Chapter 1
INTRODUCTION
TO
INSTRUMENTATION
OBJECTIVES
At the end of this chapter, students
should be able to:
1.
2.
3.
Explain the static and dynamic
characteristics of an instrument.
Calculate and analyze the measurement
error, accuracy, precision and limiting
error.
Describe the basic elements of electronic
instrument.
INTRODUCTION
Instrumentation is a technology of measurement
which serves sciences, engineering, medicine and
etc.
Measurement is the process of determining the
amount, degree or capacity by comparison with the
accepted standards of the system units being used.
Instrument is a device for determining the value or
magnitude of a quantity or variable.
Electronic instrument is based on electrical or
electronic principles for its measurement functions.
FUNCTION AND ADVANTAGES
The 3 basic functions of instrumentation : Indicating – visualize the process/operation
 Recording – observe and save the measurement
reading
 Controlling – to control measurement and process
Advantages of electronic measurement
 Results high sensitivity rating – the use of amplifier
 Increase the input impedance – thus lower loading
effects
 Ability to monitor remote signal
PERFORMANCE CHARACTERISTICS
Performance Characteristics - characteristics that show
the performance of an instrument.
 Eg: accuracy, precision, resolution, sensitivity.
Allows users to select the most suitable instrument for a
specific measuring jobs.
Two basic characteristics :
 Static – measuring a constant process condition.
 Dynamic - measuring a varying process condition.
PERFORMANCE CHARACTERISTICS
Accuracy – the degree of exactness (closeness) of
measurement compared to the expected (desired) value.
Resolution – the smallest change in a measurement
variable to which an instrument will respond.
Precision – a measure of consistency or repeatability of
measurement, i.e successive reading do not differ.
Sensitivity – ratio of change in the output (response) of
instrument to a change of input or measured variable.
Expected value – the design value or the most probable
value that expect to obtain.
Error – the deviation of the true value from the desired
value.
ERROR IN MEASUREMENT
Measurement always introduce error
Error may be expressed either as absolute or percentage
of error
Y
X
n
Absolute error, e = n
where Yn – expected value
Xn
– measured value
% error =
Yn X n
100
Yn
ERROR IN MEASUREMENT
Relative accuracy, A 1
Yn
Xn
Yn
% Accuracy, a = 100% - % error
= A 100
Precision, P = 1
Xn
Xn
Xn
where X n - value of the nth measurement
X n- average set of measurement
The precision of a measurement is a quantitative or
numerical indication of the closeness with which a
repeated set of measurement of the same variable
agree with the average set of measurements.
Example 1.1
Given expected voltage value across a resistor is 80V.
The measurement is 79V. Calculate,
The
ii. The
iii. The
iv. The
i.
absolute error
% of error
relative accuracy
% of accuracy
Solution (Example 1.1)
Given that , expected value = 80V
measurement value = 79V
i. Absolute error, e = Y X = 80V – 79V = 1V
n
n
ii. % error = Yn X n
100
Yn
iii. Relative accuracy,
A 1
= 80 79
= 1.25%
100
80
Yn
Xn
= 0.9875
Yn
iv. % accuracy, a = A x 100% = 0.9875 x 100%=98.75%
Example 1.2
From the value in table 1.1 calculate
the precision of 6th measurement?
Table 1.1
Solution
the average of measurement value
98 101 .... 99 1005
Xn
100.5
10
10
the 6th reading
Precision = 1 100 100 .5
100 .5
0 .5
1
100 .5
0.995
No
Xn
1
98
2
101
3
102
4
97
5
101
6
100
7
103
8
98
9
106
10
99
LIMITING ERROR
The accuracy of measuring instrument is
guaranteed within a certain percentage (%)
of full scale reading
E.g manufacturer may specify the instrument
to be accurate at 2 % with full scale
deflection
For reading less than full scale, the limiting
error increases
LIMITING ERROR (cont)
Example 1.6
Given a 600 V voltmeter with accuracy 2% full scale.
Calculate limiting error when the instrument is used to
measure a voltage of 250V?
Solution
The magnitude of limiting error, 0.02 x 600 = 12V
Therefore, the limiting error for 250V = 12/250 x 100 = 4.8%
LIMITING ERROR (cont)
Example 1.7
Given for certain measurement, a limiting error for
voltmeter at 70V is 2.143% and a limiting error for ammeter
at 80mA is 2.813%. Determine the limiting error of the
power.
Solution
The limiting error for the power = 2.143% + 2.813%
= 4.956%
Exercise
A voltmeter is accurate 98% of its full
scale reading.
i.
ii.
If the voltmeter reads 200V on 500V
range, what is the absolute error?
What is the percentage error of the
reading in (i).
Significant Figures
Significant figures convey actual information regarding
the magnitude and precision of quantity
More significant figure represent greater precision of
measurement
Example 1.3
Find the precision value of X1 and X2?
X n 101
X1
X2
98 ===>> 2 s.f
98.5 ===>> 3 s.f
Solution (Example 1.3)
Xn
101
X1
98 ===>> 2 s.f
X2
98.5 ===>> 3 s.f
X1
98 101
Precision = 1
101
X2
98 .5 101
Precision = 1
101
0.97
0.975 ===>more precise
Significant Figures (cont)
Rules regarding significant figures in calculation
1) For adding and subtraction, all figures in columns to the
right of the last column in which all figures are significant
should be dropped
Example 1.4
V1 = 6.31 V
+ V2 = 8.736 V
Therefore
VT = 15.046 V
15.05 V
Significant Figures (cont)
2)
For multiplication and division, retain only as many
significant figures as the least precise quantity contains
Example 1.5
From the value given below, calculate the value for R1,
R2 and power for R1?
I = 0.0148 A ===> 3 s.f
V1 = 6.31 V ===> 3 s.f
V2 = 8.736 V ===> 4 s.f
Solution (Example 1.5)
V1
I
R1
R2
V2
I
6.31V
0.0148A
8.736V
0.0148A
P1 V1 I
6.31V
426.35
590.27
426
590
0.0148 A
= 0.09339
= 0.0934 ===> 3 s.f
===> 3 s.f
===> 3 s.f
Significant Figures (cont)
3)
When dropping non-significant figures
0.0148 ==> 0.015 (2 s.f)
==> 0.01 (1 s.f)
TYPES OF STATIC ERROR
Types of static error
1) Gross error/human error
2) Systematic Error
3) Random Error
TYPES OF STATIC ERROR
1) Gross Error
 cause by human mistakes in reading/using instruments
 may also occur due to incorrect adjustment of the instrument





