Characteristics of Instruments

Basic Steps in Development of Instruments

• Development of Mathematical Model for Identification of Parameters to be measured.
• Identification of characteristics to be possessed by a general Instruments.
• Qualitative (visual display of important components and linkages between them) and Quantitative models (mathematically focused and based on complex formulas) for determination of Instrument design details.
• Selection of geometrical and physical parameters.

Characteristics of measurement systems

• To choose the instrument, most suited to a particular measurement application, we have to know the system characteristics.
• The performance characteristics may be broadly divided into two groups, namely ‘static’ and ‘dynamic’ characteristics.

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• Static characteristics
• The performance criteria for the measurement of quantities that remain constant, or vary slowly.

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• Dynamic characteristics
• The relationship between the system input and output when the measured quantity (measurand) is varying rapidly.

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Generalized Instrument System

Thermal Variable

ELECTRICAL TRANSDUCERS

• The transducers that converts the mechanical input signals of the physical quantity into electrical output signals

Mechanical transducers�

• Mechanical elements that are used for converting one form of energy into other form that can be measured easily

Thermal transducer

• Mechanical thermometers
• Electrical resistance thermometers
• Thermocouple
• Semiconductor devices and integrated circuit thermal sensors
• Radiation thermometry
• Liquid crystal thermometry

Displacement, position, and motion transducers

• Potentiometric transducers
• Capacitative potentiometers
• Variable inductance transducers
• Linear variable differential transformer
• Optical transducers

Velocity and acceleration transducers

• Doppler effect
• Spring mass accelerometer
• Piezoelectric transducers

Force transducers

• Strain
• Electrical resistance strain gauge
• Semiconductor or piezoresistive type strain gauge
• Strain gauge load cell
• Optoelectric sensors
• Binary sensors
• Pressure transducers

Flow transducers

• Pressure gradient flow transducers
• Magnetic flow transducers
• Ultrasonic flow transducers
• Laser doppler
• Thermal transport flow transducers

Generalized Instrument System

Static Performance of Instrument

• SYSTEMATIC CHARACTERISTICS
• Accuracy
• Range
• Span
• Linearity
• Sensitivity
• Environmental effects
• Hysteresis
• Resolution
• Dead zone

Accuracy

• Accuracy determines the closeness of an instrument reading to the true value of the measurand
• A known voltage of 200 V is being measured by a voltmeter and the successive readings are 204,205,203,203 and 205 volts, the accuracy is about 2.5%

Range

• The input range defines the minimum and maximum value of the variable to measure.
• The output range defines the minimum and maximum value of the signal given by the transducer.
• Assume a temperature transducer which temperature range is from 100°C to 250°C and the output range is given from 4 to 10 mV.

Span

• The input span is the maximum change of the input and the output span is the maximum change of the output.
• Input span:

• Output span:

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

• No-linearity is defined as the maximum deviation of the output over the straight line

No-Linearity can be quoted by:

Maximum % of No-Linearity :

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 (or)
• The absolute ratio of the increment of the output signal to that of the input signal
• S = Δqo/ Δqi ; where qo and qi are output and input quantities
• Thus, sensitivity is the ratio:

• Suppose a mercury in glass thermometer the meniscus moves by 1 cm when the temperature changes by 10 degree Celsius, the sensitivity of the thermometer is 1mm/degree celsius

Environmental effects

• All calibrations and specifications of an instrument are only valid under controlled conditions of temperature, pressure etc (ambient conditions).
• These standard ambient conditions are usually defined in the instrument specification.
• As variations occur in the ambient temperature, etc., certain static instrument characteristics change, and the sensitivity to disturbance is a measure of the magnitude of this change.
• Such environmental changes affect instruments in two main ways, known as zero drift and sensitivity drift.
• Zero drift is sometimes known by the alternative term, bias.

Instrument Drift

• This is caused by variations taking place in the parts of the instrumentation over time.

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• Prime sources occur as chemical structural changes and changing mechanical stresses.

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• Drift is a complex phenomenon for which the observed effects are that the sensitivity and offset values vary.

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• It also can alter the accuracy of the instrument differently at the various amplitudes of the signal present.

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Classification of Drift

REPRODUCIBILITY

• It determines the precision of an instrument
• The degree of closeness with which a particular reading of an instrument taken at different times, repeats itself.
• For example, measure a steady state signal many times. In this case if the values are close together then it has a high degree of precision or reproducibility
• If there is no drift the reproducibility is 100%

HYSTERESIS AND BACKLASH

• Careful observation of the output/input relationship of a block will sometimes reveal different results as the signals vary in direction of the movement.
• Mechanical systems will often show a small difference in length as the direction of the applied force is reversed.
• The deflection of a diaphragm type pressure gauge may be different for the same pressure, but one for increasing and other for decreasing
• The same effect arises as a magnetic field is reversed in a magnetic material.

