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5/19/2018 Lecture 6Lecture 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 Lec...

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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 =

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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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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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LSD

Resolution is effectively the smallest change a meter can display. Forinstance a 4 digit voltmeter displaying the 12 volt system battery voltagecould display, as it's smallest change, 0.01 volts. It isn't possible for it todisplay anything smaller than this because there simply aren't enoughdigits available.

All measurements contain some error. The accuracy (or error) is usuallydefined as the percentage error. So a meter with a specified accuracy of1% displaying 12.50 volts, would mean that the actual voltage is within1% of this 12.5 volts, i.e. within the range 12.375 to 12.625 volts.

On top of this is the fact that, in the case of digital instruments, there is

another error. That of the last digit. A typical specification would statesomething like 1% +/-1 LSD. This means the meter will read accuratelyto within 1% of the actual voltage (giving the range in the aboveexample of 12.375 to 12.635 volts) plus or minus 1 Least SignificantDigit. As a 4 digit meter would not have the last digit (the 5) in theabove example, it would display somewhere in the range of 12.37 to12.64 plus or minus 1 LSD giving a final range of 12.36 to 12.65 volts.

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Example

The scale of temperature measurement has 100 uniform

divisions, full scale reading is 200 C and one tenth of a scale

division can be estimated with fair degree of accuracy.

Determine the resolution.

Solution Full Scale Reading = 2000C

There are 100 divisions; therefore each division reads 2C. One

tenth of scale division corresponds to resolution so Resolution

= 0.2 C.

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Sensitivity Static sensitivity or scale factor or gain is the ratio of change in

instrument output to change in magnitude of measurand.

The reciprocal of sensitivity is called deflection factor or inversesensitivity.

Higher sensitivity implies better resolution/threshold.

Example

A Wheatstone bridge requires a change of 7 in the unknown armof the bridge to produce a change in deflection of 3mm of thegalvanometer. Determine the sensitivity. Also determine thedeflection factor.

Solution

Sensitivity =

= = 0.429 mm /

Inverse sensitivity or Scale factor = = 7 / 3mm = 2.33 /mm. 17

inputofmagnitude

responseoutputofmagnitude

7

mm3


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Static Characteristics :

Linearity, The linearity is defined as the departure of the calibration

point from a straight line.

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This is the closeness to a straight line ofthe relationship between the true

process variable and the measurement.

Lack of linearity does not necessarilydegrade sensor performance.

If the nonlinearity can be modeled andan appropriate correction applied to themeasurement before it is used formonitoring and control, the effect of thenon-linearity can be eliminated.


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Static Characteristics: Drift

and Hysteresis.

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Static Characteristics: Drift

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