and the computational mistakes
cannot be treated mathematically
cannot eliminate but can minimize
Eg: Improper use of an instrument.
 This error can be minimized by taking proper care in reading
and recording measurement parameter.
In general, indicating instruments change ambient conditions to
some extent when connected into a complete circuit.
Therefore, several readings (at three readings) must be taken to
minimize the effect of ambient condition changes.
TYPES OF STATIC ERROR (cont)
2) Systematic Error
- due to shortcomings of the instrument (such as
defective or worn parts, ageing or effects of the
environment on the instrument)
In general, systematic errors can be subdivided into static
and dynamic errors.
 Static – caused by limitations of the measuring device or
the physical laws governing its behavior.
 Dynamic – caused by the instrument not responding very
fast enough to follow the changes in a measured
variable.
TYPES OF STATIC ERROR (cont)
- 3 types
(i)
(ii)
(iii)
of systematic error :Instrumental error
Environmental error
Observational error
TYPES OF STATIC ERROR (cont)
(i) Instrumental error
- inherent while measuring instrument because of
their mechanical structure (eg: in a D’Arsonval meter,
friction in the bearings of various moving component,
irregular spring tension, stretching of spring, etc)
- error can be avoid by:
(a) selecting a suitable instrument for the particular
measurement application
(b) apply correction factor by determining
instrumental error
(c) calibrate the instrument against standard
TYPES OF STATIC ERROR (cont)
(ii) Environmental error
- due to external condition effecting the
measurement including surrounding area condition
such as change in temperature, humidity,
barometer pressure, etc
- to avoid the error :(a) use air conditioner
(b) sealing certain component in the instruments
(c) use magnetic shields
(iii)
Observational error
- introduce by the observer
- most common : parallax error and estimation error
(while reading the scale)
- Eg: an observer who tend to hold his head too far to the left
while reading the position of the needle on the scale.
TYPES OF STATIC ERROR (cont)
3) Random error
- due to unknown causes, occur when all systematic
error has accounted
- accumulation of small effect, require at high degree of
accuracy
- can be avoid by
(a) increasing number of reading
(b) use statistical means to obtain best approximation
of true value
Dynamic Characteristics
Dynamic – measuring a varying process condition.
Instruments rarely respond instantaneously to
changes in the measured variables due to such
things as mass, thermal capacitance, fluid
capacitance or electrical capacitance.
Pure delay in time is often encountered where the
instrument waits for some reaction to take place.
Such industrial instruments are nearly always used
for measuring quantities that fluctuate with time.
Therefore, the dynamic and transient behavior of the
instrument is important.
Dynamic Characteristics
The dynamic behavior of an instrument is
determined by subjecting its primary element
(sensing element) to some unknown and
predetermined variations in the measured
quantity.
The three most common variations in the
measured quantity:



Step change
Linear change
Sinusoidal change
Dynamic Characteristics
Step change-in which the primary element is
subjected to an instantaneous and finite change in
measured variable.
Linear change-in which the primary element is
following the measured variable, changing linearly
with time.
Sinusoidal change-in which the primary element
follows a measured variable, the magnitude of which
changes in accordance with a sinusoidal function of
constant amplitude.
Dynamic Characteristics
The dynamic performance characteristics of
an instrument are:




