Chapter 5
Data presentation and recording
Analogue instruments
Direct Current Instruments:
 this type of instruments is based on the
electromagnetic induction theory
 which maintains that – if a current is passed through
a coil suspended in the field of a permanent
1
magnet, the coil experiences a torque which is given
by:
 T = BANI where
 B = flux density in the air gap between the coil and
the magnet
Cont’d
 A = area of coil
 N = number of turns and
2
 I = current
 for a given system, B, A, N, are constant i.e. T
I or T =
kI
Cont’d
 It consists of a horse – shoe permanent magnet
with N and S soft iron pole pieces at its ends.
 Between the N and S pole pieces is suspended a
cylindrical-shaped soft iron core with a coil of fine
wire wound over it.
3
 The current being measured passes through the coil
and causes the pointer to deflect up-scale against
the tension of a spring mechanism, T2 such that
when the two torques are balanced, T2 = k2θ = T =
BANI
PMMC
4
5
6
Cont’d
 Where k2 = spring constant
 & θ = angular displacement of the coil
 At balance, k2θ = BANI and θ = SI
 Where
S=
BAN is the sensitivity or
calibration k2
7
Cont’d
constant of the Galvanometer.
 Very often, large currents need to measured and
modification of the basic movement is necessary.
 One way is to use a low value resistor across the coil
in order to shunt away part of the current from the
coil as shown below:
I Im Rm
8
Cont’d
Rsh
I sh
 Where I is current to be measured (i.e. full
scale deflection current of the modified
instrument.)

Im is full scale current of the basic PMMC
9
Cont’d
R m is internal resistance of the meter
movement.

Ish is current through the shunt resistor.
 How then system works:
𝑉�𝑚��=�𝑅�𝑚�𝐼�𝑚��=�𝑅�𝑠�ℎ𝐼�𝑠�ℎ
𝐼�𝑠�ℎ�=�𝐼�−𝐼�𝑚�
10
Cont’d
∴�𝑅�𝑚�𝐼�𝑚��=�𝑅�𝑠�ℎ(𝐼�−𝐼�𝑚�)
𝑅�𝑚�𝐼�𝑚�
∴�𝑅�𝑠�ℎ�=�
𝐼�−𝐼�𝑚�
 To evaluate Rsh, both Rm and Ifs must be
known.
11
Cont’d
 It is convenient in design to choose a number,
R
n, such that n = I/Im i.e.Rsh =
m
n−1
 Rm ranges from a few ohms to several
hundred ohms.
 The multi-range meter:
12
Cont’d
I m =100 A
Ish
R m = 1k
Rb
Rc
1A
100mA
Ra
10mA
•
13
Cont’d
 The assignment is to find Ra, Rb, and Rc for the
three ranges. For example on the 10mA
range, Rsh = Ra + Rb + Rc and on this range,
n=
10mA
=100
100 A
14
Cont’d

