CHARACTERISTICS OF MEASUREMENT SYSTEMS

• A knowledge of the performance characteristics of an instrument is essential for selecting the most suitable instrument for specific measuring jobs
• The performance characteristics may be broadly divided into two groups, namely

Static characteristics

Dynamic characteristics

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�STATIC and DYNAMICS CHARACTERISTICS OF MEASUREMENT SYSTEMS�

STATIC PERFORMANCE OF INSTRUMENT

• Static characteristics of an instruments are concerned only with steady state readings
• Accuracy and Precision
• Range or Span
• Linearity & Sensitivity
• Repeatability
• Reproducibility
• Hysteresis
• Threshold
• Resolution
• Dead space

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RANGE OR SPAN AND FULL SCALE

• The range or span of an instrument defines the minimum and maximum values of a quantity that the instrument is designed to measure

Example: A particular micrometer is designed to measure dimensions between 50 and 75 mm. What is its measurement range?

Ans: The measurement range is simply the difference between the maximum and minimum measurements. (25 mm)

ACCURACY

• The accuracy of an instrument is a measure of how close the output reading of the instrument is to the true value
• In practice, it is more usual to quote the inaccuracy or measurement uncertainty value rather than the accuracy value of an instrument
• Inaccuracy or measurement uncertainty is often quoted as a percentage of the full-scale reading of an instrument
• Accuracy can be improved by calibration

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PRECISION

• Precision is a term that describes an instrument’s degree of freedom from errors . If a large number of readings are taken of the same quantity by a high-precision instrument, then the spread of readings will be very small
• Accuracy can be improved by calibration but not precision
• If you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Precision is independent of accuracy. You can be very precise but inaccurate

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ACCURACY and PRECISION

REPEATABILITY and REPRODUCIBILITY

• Repeatability and Reproducibility (R & R) Studies evaluate the precision of a measurement system. It is important that the instrument properly calibrated before starting R & R study
• Repeatability describes the closeness of output readings when the same input is applied repetitively over a short period of time, with the same measurement conditions, same instrument and observer, same location, and same conditions of use maintained throughout

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• Reproducibility describes the closeness of output readings for the same input when there are changes in the method of measurement, observer, measuring instrument, location, conditions of use, and time of measurement

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THRESHOLD

• If the input to an instrument is gradually increased from zero, the input will have to reach a certain minimum level before the change in the instrument’s output reading. This minimum level of input is known as the threshold of the instrument.

Linearity

• It is normally desirable that the output reading of an instrument is linearly proportional to the quantity being measured.
• An instrument is considered if the relationship between output an input can be fitted in a line.

I_min

I_max

O_min

O_max

RESOLUTION

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• When an instrument is showing a particular output reading, there is a lower limit on the magnitude of the change in the input measured quantity that produces an observable change in the instrument output.
• One of the major factors influencing the resolution of an instrument is how finely its output scale is divided into subdivisions.

SENSITIVITY

• The sensitivity of measurement is a measure of the change in instrument output that occurs when the quantity being measured changes by a given amount Thus, sensitivity is the ratio:

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DYNAMIC CHARACTERISTICS

• As the input varies from instant to instant output also varies from instant to instant
• This is called dynamic response of the system
• In many applications, the transient response of the system, i.e., the way system settles down to its final steady state conditions is more important than the steady state response.
• It is determined by applying some known variations of input to the sensing element

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• The dynamic characteristics of the instruments are
• Speed of response
• Response Time
• Measured lag
• Fidelity
• Dynamic error

Speed of response

• The speed of response of measuring instrument is defined as the quickness with which an instrument responds to a change in the input signal.
• It gives the information about how fast the system reacts to the changes in the input
• It indicates activeness of the system
• The system should respond very quickly to the changes in the input

Response Time

• Response Time is the time required by instrument or system to settle to its final steady position after the application of the input.

Measured lag

• It is delay in the response of an instrument to a change in the input signal.

(a) Retardation type:

In this case the response of the measurement system begins immediately after the change in measured quantity has occurred.�(b) Time delay:

In this case the response of the measurement system begins after a dead time and after the application of the input.

Fidelity

• It is the ability of a measurement system to reproduce the output in the same form as the input.
• It is the degree to which a measurement system indicates changes in the measured quantity without any dynamic error.
• Supposing if a linearly varying quantity is applied to a system and if the output is also a linearly varying quantity the system is said to have 100 percent fidelity

Dynamic error

• It is the difference between the true value of the quantity changing with time & the value indicated by the measurement system if no static error is assumed.
• It is also called measurement error.�

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Measurement

• Measurement is the process of determining or finding the size, quantity or degree of something .
• The principle dimensional measurement is length; secondary measurement is angle and curvature. You can describe shape without describing size.

TYPES OF MEASUREMENTS

Direct Measurement

• Comparing the unknown with standard
• No mathematical calculations
• Not accurate Human insensitiveness in judgement

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Source: https://physics.nist.gov/cuu/Units/meter.html

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Measurement Types

Indirect Measurement

• Transducer elements which converts the measurand into another form which is then compared with a standard

Deflection Method

• Measurand causes a deflection or a mechanical displacement on a calibrated scale.

