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T Srinivasa Rao Electronic Measurements and Instrumentation (EC-315) 2

EC-315 Electronic measurement and
Instrumentation

UNIT - I
T Srinivasa Rao
Dept. of ECE
Bapatla Engineering College

Objective of course
• To provide students with a fundamental
understanding of the concepts, principles,
procedures, and computations used by engineers
and technologists to analyze, select, specify,
design, and maintain modern instrumentation and
control systems

Electronic Measurements and
T Srinivasa Rao 4
Instrumentation (EC-315)

Part 1
MEASURENT AND ERROR: Definitions, Accuracy and precision,
Types of errors, Statistical analysis, robability of errors, Limiting
Errors.
Part 2
DIRECT CURRENT INDICATING INSTRUMENTS: DC ammeters, DC
voltmeters, Series type ohmmeter, Shunt type ohmmeter,
Multimeter, Calibration of DC Instruments.
Part 3
DC & AC BRIDGES: Wheatstone, Kelvin, Guarded Wheatstone,
Maxwell, Hay, Schering and Wein bridges, Wagner ground
connection..


• Error: The difference between the reported value and the (usually unknown)
true value of a quantity.
• Validity: How well an instrument (or measurement technique) reflects what it is
purported to measure. Depends on details of the instrument, and varies with the
operating conditions.
• Robustness: When the input to an instrument varies slightly, does its output
stably reflect the changes, or does it become unstable, or chaotic?
• Reliability: Given very different values, or measurements taken at very different
times, are the measurements consistent?
• Repeatability: Do repeated measurements, on a constant true value, give the
same answer?
• Accuracy: How close is the mean measurement of a series of trials to the true
value?
• Precision: How much do the measurements vary from trial to trial?
• Resolution: How finely can we and/or the instrument separate one value from
another that's close to it?
• Mistake: .Human error.!
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Instruments
• Detector
– Device that indicates a change in one variable in its
environment (eg., pressure, temp, particles)
– Can be mechanical, electrical, or chemical
• Sensor
– Analytical device capable of monitoring specific
chemical species continuously and reversibly
• Transducer
– Devices that convert information in nonelectrical
domains to electrical domains and the converse

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Simple instrument model

Instrument model with amplifier, analog to digital converter and computer
output
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CONTENTS

• Definitions
• Accuracy and Precision
• Significant Figures
• Types of Error
• Statistical Analysis
• Probability of Errors
• Probable Error
• Limiting Errors
• Systems of Units of Measurement
• Standards of Measurement

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• Limiting Errors
• Systems of Units of Measurement
• Standards of Measurement

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Definitions
• Measurement : generally involves using an instrument as a physical means
of determining a quantity or variable
• Instrument : a device for determining the value or magnitude of a quantity
or variable
• Accuracy : closeness with which an instrument reading approaches the
true value of the variable being measured.
• Precision : a measure of the reproducibility of the measurements; i.e.,
given a fixed value of a variable, precision is a measure of the degree to
which successive measurements differ from one another
• Sensitivity : the ratio of output signal or response of the instrument to a
change of input or measured variable.
• Resolution : the smallest change in measured value to which th
instrument will respond.
• Error : deviation from the true value of the measured variable.

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Accuracy and Precision
• Precision is composed of two characteristics : conformity and the number
of significant figures to which a measurement may be made
• Conformity is a necesary, but not sufficient, condition for precision
because of the lack of significant figures obtained
• Precision is a necesary, but not sufficient, condition for accuracy.

T Srinivasa Rao 14

Significant Figures
• Significant figures convey actual information regarding the magnitude and
the measurement precision of a quantity
• The more significant figures, the greater the precision of the
measurement
• When a number of independent measurements are taken in an effort to
obtain the best possible answer (closest the true value), the result is
usually expressed as the arithmetic mean of all readings, with the range of
possible error as the largest deviation from that mean
• When two or more measurements with different degrees of accuracy are
added, the result is only as accurate as the least accurate measurement.

