Classification of the sensors• Active and Passive

Active: Input excitation is required (Electrical, Pneumatic, Hydraulic etc) Example : potentiometer as displacement sensorPassive: Input excitation is not required

Example : Mercury Thermometer • Null and Deflection Type

Null : Balancing a bridge to find resistance Passive: Finding the defection due to resistance

change in bridge circuit

Classification of the sensors

• Analog and Digital TypeAnalog: Output varies continuously, infinite position for the pointerDigital: Output varies in discrete form. Finite number of positions

Static Characteristics of Instruments1) Span & Range

Range : High measurement possibleSpan : Difference between max. and min measurement possible E.g. Thermocouple (700 0C to 1200 0C) Ammeter (0 to 10 A)

2) Mean, Spread & Standard deviation Mean : Average values of the same measurement

n1 2 3 n i

meani=1

x + x + x …+ x xX = =n n

Spread : Deviation from mean

Standard deviation * :

Static Characteristics continued

i meand = (x x )i

2 2 2 2 2n1 2 3 n i

i=1

d + d + d …+ d dσ = =n -1 n -1

* http://en.wikipedia.org/wiki/Bessel%27s_correction

3) AccuracyIt is the closeness with which an instrument reading approaches the true value of the quantity measured

Static Characteristics continued4) Precision: The degree to which repeated measurements

show the same results

Accurate but less Precise Precise but less Accurate

Resolution and Sensitivity• Resolution: The smallest detectable incremental

change of the input parameter that can be detected in the output signal. Eg; Scale, Multi range meters

Expressed either as a proportion of the readingOR

Absolute values

• Sensitivity: For an instrument or sensor with input x and output y. Sensitivity = dy/dx

ORMinimum input of physical parameter that will create a detectable output change. Eg; Ammeter(2A,100 div, 90o)

Practical and Theoretical Parameters

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Dead zone/space and Dead time

Dead space: The largest of a measured variable for which the instrument does not respondCause: friction in mechanical measurement system

Dead time: The time before the instrument begins to respond after the measured quantity has been changed.E.g: Camera, Data acquisition card, Ammeter

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HysteresisIt refers to the differencebetween upscale sequenceof calibration and downscalesequence of calibration

he=({y}upscale-{y}downscale)x=x1

Hysteresis error = [he(max)/FSOR] ×100FSOR : Full Scale Output Reading

Fig. Internal force verses extension of a rubber band follows hysteresis. External force is in opposition to internal force

E.g. Potentiometer used as displacement sensor with significant losses

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Linearity• If input-output relationship is a straight line passing

through origin• Calibration easy• Uniform sensitivity

Y ∆y

Measured quantity

Out

put r

eadi

ng

• Nonlinearity cause lot of problem during signal conditioning even though it is more accurate in some cases

• E.g. LVDT (linear) Thermistor (Non-linear)

Δy(Max. deviation)%Nonlinearity = ×100Y(FSOR)

Tolerance Maximum deviation of a manufactured

component from some specified value.

Tolerance Color±1% brown

±2% red

±5% gold

±10% silver

Static Error

0 m t= δA = A - AStatic Error/Absolute Error

=Measured Value,mAtA =True Value

Relative or Fractional Error

Percentage Error

t

δAAr

% = 100r r

Electromagnetic-Electromechanical Indicating Instruments

Electromechanical Indicating InstrumentsInput is electrical signalOutput is mechanical forceAnalog (Output is a continuous

function of time)Example: PMMC Instruments

Permanent Magnet Moving Coil (PMMC) Instruments

• To measure DC current or DC voltage • Can be used for measuring AC currents and voltages by introducing additional circuit and proper calibration

Constructional Features of PMMC

Enameled or silk covered copper wire is used for coil

Constructional Features of PMMC

N S

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Various Forces/ Torques in Measuring Instruments

• The movement of the pointer in PPMC is governed by three different torques

1) Deflection Torque2) Control Torque3) Damping Torque

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Deflection Torque

18

Deflection Torque

19

Deflection Torque

Deflection Torque

20

The equation (42.2) is valid while the iron core is cylindrical and the air gap between the coil and pole faces of the permanent magnet is uniform. This result the flux density B is constant and the torque is proportional to the coil current and instrument scale is linear.

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Control Torque

Controlling Torque: The value of control torque depends on the mechanical design of the control device. For spiral springs and strip suspensions, the controlling torque is directly proportional to the angle of deflection of the coil. ..,ieControl torque =Cθ (42.3) where, θ = deflection angle in radians and C = spring constant in N-m/rad

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Damping TorqueIt is provided by the induced currents in a metal former or core on which the coil is wound or in the circuit of the coil itself.