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TYPES OF MEASUREMENTS

• Null Method
• Effect of measurand is balanced by the application of another effect so as to maintain the deflection caused by the difference between the effects at zero.
• Magnitude of the opposing effect is quantified.
• Higher accuracy of measurement
• Measurand is compared with a source which is calibrated with a standard directly
• Sensitivity of the detector used is very high as it has to measure only a small range around zero
• Conditions of the measuring quantity is not altered – no loading effect.
• Requires appreciable time for balancing – not suitable if the measurand changes faster

TYPES OF MEASUREMENTS

• Analog Instruments
• Output is a continuous function of time
• Output has a constant relation to the input
• Examples: voltage, current, power and energy measurements

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• Digital Instruments
• Represents measurand in the form of a digital number
• Quantization – converting the continuous input signal into a countable output signal
• Construction – complex
• cost – high
• Consume very less power
• Free from parallax error

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Digital Instrument

TYPES OF MEASUREMENTS

• Active Instruments
• Measurand activates some external power input source which in turn produces the output
• Additional external energy source required
• High resolution
• Complex design due to relatively higher number of elements involved.
• Example: Float type level indicator
• Float system merely modulates the value of voltage from the external power source

TYPES OF MEASUREMENTS

• Passive Instruments
• Output produced entirely by the quantity being measured
• Less resolution
• Resolution cannot be adjusted
• Simple design and economical
• Examples: Voltmeter, ammeter, pressure gauges

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• Automatic and Manually Operated Instruments

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Elements of measuring Instruments

Elements of measuring Instruments

Sensing element

• Element takes energy from the measured medium and produces an output depending on the measured quantity.
• Loading effect – measurand disturbed by the act of measurement.

Stages of a Generalized Measurement System

• Basic Detector – Transducer stage
• Intermediate Modifying stage
• Terminating Device

Primary Sensing Element

• Primary Sensing Element, or PSE: A device directly sensing the process variable and translating that sensed quantity into an analog representation (electrical voltage, current, resistance; mechanical force, motion, etc.).
• Examples: thermocouple, thermistor, bourdon tube, microphone, potentiometer, electrochemical cell, accelerometer.

Transducer

• Transducer converts physical phenomenon into some other form of energy

– Pressure sensor converts pressure to electrical signal

– Thermocouple converts heat to millivolts

– RTD changes resistance with temperature

• Transducers are always the core of an industrial ‘transmitter’

Transmitter

• Transmitter converts a weak, low level transducer signal into a healthy, conditioned signal

• Electronic signal (Volt,4-20mA)

• Hardened for industrial environments
• useable over long distances (mile), relatively noise resistant

Transmitter

Transmitter

Transducer

• The device which converts the one form of energy into another is known as the transducer.
• The process of conversion is known as transduction.
• The conversion is done by sensing and transducing the physical quantities like temperature, pressure, sound, etc.

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Parts of Transducer

The transducer consists two important parts.

• Sensing Element
• Transduction Element
• Sensing or Detector Element  – It is the part of the transducers which give the response to the physical sensation. The response of the sensing element depends on the physical phenomenon.
• Transduction Element  – The transduction element converts the output of the sensing element into an electrical signal. This element is also called the secondary transducer.

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Advantages of converting the physical quantity into an electrical signal.

• The attenuation and amplification of the electrical signals are very easy.
• Produces less friction error.
• The small power is required for controlling the electrical systems.
• Easily transmitted and processed for measurement.
• The component used for measuring the electrical signal is very compact and accurate.
• The electrical signals are used in telemetry.

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Classification based on the Principle of Transduction

• The transduction medium may be resistive, inductive or capacitive depends on the conversion process that how input transducer converts the input signal into resistance, inductance and capacitance respectively.

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Resistors

• A resistor represents a given amount of resistance in a circuit.
• Resistance is a measure of how the flow of electric current is opposed or "resisted.
• It is defined by Ohm's law �

Resistance=voltage/current � R = V/I

Resistor Symbol

Capacitor

• It generally stores the charge and releases the stored charge whenever needed.
• Capacitance is measured in Farads.

C = q/V

q is the charge in coulombs

V is the voltage.

Capacitor Symbol

Inductor

• The ability of a component to generate electromotive force due to a change in the flow of current.
• A simple inductor is made by looping a wire into a coil.
• Inductors are used in electronic circuits to reduce or oppose the change in electric current.
• Inductance is measured in Henrys.

Inductor Symbol

Resistive Transducer

• The transducer whose resistance varies because of the environmental effects such type of transducer is known as the resistive transducer.
• The change in resistance is measured by the ac or dc measuring devices.

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Working Principle of Resistive Transducer

• The resistive transducer element works on the principle that the resistance of the element is directly proportional to the length of the conductor and inversely proportional to the area of the conductor. 

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• R – resistance in ohms.�A – cross-section area of the conductor in meter square.�L – Length of the conductor in meter square.�ρ – the resistivity of the conductor in materials in ohm meter.
• The resistive transducer is designed by considering the variation of the length, area and resistivity of the metal.