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Types of Error
• Gross errors : largely human errors, among them misreading of
instruments, incorrect adjustments, and computational mistakes.
• Systematic errors : shortcomings of the instruments, such as defective or
worn parts, and effects of the environment on equipment or the user.
• Random errors : those due to causes that cannot be directly established
because of random variations in the parameter or the system of
measurement.

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Statistical Analysis
• Arithmetic mean x=
x1 + x 2 + x 3 + ..... + x n ∑ x
=
n n

• Deviation from the mean d n = xn − x

• Average deviation D=
d 1 + d 2 + d 3 + ... + d n
=
∑d
n n

• Standard deviation σ=
d 12 + d 2 + d 32 + ... + d n
2 2
=
∑d i
2

n n

• Standard deviation of a finite d 12 + d 2 + d 32 + ... + d n
2 2
∑d i
2

σ= =
number of data n −1 n −1

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Probability of Errors

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Probable Error

Deviation (+) Fraction of total
(σ) area included

0.6745 0.5000

1.0 0.6828

2.0 0.9546

3.0 0.9972

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Limiting Errors
• In most indicating instruments the accuracy is guaranteed to a certain
percentage of full-scale reading. Circuit components (such as capacitors,
resistors, etc.) are guaranteed within a certain percentage of their rated
value. The limits of these deviations from the specified values are known
as limiting errors or guarantee errors.


System of Unit Measurements
Decimal multiples and submultiples

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Basic SI Quantities, Units, and Symbols


Electric and Magnetic Units

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Fundamental, Supplementary, and Derived Units


English Into SI Conversion


Standards of Measurement
• Standard of measurement is a physical representation of a unit of
measurement
• Classification :
– International standards
– Primary standards
– Secondary standards
– Working standard


Part 2

Direct Current Indicating
Instruments

CONTENTS
• Permanent-magnet moving-coil mechanism (PMMC)
• Galvanometer sensitivity
• DC ammeters
• DC voltmeters
• Voltmeter-ammeter method
• Series-Type Ohmmeter
• Shunt-Type Ohmmeter
• Multimeter or VOM
• Calibration of DC Instruments

T Srinivasa Rao 28

Suspension Galvanometer
• This instrument was the
forerunner of the moving-coil
instrument, basic to most dc
indicating instruments currently
used

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Torque and Deflection of The Galvanometer
Steady-state Deflection

• Torque deflection : T = B × A× I × N
• The practical coil area generally ranges from approximately 0.5 to 2.5 cm 2
• Flux densities for modern instruments usually range from 1,500 to 5,000
gauss (0.15 to 0.5 Wb/m2)

T Srinivasa Rao 30

Dynamic Behavior

• The motion of a moving coil in a magnetic field is characterized by three
quantities :
– The moment of inertia (J) of the moving coil about its axis of rotation
– The opposing torque (S) developed by the coil suspension
– The damping constant (D).

T Srinivasa Rao 31

Damping Mechanisms

• Galvanometer damping is provided by two mechanisms : mechanical and
electromagnetic
• A galvanometer may also be damped by connecting a resistor across the
coil --- CDRX (Critical Damping Resistance External)

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PMMC
• Permanent Magnet Moving-Coil
Mechanism
• Ofte called d’Arsonval movement
• Construction -------------------

• Details of PMMC movement
---------

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Temperature Compensation

• Both the magnetic fieldstrength and spring-tension decrease with an increase in
temperature
• The coil resistance increases with an increase in temperature
• The spring change, conversely, tends to cause the pointer to read high with an
increase in temperature
• Compensation may be accomplished by using swamping resistors in series with the
movable coil

T Srinivasa Rao 34

Galvanometer Sensitivity
d mm
• Current sensitivity may be defined as a ratio of the SI =
I µA
deflection of the galvanometer to the current producing
this deflection
• Voltage sensitivity may be defined as the ratio of the d mm
SV =
galvanometer deflection to the voltage producing this V mV
deflection
• Megohm sensitivity may be defined as the number of
megohms required in series with the (CDRX shunted) d mm
SR = = SI
galvanometer to produce one scale division deflection I µA
when 1 V is applied to the circuit
• Ballistic sensitivity and is defined as the ratio of the
maximum deflection, dm, of a galvanometer to the d m mm
SQ =
quantity Q of electric charge in a single pulse which Q µC
produces this deflection.