Speed of response- The rapidity with which an
instrument responds changes in measured
quantity.
Dynamic error-The difference between the true
and measured value with no static error.
Lag – delay in the response of an instrument to
changes in the measured variable.
Fidelity – the degree to which an instrument
indicates the changes in the measured variable
without dynamic error (faithful reproduction).
Standard
A standard is a known accurate measure of physical
quantity.
Standards are used to determine the values of other
physical quantities by the comparison method.
All standards are preserved at the International
Bureau of Weight and Measures (BIMP), Paris.
Four categories of standard:




International Standard
Primary Standard
Secondary Standard
Working Standard
Standard
International Std
 Defined by International Agreement
 Represent the closest possible accuracy attainable by the current
science and technology
Primary Std
 Maintained at the National Std Lab (different for every country)
 Function: the calibration and verification of secondary std
 Each lab has its own secondary std which are periodically checked
and certified by the National Std Lab.
 For example, in Malaysia, this function is carried out by SIRIM.
Standard
Secondary Standard
 Secondary standards are basic reference standards used by
measurement and calibration laboratories in industries.
 Each industry has its own secondary standard.
 Each laboratory periodically sends its secondary standard to the
National standards laboratory for calibration and comparison
against the primary standard.
 After comparison and calibration, the National Standards
Laboratory returns the secondary standards to particular industrial
laboratory with a certification of measuring accuracy in terms of a
primary standard.
Working Std
 Used to check and calibrate lab instrument for accuracy and
performance.
 For example, manufacturers of electronic components such as
capacitors, resistors and many more use a standard called a
working standard for checking the component values being
manufactured.
ELECTRONIC INSTRUMENT
• Basic elements of an electronics instrument
Transducer
Signal
Modifier
Indicating
Device
1) Transducer
- convert a non electrical signal into an electrical signal
- e.g: a pressure sensor detect pressure and convert it to
electricity for display at a remote gauge.
2) Signal modifier
- convert input signal into a suitable signal for the indicating
device
3) Indicating device
- indicates the value of quantity being measure
INSTRUMENT APPLICATION GUIDE
Selection, care and use of the instrument : Before using an instrument, students should be thoroughly
familiar with its operation ** read the manual carefully
 Select an instrument to provide the degree of accuracy
required (accuracy + resolution + cost)
 Before used any selected instrument, do the inspection for
any physical problem
 Before connecting the instrument to the circuit, make
sure the ‘function switch’ and the ‘range selector switch’
has been set-up at the proper function or range
INSTRUMENT APPLICATION GUIDE
Analog Multimeter
INSTRUMENT APPLICATION GUIDE
Digital Multimeter
CHAPTER REVIEW
Define the terms accuracy, error, precision, resolution, expected
value and sensitivity.
State three major categories of error.
A person using an ohmmeter reads the measured value as 470
ohm when the actual value is 47 ohm. What kind of error does
this represent?
State the classifications of standards.
What are primary standards? Where are they used?
What is the difference between secondary standards and
working standards?
State three basic elements of electronic instrument.
THE END
CHAPTER 2
DC AND AC METER
43
OBJECTIVES
At the end of this chapter, students
should be able to:
1.
2.
3.
Explain the basic contruction and working
principle of D’Arsonval meter movement.
Perfom basic electronic circuit analisis for
D’Arsonval meter family.
Identify the difference electronic circuit
design for measurement meters using
D’Arsonval meter principle.
44
CHAPTER OUTLINE
1.
2.
3.
4.
5.
6.
7.
D’Arsonval Meter Movement
DC Ammeter
DC Voltmeter
Multi-range Voltmeter
Voltmeter Loading Effects
Ammeter Insertion Effects
Ohmmeter
8. Multi-range Ohmmeter
9. Multimeter
10. AC Voltmeter using half-wave
rectifier
11. AC Voltmeter Loading Effects
12. Wheatstone Bridge
13. Kelvin Bridge
14. Bridge-controlled Circuit
45
2.1: D’ARSORVAL METER
MOVEMENT
Also called Permanent-Magnet Moving Coil
(PMMC).
Based on the moving-coil galvanometer
constructed by Jacques d’ Arsonval in 1881.
Can be used to indicate the value of DC and AC
quantity.
Basic construction of modern PMMC can be seen in
Figure 2.1.
46
2.1.1:Operation of D’Arsonval
Meter
When current flows through the coil, the core will
rotate.
Amount of rotation is proportional to the amount
of current flows through the coil.
The meter requires low current (~50uA) for a full
scale deflection, thus consumes very low power
(25-200 Uw).
Its accuracy is about 2% -5% of full scale
deflection
47
Pointe
r
Permanent
magnet
Core
Coil
Air
Gap
Figure 2.1: Modern D’Arsonval Movement
48
2.2: DC AMMETER
The PMMC galvanometer constitutes the basic
movement of a dc ammeter.
The coil winding of a basic movement is small and
