This document discusses the classification and operating principles of various analog measurement instruments for voltage and current. It covers classifications based on measured quantity, output representation, construction type, and data presentation. Key instrument types discussed include permanent magnet moving coil (PMMC), galvanometer, moving iron, electrodynamometer, and electrostatic meters. For each type, it describes the operating forces, torque equations, sources of error, and advantages/disadvantages. The document provides detailed information on analog measurement instrument fundamentals.

1. Electrical and Electronic Measurement
Measurement of Voltage and Current
Parveen Malik
Assistant Professor
School of Electronics Engineering
KIIT University
parveen.malikfet@kiit.ac.in
August 6, 2019
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2. Outline
1 Classification of Analog Instruments
2 Electromechanical Indicating Instruments
Operating Forces
3 PMMC
Galvanometer
4 Moving Iron
5 Electrodynamometer
6 Electrostatic Instruments
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3. Classifications

4. Classification of Analog Instruments I
Based upon Quantity
Current - Ammeter
Voltage - Voltmeter
Based upon kind of Current -
Alternating Current
Direct Current
Alternating and Direct Current
Based upon cause of Working
Magnetic - Ammeter voltmeter, watt-meters and Integrating Meters
Heating - Ammeter , Voltmeter, Watt-meters
Electrostatic- Voltmeters
Induction - A.C. ammeters, Voltmeters, Wattmeters and Energy
meters
Hall Effect- Flux meters, ammeters, and Poynting Vector wattmeter.
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5. Classification of Analog Instruments II
Based upon Output Representation
Indicating - (i) Electromechanical (ii) Electronic
Recording
Integrating
Based upon Quantity Measurement
Direct Measuring Instruments - Ammeter, Voltmeter, Watt-meters
and Energy Meters
Comparison Instruments - D.C. Bridge and A.C. Bridges.
Based upon Construction-
Permanent Magnet Moving Coil Instruments - D.C.
Moving Iron D.C. or A.C.
Electrodynamometer D.C. or A.C.
Electrostatic D.C. or A.C. at one frequency
Thermocouple D.C. or A.C.
Rectifier D.C. or A.C.
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6. Classification - Based upon Data Presentation
Indicating, Recording and Integrating
Indicating
Indicate the
quantity being
measured.
Use of dial and
pointer.
e.g. Voltmeter,
Ammeter
Recording
Continuous record of
quantity being measured
Pen and a recorder.
e.g. Voltmeter recordings
in sub-station.
Seismograph Readings
Temp. sensor in Reactor.
Integrating
Totalize events over a
specified time
set of pointer and
scale
e.g. Ampere hour,
Watt hour and Energy
meter.
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7. Classification
Based upon Construction

8. Classification - Based upon Construction
PMMC, Moving Iron, Electrodynamometer, Electrostatic, Thermocouple, Rectifier
Meter Type Suitability Major Uses
Permanent Magnet Moving Coil Instruments D.C.
Measurement of D.C. Current and Voltages
and Resistance measurement in low and medium impedance circuits.
Moving Iron
D.C.
A.C.
Inexpensive
Rough indication of currents and voltages
Electrodynamometer
D.C.
A.C.
Widely used for precise a.c. current and voltage measurement at power frequencies
Used as standard meters for calibration and transfer instruments
Electrostatic
D.C.
A.C. at one frequency
Measurement of high voltages
where very little current can be supplied under measurement
Thermocouple
D.C.
A.C.
Measurement of Radio frequency A.C. signals.
Rectifier
D.C.
A.C.
Widely used for medium sensitivity service type
voltage measurements in medium impedance circuits
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9. Operating Forces

10. Operating Forces
Deflecting, Controlling and Damping
Deflecting Force
Required for moving the pointer from zero position.
Directly related to quantity being measured.
Utilize the effects like magnetic, heating, electrostatic,induction or Hall
effect.
Controlling Force
To produce a equal and opposite action to Deflecting Force.
Directly proportional to quantity being measured
Mainly provided by Springs or Weights.
Damping Force
Due to inertia of moving system, pointer takes time to come to steady
position.
Pointer Oscillate to and fro till it comes to rest when its kinetic energy
fully dissipated in friction.
It is provided by Air, Fluid or Electromagnetically.
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11. Operating Forces - Controlling