T Srinivasa Rao 35

DC Ammeters
Shunt Resistor

I m Rm
Rs =
I − Im

T Srinivasa Rao 36

Ayrton Shunt

• Schematic diagram of a simple
multirange ammeter --------

• Universal or Ayrton shunt --


DC Voltmeters

• Basic dc voltmeter circuit --

V − I m Rm V
Rs = = − Rm
Im Im

• Multirange voltmeter ---------

• Voltmeter sensitivity :
1 Ω
S=
I fsd V

T Srinivasa Rao 38

Voltmeter-Ammeter Method
• A popular type of resistance
measurement
• Effect of voltmeter and ammeter
positions in voltmeter-ammeter
measurements -----------------

• Effect of the voltmeter position in
a voltmeter-ammeter
measurements ------------------

T Srinivasa Rao 39

Series-Type Ohmmeter

• Certain disadvantage : when the battery is old, the full-scale current drops and the
meter does not read "0" when A and B are shorted
• The design can be approach by recognizing that, if introducing Rh reduces the
1
meter current to 2
I fsd

I fsd R m Rh
R1 = R h −
E

T Srinivasa Rao 40

Shunt-Type Ohmmeter
• Particularly suited to the measurement of
low-value resistors
• When R = ∞ the full-scale meter current
x

will be E
I fsd =
R1 + R m
• The meter current for any value of Rx ,
expressed as a fraction of the full-scale
current, is
Rx
s=
Rx + R p
• At half-scale reading of the meter
R1 Rm
Rh =
R1 + Rm

T Srinivasa Rao 41

Multimeter or VOM

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• Schematic diagram of the
Simpson Model 260 multimeter

• dc voltmeter section of the
Simpson Model 260 multimeter

T Srinivasa Rao 43

• DC Ammeter section of the multimeter

• Ohmmeter section of the multimeter

T Srinivasa Rao 44

Calibration of DC Instruments

• Potentiometer method of
calibrating a dc ammeter ---

• Potentiometer method of
calibrating a dc voltmeter ---

T Srinivasa Rao 45

Introduction to Alternating-current
Indicating Instruments
• The d'Arsonval movement responds to the average or dc value of the
current through the moving coil
• If the movement carries an alternating current with positive and negative
half cycles, the driving torque would be in one direction for the positive
alternation and other direction for the negative alternation
• If the frequency of the ac is very low, the pointer would swing back and
forth around zero point on the meter scale
• At higher frequencies, the inertia of the coil is so great that the pointer
cannot follow the rapid reversals of the driving torque and hovers around
the zero mark, vibrating slightly.

T Srinivasa Rao 46

CONTENTS

 Introduction
 Wheatstone bridge
 Kelvin bridge
 Maxwell
 Hay
 Schering
 Wein bridges
 Wagner ground connection
 Comparison bridges

T Srinivasa Rao 48

Introduction
• Bridge circuits are extensively used for measuring component values, such
as resistance, inductance, or capacitance, and of other circuit parameters
directly derived from component values
• Its accuracy can be very high.
Bridges are electrical circuits for performing null measurements on
resistances in DC and general impedances in AC

T Srinivasa Rao 49

Wheatstone bridge

• Photograph of the instrument

• Simplified schematic of the
bridge circuit------------------

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Wheatstone bridge

R1RX = R2R3

T Srinivasa Rao 51

• Basic operation R2
R x = R3
R1
• Measurement errors :
– Found in the limiting errors of the three known resistors
– Insufficient sensitivity of the null detector
– Changes in resistance of the bridge arms due to the heating effect of the
current through the resistors
– Thermal emfs in the bridge circuit or the galvanometer circuit (when low-
value resistors are being measured)
– Errors due to the resistance of leads and contacts exterior to the actual bridge
circuit