light, so it can carry only very small currents.
A low value resistor (shunt resistor) is used in DC
ammeter to measure large current.
Basic DC ammeter:
49
+
I
Ish
Rsh
Im
+
Rm
_
D’Arsonval
Movement
_
Figure 2.2: Basic DC
Ammeter
50
Referring to Fig. 2.2:
Rm = internal resistance of the
movement
Rsh = shunt resistance
Ish =shunt current
Im = full scale deflection current
of the movement
I
= full scale current of the
ammeter + shunt (i.e. total
current)
51
I sh Rsh
I m Rm
I sh
I
Im
Rsh
I m Rm
I Im
52
EXAMPLE 3.1
A 1mA meter movement with an
internal resistance of 100Ω is to be
converted into a 0-100 mA. Calculate
the value of shunt resistance required.
(ans: 1.01Ω)
53
2.2.1: MULTIRANGE AMMETER
The range of the dc ammeter is extended
by a number of shunts, selected by a range
switch.
The resistors is placed in parallel to give
different current ranges.
Switch S (multiposition switch) protects the
meter movement from being damage during
range changing.
Increase cost of the meter.
54
+
R1
R2
R3
R4
+
Rm
_
D’Arsonval
Movement
S
_
Figure 2.3: Multirange
Ammeter
55
2.2.2: aryton shunt or universal
shunt
Aryton shunt eliminates the possibility of having the
meter in the circuit without a shunt.
Reduce cost
Position of the switch:
a)‘1’: Ra parallel with series combination of Rb, Rc and
the meter movement. Current through the shunt is
more than the current through the meter movement,
thereby protecting the meter movement and reducing
its sensitivity.
b)‘2’: Ra and Rb in parallel with the series combination
of Rc and the meter movement. The current through
the meter is more than the current through the shunt
resistance.
c)‘3’: Ra, Rb and Rc in parallel with the meter.
Maximum current flows through the meter movement
and very little through the shunt. This will
increase the sensitivity.
56
Rc
+
3
1
2
+
Rm
_D’Arsonval Meter
Rb
Ra
_
Figure 2.4: Aryton
Shunt
57
EXAMPLE 2.2
Design an Aryton shunt to provide an ammeter with a
current range of 0-1 mA, 10 mA, 50 mA and 100 mA. A D’
Arsonval movement with an internal resistance of 100Ω
and full scale current of 50 uA is used.
1m
A
+
R4
10m
A
50mA
R3
R2
+
_ D’Arsonval
Movement
100m
A
_
R1
58
REQUIREMENT OF A SHUNT
1) Minimum Thermo Dielectric
Voltage Drop
Soldering of joint should not cause a
voltage drop.
2) Solderability
- never connect an ammeter across a
source of e.m.f
- observe the correct polarity
- when using the multirange meter,
first use the highest current range.
59
2.3: BASIC METER AS A DC
VOLTMETER
To use the basic meter as a dc voltmeter, must know
the amount of current (Ifsd) required to deflect the basic
meter to full scale.
The sensitivity is based on the fact that the full scale
current should results whenever a certain amount of
resistance is present in the meter circuit for each
voltage applied.
S
1
I fsd
60
EXAMPLE 2.3
Calculate the sensitivity of a 200 uA
meter
movement which is to be used as a dc
voltmeter.
S
Solution:
1
I fsd
1
200 uA
5k / V
61
2.4: A DC VOLTMETER
A basic D’Arsonval movement can be converted into
a DC voltmeter by adding a series resistor (multiplier)
as shown in Figure 2.3.
+
Rs
Multiplier
V
Im
Rm
_
Figure 2.5: Basic DC
Voltmeter
Im =full scale deflection current of
the movement (Ifsd)
Rm=internal resistance of the 62
From the circuit of Figure 2.5:
V
Rs
Rs
I m ( Rs
V
V
Im
Rm )
I m Rm
Im
Rm
Therefore,
63
V
Im
Rm
EXAMPLE 2.4
A basic D’ Arsonval movement with a
full-scale deflection of 50 uA and
internal resistance of 500Ω is used as
a DC voltmeter. Determine the value
of the multiplier resistance needed to
measure a voltage range of 0-10V.
Rs
Solution:
V
Im
Rm
10V
500
50 uA
64
199 .5k
Sensitivity and voltmeter range can be
used to calculate the multiplier
resistance, Rs of a DC voltmeter.
Rs=(S x Range) - Rm
From example 2.4:
Im= 50uA, Rm=500Ω,
Range=10V
1
1
S
20 k / V
Sensitivity,
I m 50 uA
So, Rs = (20kΩ/V x 6510V) – 500 Ω
2.5: MULTI-RANGE
VOLTMETER
A DC voltmeter can be converted into
a multirange voltmeter by connecting
a number of resistors (multipliers) in
series with the meter movement.
A practical multi-range DC voltmeter
R1
R2
R3
R4
is shown in Figure 2.6.
V1
+
V2
V3
V4
_
Figure 2.6: Multirange voltmeter
66
Rm
Im
EXAMPLE 2.5
Convert a basic D’ Arsonval movement
with an internal resistance of 50Ω and
a full scale deflection current of 2 mA
into a multirange dc voltmeter with
voltage ranges of 0-10V, 0-50V,
0-100V and 0-250V.
67
2.6: VOLTMETER LOADING
EFFECTS
When a voltmeter is used to measure
the voltage across a circuit
component, the voltmeter circuit itself
is in parallel with the circuit
component.
Total resistance will decrease, so the
voltage across component will also
decrease. This is called voltmeter
loading.
The resulting error is called a loading
68
error.
2.7 AMMETER INSERTION
EFFECTS
Inserting Ammeter in a circuit always
increases the resistance of the circuit
E
and, thus always
reduces the current in
Ie
R1
the circuit. The expected
current:
(2-4)
E
PlacingIthe
meter in series with R1
m
R1 R
causes the current
tomreduce to a value
equal to:
69
(2-5)
2.7 AMMETER INSERTION
EFFECTS
Dividing equation (2-5) by (2-4) yields:
Im
Ie
R1
R1 Rm
(2-6)
Im
Xerror
100 is given by
The Ammeter1 insertion
Ie