12. Operating Forces - Controlling
Gravity Control
Tc = W sin θ × l
= Wl sin θ
= Kg sin θ
Tc ∝ sin θ
Where W is controlling weight,
l = length of weight arm
Spring Control
Tc = Ebt3
12 L θ Nm
Tc = Ksθ
Tc ∝ θ
Where E = Young’s modulus
(N
m2), (b,t,l)= width,thickness
and length of spring (m)
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13. Controlling Forces
Spring Vs Gravity Control
Gravity Control
1 It is cheap.
2 Independent of temp.
variations
3 It does not deteriorates with
time.
4 They must be used in
vertical position
5 Non-linear Scale
Spring Control
1 It is Expensive
2 Dependent of temp.
variations. Stiffness
decreases with temp.
3 Continuous use of spring
results in inelastic yield.
4 Doesn’t depend upon the
position of instrument.
5 Linear Scale
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14. Operating Force - Damping Force

15. Operating Force - Damping Force
Air Damping
Generally employed in
the instruments where
main magnetic flux
density is week.
Very simple and
cheap.
e.g. - Moving iron and
electrodynamometer.
Fluid Friction Damping
(1) Rarely used in
commercial type
instruments.
(2) Instrument must be
held in vertical position
or Creeping of oil occurs
(3) Frictional error is
less
e.g. Electrostatic
Instruments
Eddy current
Damping
Most Efficient form of
damping
e.g. PMMC
Instruments
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16. Errors in indicating types of
instruments

17. Errors in indicating types of instruments
Frictional Error
Td = Tc + Tf
⇒ Tc = Td − Tf
Tf = µW = µmg
Tf ∝ W
W ↑ Tf ↑
Td
Tf
∝ Td
W 1
Temperature Error
As Temp. rises, Rm
rises and current
decreases, so does
deflecting torque.
T ↑ Rm ↑ Im ↓
Frequency Error
As frequency rises,
current decreases, so
does deflecting
torque.
I =
VAC
q
R2 + (j 2πfL)2
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18. Classification
Based upon Construction
Permanent Magnet Moving Coil

19. Permanent Magnet Moving Coil Instruments
Construction

20. PMMC - Torque Equation and Deflection1
Deflecting Torque
τd = BINA
Controlling Torque
τc = Kθ
When deflecting torque is equal
to controlling torque, i.e.
BINA = Kθ
θ = (BNA
K )I
θ ∝ I (Scale − Linear)
1
Figure - Courtesy -http://www.bitlanders.com/blogs/instrumentation-and-
measurements-chapter-03/320273
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21. PMMC - Errors, Advantages and Disadvantages
Error in PMMC
(1) Weakening of permanent
magnets due to ageing magnets
- Treat magnets with heat and
vibration.
(2) Weakening of springs due to
ageing and temperature
- Careful use of material and
pre-ageing.
(3) Change of resistance of moving
coil with temperature
- Swamping resistance is used.
Disadvantages
(1) Useful only for D.C. applications
(2) The cost is very high as
compared to Moving iron
instruments.
Adavantages
(1) The scale is uniformly
divided.
(2) The power consumption is
very low -( 25µW to 200µW
(3) The torque-weight ratio very
high (Accuracy 2% of FSD)
(4) A single instrument may be
used for many different current
and voltage ranges.
(5) Large flux density
(0.5Wb/m2),the stray magnetic
field can be ignored.
(6) Self shielding magnets have
wide application in multi-panel
applications like aerospace.
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22. D’Arsonval Galvanometer
Deflecting Torque
Td = NBAI
Td = GI
where G is displacement constant
of the galvanometer.
Controlling Torque
TC = Kθ
When,
Td = Tc
GI = Kθ
θ = G
K I
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23. Dynamic behaviour of Galvanometer
Equation of motion
Tj + TD + TC = Td
J d2θ
dt2 + D dθ
dt + Kθ = GI
Where Tj - Inertial Torque
J - Moment of inertia or inertia
constant (Kgm2)
TD - Damping Torque
D is Damping constant(Nm/rad)
Tc - Controlling Torque
K - Spring Constant (Nm/rad)
Td - Deflecting Torque
G - Displacement Constant
(Nm/A)
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24. Moving Iron