T Srinivasa Rao 52

Thevenin Equivalent Circuit

• Wheatstone bridge configuration
--------------------

• Thevenin resistance looking into
terminals c and d --------

• Complete Thevenin circuit, with
the galvanometer connected to
terminals c and d


 R1 R2 
• The Thevenin, or open circuit voltage : E cd 
= E − 

 R1 + R3 R 2 + R4 

• The Thevenin resistance : R1 R3 R2 R4
RTH = +
R1 + R3 R 2 + R 4

• The galvanometer current : ETH
Ig =
RTH + R g


Kelvin Bridge

• Wheatstone bridge circuit,
showing resistance Ry of the lead
from point m to point n
R1
Rx = R3
R2
• Basic Kelvin double bridge circuit
--------------------------

R1
R x = R3
R2


Loop Tests with The Portable Test Set
• Murray-loop test, used for
locating a ground fault (short
circuit) -----------------------------

B
l x = 2l
A+ B
• Varley-loop test: (a) no.1; (b) no.
2; (c) no.3, used to locate
grounds, crosses, or short circuits
in multiconductor cable

R2
• X1 =
2


Guarded Wheatstone Bridge
• Used for high resistance measurements


General Form of The AC Bridge

Z1Z 4 = Z 2 Z 3

∠θ 1 + ∠θ 4 = ∠θ 2 + ∠θ 3

Comparison Bridges
• Capacitance comparison bridge
• Equating the real terms :
R
R x = Rs 2
R1
• Equating the imaginary terms :
R1
C x = Cs
R2

• Inductance comparison bridge
R2
L x = Ls
R1
R2
R x = Rs
R1

• Inductance comparison bridge with extended measurement range
R
• With the switch in position 1 : R x = ( Rs + r ) 2
R1

R2
• With the switch in position 2 : R x = Rs −r
R1


Maxwell Bridge

• The Maxwell bridge measures an
unknown inductance in terms of a
known capacitance.
• The maxwell bridge is limited to the
measurement of medium-Q coils
(1<Q<10).
R 2 R3
Rx =
R1

L x = R 2 R 3 C1

T Srinivasa Rao 61

Hay Bridge
• The Hay circuit is more convenient
for measuring high-Q coils
• Hay bridge for inductance
measurements ---------------------

• Impedance triangles illustrate
inductive and capacitive phase angles
--------------------------------
• for Q>10 :

L x = R 2 R3 C


Hay Bridge


Schering Bridge
• The Schering bridge, one of the
most important bridges, is used
extensively for the measurement
of capacitors.
• Schering bridge for measurement
of capacitance --------------------
C1
R x = R2
C3

R1
C x = C3
R2
• Dissipation factor :

D = ωR1C1
T Srinivasa Rao 64

Unbalance Conditions


• Bridge balancing problem :
– (a) unbalanced condition
– (b) bridge balance is restored by
adding a resistor to arm 1 (maxwell
configuration)
– (c) Alternative method of restoring
bridge balance, by adding a capacitor
to arm 3


Wien Bridge
• Applications :
– Frequency measureent
– Notch filter
– Frequency-determining element

• Frequency measurement with the
Wien bridge -----------------------

1
f =
2πRC


Wagner Ground Connection
• The wagner ground connection
eliminates the effect of stray
capacitances across the detector


Universal Impedance Bridge

• Universal impedance bridge


• Bridge configurations of the universal impedance bridge


Summary
• Wheatstone
• Kelvin
• Capacitive Comparision
• Inductive Comparision
• Maxwell
• Hay
• Schering
• Wein
T Srinivasa Rao 71

T Srinivasa Rao 72

T Srinivasa Rao 73

• Wein’s Bridge

• Schering’s Bridge
74

x t…
Ne
– II
U NIT


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