:
Insertion Error
(2-7)
70
2.8 OHMMETER (Series Type)
Current flowing through meter movements depends on the
magnitude of the unknown resistance.(Fig 4.28 in text book)
The meter deflection is non-linearly related to the value of the
unknown Resistance, Rx.
A major drawback – as the internal voltage decreases, reduces the
current and meter will not get zero Ohm.
R2 counteracts the voltage drop to achieve zero ohm. How do you get
zero Ohm?
R1 and R2 are determined by the value of Rx = Rh where Rh = half of
full scale deflection resistance.
Rh
R1 ( R2 // Rm )
R1
The total current of the circuit, It=V/Rh
The shunt current through R2 is I2=It-Ifsd
71
R2 Rm
R2 Rm
(2-8)
2.8 OHMMETER (Series Type)
The voltage across the shunt, Vsh= Vm
So,
Since
I2 R2=Ifsd Rm
I2=It-Ifsd
Then,
R2
I fsd Rm
It
I fsd
Since
It=V/Rh
So,
R2
I fsd Rm Rh
V
(2-9)
I fsd Rh
72
2.8 OHMMETER (Series Type)
From equation (2-8) and (2-9):
R1
Rh
I fsd Rm Rh
V
73
(2-10)
Figure 2.7: Measuring circuit resistance with an
ohmmeter
74
Example:
1) A 50µA full scale deflection current meter movement is to
be used in an Ohmmeter. The meter movement has an
internal resistance Rm = 2kΩ and a 1.5V battery is used in
the circuit. Determine Rz at full scale deflection.
2) A 100Ω basic movement is to be used as an ohmmeter
requiring a full scale deflection of 1mA and internal battery
voltage of 3V . A half scale deflection marking of 2k is
desired. Calculate:
i. value of R1 and R2
ii. the maximum value of R2 to compensate for a 5% drop in
battery voltage
75
2.9 MULTI-RANGE
OHMMETER
Another method of achieving flexibility
of a measuring instrument is by
designing it to be in multi-range.
Let us analyse the following examples.
(figure 4.29 of your textbook)
76
2.10 MULTIMETER
Multimeter consists of an ammeter,
voltmeter and ohmmeter in one unit.
It has a function switch to connect the
appropriate circuit to the D’Arsonval
movement.
Fig.4.33 (in text book) shows DC
miliammeter, DC voltmeter, AC
voltmeter, microammeter and
ohmmeter.
77
2.11 AC VOLTMETER USING
HALF-WAVE RECTIFIER
The D’Arsonval meter movement can be used to measure
alternating current by the use of a diode rectifier to produce
unidirectional current flow.
In case of a half wave rectifier, if given input voltage, Ein = 10
Vrms, then:
Peak voltage,
Ep
10Vrms 1.414
14 .14V
Average voltage,
Eave Edc 0.636 E p 8.99V
o Since the diode conducts only during the positive half cycle as
shown in Fig 4.18(in text book), the average voltage is given by:
Eave / 2=4.5V
78
2.11 AC VOLTMETER USING
HALF-WAVE RECTIFIER
Therefore, the pointer will deflect for a full scale if 10 Vdc
is applied and only 4.5 V when a 10 Vrms sinusoidal signal
is applied.
The DC voltmeter sensitivity is given by:
S dc
1
Im
1
1mA
1k / V
For the circuit in Figure 4.18, the AC voltmeter sensitivity is
given by:
S ac
0.45 S dc
0.45 k / V
This means that an AC voltmeter is not as sensitive as a DC
voltmeter.
79
2.11 AC VOLTMETER USING
HALF-WAVE RECTIFIER
To get the multiplier resistor, Rs value:
Edc
0.45 Erms
Rs
Edc
I dc
Rm
0.45 Erms
I dc
(2-11)
Rm
o The AC meter scale is usually calibrated to give the RMS value of an
alternating sine wave input.
A more general AC voltmeter circuit is shown in Fig. 4.17 (in text
book)
A shunt resistor, Rsh is used to draw more current from the diode D1
to move its operating point to a linear region.
Diode D2 is used to conduct the current during the negative half
cycle.
The sensitivity of AC voltmeter can be doubled by using a full wave
rectifier.
80
EXAMPLE
Calculate the value of the multiplier
resistor for a 10 Vrms range on the
voltmeter shown in Fig 4.19 (in text
book)
81
2.11 AC VOLTMETER USING
FULL-WAVE RECTIFIER
Consider the circuit in Fig 4.20 (in text book)
Rs
S ac range Rm
Example:
Calculate the value of the multiplier resistor for a 10 Vrms ac
range on the voltmeter in Fig. 4.21
82
2.12 WHEATSTONE BRIDGE
Accurate method for measuring
resistance between 1Ω ~ 1MΩ.
Figure 11.1 shows the schematic
diagram of a Wheatstone Bridge.
When the bridge is set to null condition,
I1 R1
I 2 R2
voltages at point C & D are equal.
Thus I 3 R3 I 4 R4
(2-12)
(2-13)
83
2.12 WHEATSTONE BRIDGE
Since I1 = I3 and I2 = I4, divide equation 2-12 by equation 2-13:
R1
R3
R2
R4
So,R X
R2 R3
R4
R1
(2-14)
Usually, the resistor R3 is a variable resistor to balance the bridge.
RX is the unknown resistor to be measured.
When bridge is balance, the value of the unknown resistor RX is
equal to resistance value of R3
84
2.12 WHEATSTONE BRIDGE
Example:
1. Given the Wheatstone bridge with R1
= 15 kΩ, R2 = 10 kΩ, and R3 = 4.5
kΩ. Find RX.
2. Calculate the current through the
Galvanometer in the circuit. Given R1
= 1 kΩ, R2 = 1.6 kΩ, R3 = 3.5 kΩ, R4
= 7.5 kΩ, RG = 200Ω and V = 6V.
85
2.13 KELVIN BRIDGE
Kelvin Bridge is used to measure
resistance below 1 Ω.
In low resistance measurement, the
leads connecting the unknown resistor
to the bridge may effect the
measurement.
Kelvin’s Double Bridge known as Kelvin
Bridge is constructed to overcome this
problem.
86
2.13 KELVIN BRIDGE
The resistor RY represents the lead and contact resistance
present in the Wheatstone Bridge.
The resistors Ra and Rb are used to compensate this low leadcontact resistance.