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• This characteristic is called hysteresis

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Hysteresis = [H/ (O_MAX-O_MIN)] X 100

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• Where this is caused by a mechanism that gives a sharp change, such as caused by the looseness of a joint in a mechanical joint, it is easy to detect and is known as backlash.

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THRESHOLD

• The minimum input which is necessary to activate an instrument to produce an output is termed as its threshold
• Considered an instrument in its zero position i.e., no input
• Now input is given gradually, the instrument require some minimum value of input before shows the output

Resolution

• Over and above the threshold input, an instrument needs a minimum increment in input to produce a observable output
• This minimum increment is called resolution

STATIC ERRORS

ERRORS

SYSTEMATIC

RANDOM

HUMAN

INSTRUMENTAL

GROSS ERROR

MISUSE

OBSERVATIONAL

ENVIRONMENTAL

INHERENT SHORTCOMINGS

LOADING EFFECTS

HUMAN ERRORS

• Gross errors
• Misuse errors
• Observational errors

Gross errors

• Human mistakes in reading or recording values
• Instrument shows a value 47 while observer reads it as 42 or
• Reads the correct value but records it as 41
• Eliminated by automation or minimized by taking multiple readings of same value at different times and by different observers

Misuse errors

• Because of casual approach of operator
• In electrical measurements – if the leads are not connected properly
• Initial adjustment (zero checking) is not done properly
• Alertness and awareness on the part of operator are the only remedies

Observational errors

• Due to observers lack of knowledge in measurement methods
• Example is measurement of time period of a pendulum by a stop watch
• Precision of the measurement depends on the reflexes of the observer who clicks the stopwatch ‘on’ or ‘off’

Systematic errors

• Instrumental errors
• inherent shortcomings
• loading effects
• Environmental errors

Inherent shortcomings

• Due to malfunctioning of the components of the instruments caused by ageing
• For example, spring of a galvanometer may become weak, thus changing its calibration
• To avoid this, calibration of the instrument should be checked time to time

Loading effects

• Any measurement involves extraction of energy (may be small) from the measured medium changing thereby the value of the measurand
• This is called loading effects
• Ex : voltage measurement
• Here Z_L >Z₀
• Where Z_L and Z₀ are impedance of the circuit and true impedance

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Environmental errors

• Error due to environmental factors such as temperature, pressure and humidity
• Affect certain parameters of the instruments
• Theoretical corrections may be made for factors such as pressure, gravity etc., which cannot be controlled

Random errors

• It is also called as residual errors
• Errors due to cosmic ray showers, changes in geomagnetism, thunder cloud activities, seismic load etc.,

Minimization of errors

• Calibration of the instrument against the standard value of the quantity
• Correct selection of instrument taking into consideration of process condition of measurement
• Correction factor considering the amount of error in the true quantity and the measured quantity
• Use of air conditioning to minimize error

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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
• More important than the static characteristics of the instrument
• It is determined by applying some known variations of input to the sensing element

• Three most common variations are
• Step change
• Linear change
• Sinusoidal change

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Step change

• The primary element of the instrument is subjected to an instantaneous and finite known magnitude of the variation and follows the measured quantity

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• F(s) = A/s .. Laplace of step input

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If A=1 it is called unit step input

Linear change

• The primary element of the instrument is subjected to the linear variation with time and follows the measured quantity
• Also known as ramp input

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• F(s) = A/s² .. Laplace of ramp input

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If A=1 it is called unit ramp input

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Sinusoidal change

• The primary element of the instrument is subjected to the sinusoidal variation of constant amplitude and follows the measured quantity
• Sinusoidal input is A sin ωt, where A is its amplitude
• F(s) = A ω /(s² + ω²⁾ .. Laplace of sinusoidal input

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• The dynamic characteristics of the instruments are
• Speed of response
• 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

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 lag:�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.��Example: if the input to the system is a sine wave, the system is said to have 100% fidelity if the output also is a sine wave.�

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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Overshoot

• It is the ratio of the difference between the maximum and the final values of the response of the instrument to the minimum and the final values of the response of the instrument

Transducers

• Converts the energy from one form to another form
• Converts the units between input and output signals
• Conversion of the physical quantities of one form into another form

Classification of transducers

• Primary and secondary transducers
• Analog and digital transducers
• Active and passive transducers