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Applications of Resistive Transducer

• Potentiometer - Measurement of displacement.  
• Strain gauges- Measurement of the pressure, force-displacement
• Resistance Thermometer- Measuring the temperature
• Thermistor

Capacitive Transducer

• It is a passive transducer that means it requires external power for operation.
• The capacitive transducer works on the principle of variable capacitances.
• The capacitance of the capacitive transducer changes because of many reasons like overlapping of plates, change in distance between the plates and dielectric constant.

Capacitive Transducer

• The capacitive transducer contains two parallel metal plates.
• These plates are separated by the dielectric medium which is either air, material, gas or liquid.
• In the normal capacitor the distance between the plates are fixed, but in capacitive transducer the distance between them are varied.

Principle of Capacitive Transducer

• The principle of variable capacitance is used in displacement measuring transducers in various ways.
• Capacitance is a function of effective area of conductor, the separation between the conductors and the dielectric strength of the material.

d - Distance between the two parallel electrodes.�ε - Dielectric constant, permittivity, of the dielectric medium�A - Area of the electrode.

Working of Capacitive Transducer

• One of the two electrodes is made fixed and the other is made movable for measure displacement.
• Displacement to be measured is applied to the movable metal plate, as the plate moves the distance between the plates increases and this changes the capacitance measurement.
• Thus the change in the capacitance will be the function of the displacement of the electrode.

Capacitance will be the function

• Changing Area of the Plates of Capacitive Transducers
• Changing Distance between the Plates of Capacitive Transducers
• Changing Dielectric Constant type of Capacitive Transducers

Advantages of Capacitive Transducer

• These transducers exhibit least loading effects as it offers extremely high input impedance.
• The frequency response of these transducers is excellent.
• Highly sensitive.
• Low power consuming transducers.
• It provides high resolution.

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Applications

• The capacitive transducers are used to measure humidity in gases.
• It is used to measure volume, liquid level, density etc.
• It is used for measurement of linear and angular displacement.

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Inductive Transducers

• A current will flow through a circuit containing an inductor when the magnetic field through it changes.
• the induction of the magnetic material depends on a number of variables like
• the number of turns of the coil on the material,
• the size of the magnetic material,
• the permeability of the flux path.

common type inductive transducers are

• simple inductance type and
• two-coil mutual inductance type.

Piezoelectric transducer

• It is an electrical transducer which can convert any form of physical quantity into an electrical signal, which can be used for measurement.
• An electrical transducer which uses properties of piezoelectric materials for conversion of physical quantities into electrical signals

Piezoelectric Transducer Working

• It works with the principle of piezoelectricity.
• The faces of piezoelectric material, usual quartz, is coated with a thin layer of conducting material such as silver. When stress has applied the ions in the material move towards one of the conducting surface while moving away from the other. This results in the generation of charge.
• This charge is used for calibration of stress.
• The polarity of the produced charge depends upon the direction of the applied stress.

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Piezoelectricity

• It is the electric charge that accumulates in certain solid materials (such as crystals, certain ceramics, and biological matter such as bone, DNA and various proteins) in response to applied mechanical stress.
• The word piezoelectricity means electricity resulting from pressure and latent heat.

Piezoelectric Materials

• Quartz
• Rochelle salt
• Ammonium dihydrogen phosphate (ADP)
• Ceramics made with barium titanate, dipotassium tartarate, potassium dihydrogen phosphate and lithium sulphate

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• Quartz
• Most stable thermally and mechanically
• Internal electric losses are small
• Application restricted to uses where high tensile strength, high mechanical stability or operation at high temperature is envisaged
• Rochelle salt
• Stable at room temperature with 35 – 85% humidity
• Higher humidity – deliquesce
• Lower humidity – dehydrate
• Coating with wax – to combat humidity effects
• At 55°C – crystal will disintegrate

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Piezoelectric Transducer Applications

• They are used in seismographs to measure vibrations in rockets.
• In strain gauges to measure force, stress, vibrations etc…
• Used by automotive industries to measure detonations in engines.
• These are used in ultrasonic imaging in medical applications.

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Advantages

• These are active transducer i.e. they don’t require external power for working and are therefore self-generating.
• The high-frequency response of these transducers makes a good choice for various applications.

Limitations

• Temperature and environmental conditions can affect the behavior of the transducer.
• They can only measure changing pressure hence they are useless while measuring static parameters.

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Wheatstone bridge

• A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
• The primary benefit of the circuit is its ability to provide extremely accurate measurements.

Principles of Strain Measurement

• Strain-initiated resistance change is extremely small.
• Thus, for strain measurement a Wheatstone bridge is formed to convert the resistance change to a voltage change.
• In Fig, resistances (Ω) are R₁, R₂, R₃ and R₄ and the excitation voltage (V) is E. Then, the output voltage e _o (V) is obtained by the following equation:

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• Suppose the resistance R₁ is a strain gage and it changes by ΔR due to strain. Then, the output voltage is,

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• If R₁ = R₂ = R₃ = R₄ = R in the initial condition,

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