Rsh =
Rm
=10.1 n−1
Ra +Rb +Rc =10.1
15
Precautions to be observed when
using an ammeter
i.
always connect meter in series with circuit
under test.
ii. Observe correct polarity to avoid damage iii.
Select highest range to begin with and reduce
range for a good upscale reading. Greatest
accuracy is obtained when meter is reading
close to full – scale deflection.
16
iv. Ammeter resistance must be less than resistance
of circuit under test to avoid insertion errors.
Ammeter insertion errors
 An ammeter always exhibit some internal resistance
and its insertion into a test circuit always:
 increases the circuit resistance and reduces the current.
 the resulting error depends on the relationship between
the ammeter resistance and the original circuit
resistance.
17
 Equivalent circuit for ammeter with zero internal
resistance gives the expected value of current.
Cont’d
Example:
Ie = E/R1
R1
Ie
18
E
Rm = 0
example
 Ammeter resistance is not zero
 Then
E
I=
& E = IeR1
19
R1 + Rm
R1Ie
Im =
R1 + Rm
example
Find the error due to ammeter insertion
A current meter with internal resistance of
100Ω is used to measure current through Rc
20
Ra
1k
1k
E = 10V
Rc =1k
Rb
X
Y
solution
 Looking from x y back into the circuit, Thevenin’s
equivalent resistance is
21
R a Rb
RTH =Rc +
1.5k
=
Ra +Rb
 The ratio of the meter current to expected
current is
𝐼�𝑚�
𝑅�𝑇�𝐻�
1500Ω
=
𝐼�𝑒�
=
𝑅�𝑇�𝐻�+𝑅�𝑚��1500Ω+100Ω
Cont’d
22
I
 And Ime = 0.9375
I = 0.9375I
m
e
which implies that the error due to meter
insertion is 6.25%
Use of the PMMC for dc voltage
measurement:
23
The PMMC can be converted to measure
voltage by incorporating a series resistor
to extend the voltage range and limit the
current through the meter to its full scale
reading.
Im
Rs
Rm
24
Cont’d
Where Rs is multiplier resistor
– Analysis of the above circuit– First define sensitivity as the reciprocal of full scale
deflection current i.e S = 1/Ifs in Ω/v ( this is
normally quoted on practical meters).
– This gives us the resistance of the voltmeter for 1v
full scale deflection
– For voltage ranges greater than 1V, R s is found
25
from:
𝑉��=�𝐼�𝑚�(𝑅�𝑠��+𝑅�𝑚�)
∴�𝑅�𝑠��=�𝑆�𝑉��−𝑅�𝑚��=�𝑠�𝑒�𝑛�𝑠�𝑖�𝑡�𝑖�𝑣�𝑖�𝑡�𝑦��×𝑟�𝑎�𝑛�𝑔�𝑒��−𝑅�𝑚�
Cont’d
 A practical voltmeter must be multi-range
 The circuit below is a three- range voltmeter:
26
Rm
Rs1
Rs 2
3V
10V
Rs 3
30V
+
_
voltmeter
 Loading and loading errors:
27
 Measuring voltage across a circuit component
effectively puts the meter in parallel with
component
 Effective resistance is reduced and measured
voltage also reduced.
 The difference between expected voltage and
measured voltage is loading error.
28
Cont’d
General precautions when using a
voltmeter: i. Observe polarity ii. Place meter
across component whose voltage is to be
measured.
iii. Always use the highest range first and
decrease for a good upscale reading.
29
iv. Avoid loading errors by using higher sensitivity
voltmeters
Cont’d
Example of meter loading:
30
30V
R = 25k
A
R =5k
B
X
Y
31
example
 It is desired to measure the voltage across X Y
using meters A and B.
 Meter A has the following parameters: S =
1kΩ/V; range used is 10V and Rm = 0.2k
Meter B has the following parameters:
 S = 20kΩ/V and the rest are the same.
32
 Find and compare the loading errors for the two
meters.
solution
5
 Expected voltage across RB =
30V =5V
5+25
 Total resistance the meter presents to the circuit
= SV= 10kΩ
33
 Equivalent parallel resistance =k
3.33k
Voltage reading with meter A =
30V = 3.53V
 and loading error is
100% = 29.4%
34
Calibration of dc meters
 Calibration is the process of matching an
instrument’s reading to a standard instrument
 The following circuit configurations are used to
calibrate dc ammeters and voltmeters
respectively:
35
a. dc ammeter
Constant dc
source
V
Ammeter
under
test
Standard resistor
36
Cont’d
 Voltage across standard resistor is measured
using a standard voltmeter and the value of
the current is calculated from Ohm’s law.
b. Dc voltmeter:
Constant
Dc source
Standard
instrument
Voltmeter
37
Cont’d
Under test
Standard resistor
 The PMMC is a dc current sensing device which
is capable of measuring small dc currents.
 It consists of a permanent horse-shoe magnet
and a movable electromagnetic coil with a
pointer attached to it .
 Larger currents can be measured by adding
shunts across the meter and
38
Cont’d
 voltages by adding multipliers in series with the
meter movement.
 Loading or insertion error –
 This is the error caused by placing a meter in
the circuit to obtain a measurement.
 Sensitivity – reciprocal of full – scale current
expressed in ohm / volt.
39
Cont’d
Voltmeter-ammeter method of measuring
resistance:
V
 This is based on Ohm’s law R =
I
40
Basic configurations
Two basic configurations can be used as
shown:I Ix
I t Ix
41
t
A
A
Vx
V
V
Rx
(a)
Vx
Rx
(b)
42
Cont’d
analysis
 In (a) the true current supplied to load is
measured by ammeter.
 But the voltmeter measures the supply
voltage and not the load voltage.
 To obtain the right load voltage, voltage
across ammeter must be subtracted from
supply
43
 In (b), the true load voltage is measured by
voltmeter.
 In this case the ammeter also measures the
current drawn by the voltmeter.
 The ohmmeter:
 This is the instrument that directly measures
resistance in Ohms
 Series type
44
Cont’d
 Shunt type
Measurement of ac signals
Sinusoids
 These are completely specified by their time
domain description
 This specifies the signal amplitude at any
point in time i.e.
,
where is v(t) =Vp sin2 ft Vp the peak value.
45
 In measurements it is convenient to have a
partial signal specification where
 It is desirable to find a time-invariant source
that delivers the energy as v(t) over an interval
T (signal period) into a resistor R. energy
delivered by v(t) is:
T
1 2(t)dt
46
Cont’d
W=
0
Rv
 Energy delivered by an equivalent
2T
timeinvariant source W = V
R
47
Cont’d
 Equating the two:
T=
V
R1 T v2(t)dt
2
R
0
T
1
2
(t)dt
48
Cont’d
V=
v
 V is termed the effective value or the root T 0
mean square value of v(t)
 For a sinusoid, v(t) =Vp sin2 ft Then:
49
Cont’d
Vrms =
=