From circuit analysis, the unknown Resistor RX in a balanced
Kelvin Bridge is given by:
RX
R2
R3
R1
Rb
Ra
See example 11.4 (textbook)
87
(2-15)
2.14 BRIDGE CONTROLLED
CIRCUIT
When a bridge is imbalance, a potential difference exists at its output
terminal.
If it is used as an error detector in a control circuit, the potential
difference at the output of the bridge is called an error signal.
The error signal is given by:
Es
E
R3
R1
RV
R3
R2
RV
(2-16)
The unknown resistor RV can be any passive circuit elements such as
strain gauge, thermistor and photo resistor.
Since RV varies by only a small amount, an amplifier often needed
before being used for control purposes.
Fig. 11.14 shows the Wheatstone Bridge error detector.
88
What is a multimeter?
A multimeter is a devise used to measure voltage,
resistance and current in electronics & electrical equipment
It is also used to test continuity between to 2 points to
verify if there is any breaks in circuit or line
There are two types of multimeter Analog & Digital
 Analog has a needle style gauge
 Digital has a LCD display (Referenced during this PPT)
There are 2 styles of multimeters
Switched
Manually switch
between ranges to get
most accurate reading.
Auto Range
Switches between
ranges automatically
for best reading.
Both of these
styles work the
same
Meter leads
•Red meter lead
Is connected to Voltage/Resistance or amperage
port
Is considered the positive connection
•Probes
Are the handles used to
hold tip on the tested
connection
•Tips
Are at the end of the probe
and provides a connection
point
•Black meter lead
Is always connected to the common port
Is considered the negative connection
Display & Dial Settings
• Digital Display
Shows measured value.
• Meter Dial
Turn dial to change functions.
Turn dial to OFF position after
use.
• Panel Indicator
Shows each function and
setting range to turn dial to.
• Probe Connections
Specific for each function.
Common DMM Symbols
~
--Hz
+
AC Voltage
Ground
DC Voltage
(
Capacitor
Hertz
F
MicroFarad
Positive
Micro
Negative
m
Milli
Ohms
M
Mega
*
Diode
K
Kilo
These
are
often found onOL
multimeter
))) symbols
Audible
Continuity
Overload
and schematics.
They are designed to symbolize components
and reference values.
Measuring Voltage
Voltage (V) is the unit of electrical pressure; one volt is the
potential difference needed to cause one amp of current to
pass through one ohm of resistance
Voltage is broke up into 2 sections AC & DC
Alternating Current (AC) is house voltage (110vac)
Direct Current (DC) is battery voltage (12vdc)
On switched meters use one value higher than your expected
value
Be very careful to not touch any other electronic components
within the equipment and do not touch the tips to each other
while connected to anything else
To measure voltage connect the leads in parallel between the
two points where the measurement is to be made. The
multimeter provides a parallel pathway so it needs to be of a
high resistance to allow as little current flow through it as
possible
Measuring Voltage
Measuring Voltage
9.3vdc
Measuring Resistance and Continuity
Resistance ( ) is the opposition to current
Resistance is measured in Ohm's
Disconnect power source before testing
Remove component or part from system before testing
Measure using lowest value, if OL move to next level
Testing for continuity is used to test to verify if a circuit, wire
or fuse is complete with no open
Audible continuity allows an alarm if circuit is complete
If there is no audible alarm resistance of 1ohm to .1ohm
should be present
Measuring Resistance
Measuring or Testing Continuity
Measuring Resistance
100
Measuring Continuity
.5
Fuse
5 amp
Measuring Current
Current (amps) is the flow of electrical charge though a
component or conductor
Current is measured in amps or amperes
Disconnect power source before testing
Disconnect completed circuit at end of circuit
Place multimeter in series with circuit
Reconnect power source and turn ON
Select highest current setting and work your way down.
Measuring Current
Measuring Current
1.1amps
Review
A meter capable of checking for voltage, current, and
resistance is called a multimeter,
When measuring Voltage the multimeter must be connected
to two points in a circuit in order to obtain a good reading.
Be careful not to touch the bare probe tips together while
measuring voltage, as this will create a short-circuit!
Never read Resistance or test for Continuity with a
multimeter on a circuit that is energized.
When measuring Current the multimeter must be connected
in a circuit so the electrons have to flow through the meter
Multimeters have practically no resistance between their
leads. This is intended to allow electrons to flow through
the meter with the least possible difficulty. If this were not
the case, the meter would add extra resistance in the
circuit, thereby affecting the current
Measurement of Voltages
and Currents
 Introduction
 Sine waves
 Square waves
 Measuring Voltages and Currents
 Analogue Ammeters and Voltmeters
 Digital Multimeters
 Oscilloscopes
Chapter 11
Introduction
11.1
Alternating currents and voltages vary with
time and periodically change their direction
Sine Waves
11.2
Sine waves