As the coil moves in the field of the permanent magnet, eddy currents are set up in the metal former or core. The magnetic field produced by the eddy currents opposes the motion of the coil.

The pointer will therefore swing more slowly to its proper position and come to rest quickly with very little oscillation. Electromagnetic damping is caused by the induced effects in the moving coil as it rotates in magnetic field, provided the coil forms part of closed electric circuit.

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Let the velocity of the coil is

Then the velocity of a coil side

Note both the sides of the coil having same e.m.fs but they are additive in nature

Resultant torque in a motion of coil

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25

Two methods of supporting the moving system

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Two methods of supporting the moving system

• To increase sensitivity, the diameter of the hair spring should be reduced, but it is limited, so Taut band is used

• It is thin, metallic, ribbon like structure

• It improves sensitivity

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Reason for placing hair springs in opposite direction

F

x = 0 x

F

x

CASE-1

H

x=H

28

Reason for placing hair springs in opposite direction

F

x = 0x

F

x

CASE-2

x=H

H

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Reason for placing hair springs in opposite direction

F

x

F

x = 0 x

CASE-3

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Multi Range Ammeter

31

Make before Break

32

Multi Range Ammeter (alternative design)

33

Multi Range Voltmeter

34

Break before Make

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Advantages• Uniform scale

• Power consumption can be made very low (25 µW to 200 µW)

• Torque to weight ratio can be made high with a view to achieve high accuracy (typically 2%)

• Single instrument can be used for multi range ammeters and voltmeters

• Error due to stray magnetic field is very small

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Limitations

• They are suitable for direct current only

• The instrument cost is high

• Variation of magnet strength with time

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Errors can be reduced by• Proper pivoting and balancing weight may reduce the frictional error

• Considering the aging can reduce errors due to magnetic decay

• Manganin in series with coil reduces temperature effects

• Maintaining nominal temperature. The stiffness of spring, permeability of magnetic core decreases with increase in temperature

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Sensitivity

Ammeter Sensitivity:

Full scale current (A)

Voltmeter Sensitivity:

Total resistance of the meter /Full scale reading (V)

k

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Assignment

Q1) A PMMC instrument has a coil resistance of 100Ω and gives a full-scale deflection (FSD) for a current of 500μA. Determine the value of shunt resistance required if the instrument is to be employed as an ammeter with a FSD of 5 A.

Ans: 0.01 Ω

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Assignment

Q2) A PMMC meter with a coil resistance 100Ω and a full scale deflection current of 100μA is to be used as a voltmeter. The voltmeter ranges are to be 50 V and 100 V. Determine the required value of resistances for each range.

Ans: 0.4999 MΩ, 0.9999 MΩ

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Types of ErrorsBasically there are three types of errors on the basis; they may arise from the source. 1.Gross ErrorsThis category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category. For example while taking the reading from the meter of the instrument he may read 21 as 31. All these types of error are come under this category. Gross errors can be avoided by using two suitable measures and they are written below: A proper care should be taken in reading, recording the data. Also calculation of error should be done accurately.By increasing the number of experimenters we can reduce the gross errors. If each experimenter takes different reading at different points, then by taking average of more readings we can reduce the gross errors.2. Systematic ErrorsIn order to understand these kinds of errors, let us categorize the systematic errors as 2.1 Instrumental ErrorsThese errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments. Misuse of the instruments results in the failure to the adjust the zero of instruments. In order to minimize the gross errors in measurement various correction factors must be applied and in extreme condition instrument must be re-calibrated carefully. 2.2 Environmental ErrorsThis type of error arises due to conditions external to instrument. External condition includes temperature, pressure, humidity or it may include external magnetic field. Following are the steps that one must follow in order to minimize the environmental errors: Try to maintain the temperature and humidity of the laboratory constant by making some arrangements.Ensure that there should not be any external magnetic or electrostatic field around the instrument.2.3 Observational ErrorsAs the name suggests these types of errors are due wrong observations. The wrong observations may be due to PARALLAX. In order to minimize the PARALLAX error highly accurate meters are required, provided with mirrored scales. 2.3 Random ErrorsAfter calculating all systematic errors, it is found that there are still some errors in measurement are left. These errors are known as random errors. Some of the reasons of the appearance of these errors are known but still some reasons are unknown. Hence we cannot fully eliminate these kinds of error.