Vp
2 T
2
T
Vp
0
sin 2 ftdt =
2
Vp
Vp
2 T
1 −cos 2 ft
T 0
2
2
sin 4 ft
−
2
8 ft
since sin4
ft = 0
Vp
50
Cont’d

Vrms == 0.707Vp
2
 Average value of a sinusoid = 0 For a full
wave rectified sine wave, v(t) =Vp sin2 ft
2Vp
 Solution gives:
Vave =
for
full wave = 0.636Vp rectification and
Vp
51
Cont’d
 for half wave rectification Vave =
= 0.318Vp
 Note:
for half and full
Vave = 0.45Vrms &Vave = 0.9Vrms wave rectification
respectively.
52
Ac voltmeter
 The basic PMMC can be used to measure ac
signals using
 either full wave or half wave rectification
 If a 10Vrms signal is applied to a meter using
half wave rectification, meter reads only 4.5V
 i.e. sensitivity of a half wave rectified ac
meter has 0.45 sensitivity of a dc meter.
53
 Practical ½ wave rectified meter is shown
below
54
Cont’d
Practical half-wave rectified ac meter
Rs
A
D2
D1
Rsh
Rm
B
How it works:
55

D2 is reverse biased on the positive half
cycle and has no effect on circuit behavior.
 On the negative half cycle, it provides an
alternative route for reverse bias leakage
current.
 This would normally flow through D1 & Rm

Rsh increases current flow through
D1
56
Cont’d
 This forces it to operate in the more linear
portion of its characteristic curve.
 Example:
 In the half-wave rectified configuration,
calculate:
i. Rs
ii. Voltage sensitivity
57
Cont’d
Rm = Rsh =100 ;Im = I fs =1mA;RD! = RD2 =
400
 and ac voltage being measured is 10Vrms
Solution:
 Equivalent dc value of rectified signal

Edc = 0.45Erms = 4.5V
58
Cont’d
 Total current ,
2mAdc
It = 2I fs =
Edc 2250
 Total resistance as seen at A B =Rt = It =
 Where Rt = Rs +RD1 +
RshRm = Rs +450
Rsh +Rm
59
Cont’d
Rs =1800 &
Rt 225 /V
Sac ==
Vrms
60
Full-wave rectified ac voltmeter
A meter using full-wave rectification will give
an average of 9V from a 10Vrms
i.e. an ac meter using full-wave rectification
has sensitivity equal to 0.9 dc sensitivity.
Example:
In the following diagram of a full-wave
rectified meter, calculate Rs
61
Cont’d
Rs
E =10Vrms
I fs =1mA
Rm = 500
in
62
Cont’d
Solution:

