    % of Full Scale deflection =

    Accuracy as a percentage of the True value: Accuracy is specified interms of the true value of the quantity being measured.

    % of true value =

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    100)(x

    ValueScaleMaximum

    TrueValueValueMeasured

    100)(x

    ValueTrue

    TrueValueValueMeasured

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    Accuracy: Example

    Example

    A Voltmeter having a range 0 - 2V, 0 - 50V and 0 - 100V makes

    measurement with an accuracy of 1% FSD (full scale

    division). What will be the range of the readings when

    voltmeter is used to determine voltage of i) 1V on 2V scale ii)5V on 50V scale iii)5V on 100V scale

    Solution:

    = 0.02 So well read 1V 0.02V

    = 0.5 So well read 5V 0.5V

    = 1.0 So well read 5V 1V

    Note: Using a scale whose maximum value is close to

    measurand gives better accuracy. 9

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    Static Characteristics :

    Precision It is the measure of the reproducibility of the instruments i.e., given a

    fixed value of a quantity, precision is a measure of how close thereadings are to each other. Two terms closely related to precision are:Repeatability and Reproducibility.

    Repeatabilitydescribes closeness of output readings when the same

    input is applied repeatedly over a short period of time, with the samemeasurement conditions, same instrument and observation, samelocation and same conditions of use maintained throughout. This is alsoknown as the inherent precision of the measurement equipment.

    Reproducibility describescloseness of output readings for the same

    input when there are changes in the method of measurement, observer,measuring instrument, location, condition of use and time ofmeasurement. It is the degree of closeness with which a given valuemay be repeatedly measured. Perfect reproducibility means that theinstrument has no drift. No drift means that with a given input themeasured values do not vary with time. 10

    Precision does not guarantee accuracy but

    accuracy guarantees precision.

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    Comparison Between

    Accuracy and Precision

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    Example

    Example 3.3

    50 V is measured with certain voltmeter. Four readings taken

    are 53, 52, 51 and 52 V. Find the accuracy and precision.

    Solution

    Maximum deviation from true value of 50 V is 3 V, so accuracy

    is not better than 6%.

    Mean reading is 52 and maximum deviation from mean value

    is 1V, so precision is =

    12

    %2

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    Static Characteristics :Range

    and Span, The region between the limits within which the instrument is

    designed to operate is called range of instrument, expressedby stating lower and upper values.

    Span represents algebraic differences between the upper andlower range values.

    Example

    The instrument span is given by x (max) - x(min)

    For a pyrometer calibrated between 0 and 10000C ,

    the range is 0 to 10000C and span is 10000C.

    For a thermometer calibrated between 200C and 500C

    the range is 200C to 500C and span is 300C.

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    Static Characteristics:

    Resolution and Threshold, Threshold is the minimum value of input necessary to cause a

    detectable change from zero output.

    The range of values for which the instrument does not respond iscalled dead-zone.

    In digital systems it is the input signal which is necessary to cause LSD

    of output readings to change.

    Resolution of an instrument is defined as the minimum resolvablevalue of the measurand.

    It is the least count of instrument which is the smallest change in

    input for which there will be a change in output. Both are not zero because of friction, backlash, and inertia of moving

    parts and spacing of graduations.

    Example: potentiometer14

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