by far the most important form of alternating
quantity
 important properties are shown below
Instantaneous value


shape of the sine wave is defined by the
sine function
y = A sin
in a voltage waveform
v = Vp sin
Angular frequency




frequency f (in hertz) is a measure of the
number of cycles per second
each cycle consists of 2 radians
therefore there will be 2 f radians per
second
this is the angular frequency (units
are rad/s)
=2 f
Equation of a sine wave


the angular frequency can be thought of
as the rate at which the angle of the sine
wave changes
at any time
= t

therefore
v = Vp sin t
sin 2 ft
or
v = Vp
Example – see Example 11.2 in the
course text
Determine the equationFrom
of diagram:
the following
 Period is 50 ms = 0.05 s
voltage signal.
 Thus f = 1/T =1/0.05 = 20 Hz
 Peak voltage is 10 V
 Therefore
v Vp sin 2 ft
10 sin 2 20t
10 sin 126t
Phase angles


the expressions given above assume the
angle of the sine wave is zero at t = 0
if this is not the case the expression is
modified by adding the angle at t = 0
Phase difference

two waveforms of the same frequency may
have a constant phase difference
 we say that one is phase-shifted with respect
to the other
Average value of a sine wave


average value over one (or more) cycles is
clearly zero
however, it is often useful to1know the
Vav waveform
0Vp sin dθ
average magnitude of the
independent of its polarity Vp
cos
 we can think of this as
the average value over
half a cycle…
 … or as the average value
of the rectified signal
2Vp
0
0.637 Vp
Average value of a sine wave
r.m.s. value of a sine wave

the instantaneous power (p) in a resistor is
v2
given by
p
R
2
2
[
average
(or
mean)
of
v
]
v
 therefore
the average power is given
Pav
R
R
v
2
by
While the mean-square voltage is
useful, more often we use the square
root of this quantity,
namely the root2
v
mean-square voltage Vrms