25. Moving Iron Instruments
Attraction Type
The coil is flat and has a
narrow slot like opening.
The moving iron is flat disk
or a sector eccentrically
mounted
When the current flows the
coil , moving iron piece is
attracted from weaker field
to stronger field.
Controlling force is by
springs while damping is
provided by air friction.
Attraction type instrument
will usually have lower
inductance than repulsion,
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26. Moving Iron Instruments
Repulsion Type
There are two vanes inside
the coil, one is fixed and
other movable.
They are magnetised
similarly when current move
through them, then there is
force of repulsion between
them.
This force results in
movement of moving vane.
Repulsion type instrument
are suitable for economical
production.
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27. Moving Iron - Torque Equation and Deflection
Deflecting Torque
Td =
1
2
I2 dL
dθ
Controlling Torque
TC = Kθ
At equilibrium
Td = Tc
1
2I2 dL
dθ = Kθ
θ = 1
2
I2
K
dL
dθ
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28. Moving Iron - Errors, Advantages and Disadvantages
Error in Moving Iron
(1) Hysteresis Error Magnetization due
to ascending and descending current
(2-3%)
- Low flux density or small iron parts
(2) Temp. Error Change in resistance
of moving coil and springs with temp.
- Swamping resistance
(3) Stray Magnetic Field As operating
magnetic field is week (0.006-0.0075
Wb
m2)
- Iron case or thin iron shield.
Disadvantages
(1) Errors due to hysteresis,frequency
stray magnetic field
(2) The scale is non linear.
Advantages
(1)Universal Use Used for
a.c as well d.c.
(2) Less Friction error
Torque weight ratio is high
(3) Cheapness due to a few
turns of moving coil and
simple iron piece.
(4) Robustness- Simple
construction and current
carrying parts are not moving
(5) Accuracy is high
A.C. - 0.75% for 25 to 125
Hz
0.2% to 0.3% at 50 Hz
D.C - 2% or less
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29. Electrodynamometer

30. Electrodynamometer Instruments
There are two air cored coils
fixed and moving coil.
Fixed Coil- Usually wound
with heavy wire carrying the
main current and produce a
magnetic field. Air Cored
Moving Coil- Usually
wound on non-metallic
former to reduce eddy
currents.
Control- Usually provided
by two metallic springs.
Moving System- Moving
system consist of moving
coil mounted on Aluminium
spindle.
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31. Electrodynamometer Instruments
The pointer always move in one direction irrespective of the polarity.
Therefore , it can be used with A.C. as well as D.C. supply.
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32. Electrodynamometer - Torque Equation and Deflection
Deflecting Torque
Td = I1I2
dM
dθ
Where I1 and I2 are current through fixed and moving coil. M is mutual
inductance between fixed and moving coil.
Controlling Torque
TC = Kθ
Where K is spring constant.
At equilibrium,
Td = Tc
I1I2
dM
dθ = Kθ
θ = I1I2
K
dM
dθ
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33. Electrodynamometer - Errors, Advantages and
Disadvantages
Errors
(1) Low Torque-weight ratio.
- Increase flux density by
increasing current or no. of turns
(2) Frequency Change in
deflection is inversely
proportional to impedance
- Coil winding is made small or
time constant same for moving
and fixed parts.
(3) Eddy current errors due to
metal portions in moving coil.
(4) Temp. error and external
magnetic field.
Advantages
(1) Used for a.c as well d.c.
(2) Hysteresis error, eddy current
errors are less due to air core.
(3) Precision grade accuracy for
40 to 500Hz.
(4) Useful for rms voltage
computation.
Disadvantages
(1)Low torque weight ratio.
(2) They are more expensive
(3) Sensitive to overloads and
mechanical impacts
(4) Low sensitivity and high
power consumption
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34. Electrostatic Instruments

35. Electrostatic Instruments
In electrostatic instruments,
the deflecting torque is
produced by action of
electric field on charged
conductors.
Theu can be rotational or
linear motion between the
plates.
They are generally used as
voltmeters to measure high
voltages.
They generally consist of to
plates one is fixed while
other is movable.
Control is provided by
spring.
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36. Electrostatic - Torque Equation and Deflection
Linear Motion
Deflecting Torque
Td =
1
2
V 2 dC
dX
Controlling Torque
Tc = Kθ
At Equilibrium,
Td = Tc
Kθ = 1
2V 2 dC
dX
θ = 1
2K V 2 dC
dX
Rotational Motion
Deflecting Torque
Td =
1
2
V 2 dC
dθ
Controlling Torque
Tc = Kθ
At Equilibrium
Td = Tc
Kθ = 1
2 V 2 dC
dθ
θ = 1
2K V 2 dC
dθ
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37. Electrostatic - Advantages and Disadvantages
Advantages
(1) They draw very little power
from the main lines (A.C. or D.C)
as charging current is very less.
(2) Used for a.c as well d.c.
power supply
(3) There is no hysteresis or
waveform errors
(4) There are no errors related to
stray magnetic field
(5) They are generally suited for
measurement of high voltages
Disadvantages
(1)These instruments are
expensive, large in size and are
not robust in construction.
(2) Their scale is not uniform
(3) The operating forces are so
small.It means that their
operating torque is very small.
(4) These instruments are limited
to certain special application,
particularly in a.c. circuits of
relatively high voltages.
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