Primary transducers

• Senses one quantity and convert it into another quantity
• Example – bourdon tube pressure gauge – senses pressure and convert it into the displacement of its free end

Secondary transducers

• Senses the second quantity of the primary transducer and converts it into the another quantity
• Example – the displacement of the free end of the bourdon tube moves the core of a linear variable differential transformer (LVDT) which produces the output voltage which is proportional to the movement of the core which indicates the pressure

Analog & digital transducer

• Analog transducer converts the quantity to be measured into an analog output
• Ex: Thermocouple , Strain gauge, Thermistor
• Digital transducer converts the quantity to be measured into a digital output
• Ex : Digital tachometers

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Active & passive transducer

• Active transducer do not require external power
• They are self operating type and they develop their own electrical output (voltage or current)
• They are classified as
• Piezoelectric – mechanically stressed
• Photoelectric – dissimilar materials illumination
• Thermoelectric

Active transducers

• Examples
• Thermocouple
• Liquid in glass thermometer
• Hot wire anemometer
• Piezoelectric transducer

Thermocouple

• The emf is generated across the junctions of the two dissimilar metals or semiconductors due to temperature gradient
• Heat energy is converted into the electrical energy which is measured by the thermocouple
• It is used to measure the temperature

Liquid in glass thermometer

• The thermal expansion in volume of the liquid in glass or liquid in metal due to the increase in the temperature of the liquid in the glass bulb
• Heat energy is converted into mechanical energy in the form of displacement
• It is used to measure the temperature

Hot wire anemometer

• The resistance of the thin wire is varied by heating or cooling by varying the flow rate of the liquid
• The kinetic energy of the liquid is converted into the electrical energy
• It is used to measure the flow rate of liquid

Piezoelectric transducer

• The emf is generated when the external force is applied to certain crystalline material such as quartz
• The mechanical energy is converted into the electrical energy
• It is used to measure force

Passive transducer

• Passive transducers require the external source of power
• Resistance passive transducers

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• Resistance thermometer
• Thermistor
• Potentiometer

Resistance thermometer

• Resistance of pure metal wire with positive temperature coefficient of resistance varies with the temperature of the metal wire
• The change in the resistance of the metal wire is calibrated in terms of temperature
• The heat energy is converted into electrical resistance
• Used to measure the temperature

Resistance strain gauge

• The resistance of the wire or semiconductor varies with the elongation or compression due to the external force, torque or displacement
• Change in the resistance is calibrated as in terms of force
• Mechanical energy is converted into electrical energy
• Used to measure force, torque and displacement

Capacitive passive transducers

• Variable capacitance pressure gauge
• Dielectric gauge
• Capacitor microphone

�Variable capacitance pressure gauge�

• Capacitance varies with the change in the distance between two parallel plates by the externally applied pressure
• Change in the capacitance is calibrated in terms of applied pressure
• Pressure energy is converted into electrical energy
• Used to measure the pressure

Dielectric gauge �

• Capacitance varies with the change in the dielectric between the plates due to the change in the liquid level
• Change in the capacitance is calibrated in terms of liquid level
• Change in the liquid level is converted into electrical energy
• Used to measure liquid level

Capacitor microphone�

• Capacitance varies between the fixed plate and the moveable diaphragm due to the sound pressure
• Variation of the capacitance is calibrated in terms of sound pressure
• Used for the acoustic measurement

Inductive passive transducers

• Magnetic circuit transducer
• Differential transducer
• Eddy current gauge
• Electrodynamic transducer

Magnetic circuit transducer�

• Mutual inductance of an AC coil varies due to change in the magnetic core of the coil due to externally applied pressure
• Change in the inductance is calibrated in terms of pressure
• Pressure energy is converted into electrical energy
• Used to measure pressure and displacement

Differential transducer�

• Linear Variable Differential Transducer (LVDT)
• Differential voltage of the two secondary windings varies linearly due to the displacement of the magnetic core by the externally applied pressure
• Differential voltage is calibrated in terms of displacement
• Mechanical energy is converted into electrical energy
• Used to measure displacement

Eddy current gauge�

• Inductance of the coil varies the change in the eddy current due to the displacement of the plate
• Eddy current is calibrated in terms of displacement
• Mechanical energy is converted into electrical energy
• Used to measure displacement

Electrodynamic transducer�

• Motion of the coil due to displacement varies with the magnetic field
• Electric voltage is generated due to change in the magnetic field
• Electric voltage is calibrated in terms of displacement
• Mechanical energy is converted into electrical energy
• Used to measure the displacement