where Vrms =
we can also define Irms =
Vrms

i2
1 V
p
2
0.707 Vp
Irms
1 I
2 p
0.707 I p
it is relatively easy to show that (see text
for analysis)
r.m.s. values are useful because their
relationship to average power is similar
to the corresponding DC values
P
av
P
V
rms rms
av
2
V
rms
R
av
P
I
I
2
rms
R
Form factor

for any waveform the form factor is
r.m.s. value
defined
Formas
factor
average value
0.707 V

p
Form
factor
1.11
for a sine wave
this
gives
0.637 V
p
Peak factor

for any waveform the peak factor is
peak value
defined
Peakasfactor
r.m.s. value
V

p
Peak
factor
1.414
for a sine wave
this
gives
0.707 V
p
Square Waves
Frequency, period, peak value and
peak-to-peak value have the same
meaning for all repetitive waveforms
11.3
Phase angle




we can divide the period
into 360 or 2 radians
useful in defining phase
relationship between signals
in the waveforms shown
here, B lags A by 90
we could alternatively give
the time delay of one with
respect to the other
Average and r.m.s. values



the average value of a symmetrical
waveform is its average value over the
positive half-cycle
V
V
thus the average
of a symmetrical
av value
p
square wave is equal to its peak value
similarly, since
V theVinstantaneous value of
rms
p
a square wave is either its peak positive or
peak negative value, the square of this is
Form factor and peak factor

from the earlier definitions, for a square
V
wave
p
r.m.s. value
Form factor
1.0
average value
Peak factor
peak value
r.m.s. value
V
p
V
p
V
p
1.0
Measuring Voltages and
Currents
Measuring voltage and current in a
circuit


when measuring voltage we connect across the component
when measuring current we connect in series with the
component
11.4
Measuring Voltages and
Currents
Loading effects –
voltage
measurement


our measuring instrument will
have an effective resistance (RM)
when measuring voltage we
connect a resistance in parallel
with the component concerned
which changes the resistance in
the circuit and therefore changes
the voltage we are trying to
measure
11.4
Measuring Voltages and
Currents
Loading effects –
current measurement

our measuring instrument will have an
effective resistance (RM)


when measuring current we connect a
resistance in series with the component
concerned which again changes the
resistance in the circuit and therefore
changes the current we are trying to
measure
this is again a loading effect
11.4
Analogue Ammeters and
Voltmeters
11.5
Most modern analogue
ammeters are based on
moving-coil meters

see Chapter 4 of textbook
Meters are characterised by their full-scale deflection (f.s.d.)
and their effective resistance (RM)

typical meters produce a f.s.d. for a current of 50 A – 1 mA

typical meters have an RM between a few ohms and a few kilohms
Measuring direct
currents using a
moving coil meter


use a shunt
resistor to adjust
sensitivity
see Example 11.5
in set text for
numerical
calculations
Measuring direct
voltages using a
moving coil meter


use a series
resistor to adjust
sensitivity
see Example 11.6
in set text for
numerical
calculations
Measuring alternating quantities





moving coil meters respond to both positive and negative
voltages, each producing deflections in opposite directions
a symmetrical alternating waveform will produce zero
deflection (the mean value of the waveform)
therefore we use a rectifier to produce a unidirectional
signal
meter then displays the average value of the waveform
meters are often calibrated to directly display r.m.s. of sine
waves
 all readings are multiplied by 1.11 – the form factor for a sine
wave

as a result waveforms of other forms will give incorrect
readings
Analogue multimeters




general purpose instruments use a
combination of switches and resistors
to give a number of voltage and
current ranges
a rectifier allows the measurement of
AC voltage and currents
additional circuitry permits resistance
measurement
very versatile but relatively low input
resistance on voltage ranges produces
considerable loading in some
situations
A typical analogue multimeter
Digital Multimeters
11.6
Digital multimeters (DMMs) are often
(inaccurately) referred to as digital
voltmeters or DVMs

at their heart is an analogue-to-digital
converter (ADC)
A simplified block diagram
Measurement of voltage, current and
resistance is achieved using appropriate
circuits to produce a voltage proportional
to the quantity to be measured


in simple DMMs alternating signals are
rectified as in analogue multimeters to
give its average value which is multiplied
by 1.11 to directly display the r.m.s. value
of sine waves
more sophisticated devices use a true
r.m.s. converter which accurately
produced a voltage proportional to the
r.m.s. value of an input waveform
A typical digital multimeter
Oscilloscopes
11.7
An oscilloscope displays voltage waveforms
A simplified block diagram
A typical analogue oscilloscope
Measurement of phase difference
Key Points
The magnitude of an alternating waveform can be
described by its peak, peak-to-peak, average or r.m.s.
value
The root-mean-square value of a waveform is the value
that will produce the same power as an equivalent direct
quantity
Simple analogue ammeter and voltmeters are based on
moving coil meters
Digital multimeters are easy to use and offer high accuracy
Oscilloscopes display the waveform of a signal and allow
quantities such as phase to be measured.