Sdc =
I fs
1
=1k /V
63
Rs = Sac − Rm

&Sac = 0.9Sdc = 900 /V
Rs = 8.5k
64
3-range ac voltmeter
Rs1
Rs 2
D1
Rs 3
•
•
•
Rsh
Rm
D2
65
Recording Instruments Electromechanical and Magnetic
Electromechanical Recorders:
These provide a graphic record on paper of
some physical event over time Basic
elements are: i. paper chart ii. writing
instrument (pen or stylus) iii. interfacing
apparatus between the measurand and
writing instrument
66
Cont’d
Two types of electromechanical
recorders: a. Instruments that record one or
more variables that change with time – Strip
– chart and galvanometer recorders.
b. Instruments that record one or more
dependent variables that change with
67
respect to some independent variable –
called X-Y recorders or function plotters.
Cont’d
Frequency response in electromechanical
recorders is very low (typically 0 to 125 Hz)
This is caused by friction and inertia in moving
parts and friction between writing instrument
and paper.
68
In the case of a galvanometer recorder, use of a
light beam in place of a writing instrument and
photographic paper in place of paper chart
improves frequency response to a few thousand
Hertz.
69
The X-Y Recorder (Function Plotter)
 the X-Y recorder consists of two servo motors
driven from two error detectors and two
servo amplifiers.
 the two motors drive one writing instrument
in the X and Y directions simultaneously.
70
 one signal is the independent variable and
the other is the dependent variable.
 unlike the strip chart, the paper is stationary
X-Y recorder
Applications:
i. Plotting characteristic curves of vacuum tubes,
transistors, diodes, etc.
71
ii. Plotting speed-torque curves for electric motors
iii. Plotting resistance of materials as a function
of temperature.
iv. Physical and mechanical measurements such as
pressure- volume, temperature-linear
expansion, stress-strain, etc.
Strip chart
A strip chart records the variation of a quantity
with respect to time
72
Pen or stylus traces a straight line on the sheet of
paper
The paper is driven past the writing instrument
by another motor.
This can be used in conjunction with a
thermocouple or a resistive type of temperature
transducer to record temperature variation with
time.
As shown in the diagram:
73
iron
iron
hot
iron
constantan
Strip-chart
recorder
Ice bath
Applications
Recording of sound levels:
74
Cont’d
 Used in conjunction with a microphone,
sound level variations with time can be
recorded.
 If levels are not high enough, an amplifier is
imposed before the recorder.
Recording amplifier drift:
 Drift is change in operating point of
semiconductor devices over a long period.
75
 Drift is temperature dependent and can be
recorded by a strip-chart recorder The
setup is shown below:
Load
Amp
Strip −chart
recorder
76
Cont’d
Magnetic Tape Recording:
 Low frequency limitation( 0 to 125Hz)
encountered in electromechanical recorders is
overcome by use of magnetic recorders.
 magnetic tape recording relies on the altering
or reorientation of the domain structure of
fine metal oxide particles deposited uniformly
77
on a plastic ribbon or tape (also applicable to
magnetic discs).
 The recorder must have at least 2 heads, an
erase head and a record / reproduce head.
Advantages over the electromechanical types:
 Much higher frequency response
i. Record and repay speeds can be changed
easily.
78
Cont’d
ii. Recorded material can be played very many
times without noticeable deterioration
Cont’d
iii. Recorded material is readily available as an
electrical signal if needed for further processing
iv. Tape can be erased and re-recorded many times
v. Possibility of easy multi-track recording.
Major Disadvantages:
79
sensitivity to heat and affected by stray magnetic
fields.
80
The cathode ray oscilloscope(CRO)
 This is one of the most versatile instruments
in any laboratory.
 Usefulness is only limited by user’s ability and
imagination.
 It finds applications in measurement of: i. Ac
and dc voltages and currents ii. Time
81
Cont’d
iii. Phase relationships iv.
Frequency and
v. To perform waveform evaluations e.g. rise
time, fall time, ringing, overshoot, etc. vi. Non
electrical quantities can be measured by
incorporating suitable transducers
82
vii. e.g. a temperature probe for temperature
measurements.
Cont’d
The oscilloscope consists of six major
subsystems:
i. Cathode ray tube (CRT) ii.
Vertical amplifier iii.
Horizontal amplifier iv.
83
Triggered sweep generator v.
Trigger circuits vi.
Associated power supplies.
84
Block diagram
Vertical
amplifier
INT EXT
CRT
Triggered
Sweep
generator
INT
Power
supplies
Horizontal
amplifier
XY
85
description
The purpose of all circuits in the CRO is to
display on the screen a faithful reproduction
of the input signal.
 The signal to be displayed is fed to the
vertical input.
 The signal is amplified and fed to
nongrounded vertical deflection plate.
86
 This causes the beam to be deflected in the
vertical plain as dictated by the input signal.
87
Cont’d
 Output of vertical amplifier is also fed to the
triggered sweep generator
 This generates a saw tooth waveform which is
sent to the horizontal amplifier.
 This waveform causes the beam to move
from left to right.
88
 Horizontal amplifier amplifies the signal from
the sweep generator with S2 in the INT.
position
Subsystem description
Cathode ray tube:
 This is similar to a TV picture tube except
that deflection is electrostatic and the
deflection plates are inside the tube.
89
Cont’d
 Electrons are produced by a process called
“thermionic emission” from a heated
cathode
 The cathode is surrounded by a cylindrical
cap held at a negative potential.
 Because of the negative potential, electrons
are repelled from the cylinder walls
90
 They are forced to exit a small hole on the
cylinder axis into the focusing field .
 Accelerating electrodes increase the electron
velocity.
Vertical amplifier
 This is critical in determining the sensitivity,
bandwidth and input impedance of the scope.
91
Cont’d
 Sensitivity is defined as volts per centimeter
of vertical deflection
 The amplifier is specified by its gain
/bandwidth product which is constant for
each amplifier
 At the vertical amplifier input is a rotary
switch marked volts/division.
92
 Sensitivity of the scope is the smallest
deflection factor that can be selected by the
switch.
 E.g. if smallest setting of the switch is
5mV/div, then sensitivity is 5mV/div
 Bandwidth determines the range of
frequencies that can be accurately reproduced
on the CRT screen.
93
Cont’d
Horizontal amplifier
This serves two purposes –
i. It amplifies sweep generator output in internal
mode ii. It amplifies the external signal in X-Y
mode.
 Specifications are not as stringent as the vertical
amplifier.
94
 It is only required to faithfully reproduce the
sweep signal which has a high amplitude and a
slow rise time
95
Sweep generator
It is required in oscilloscopes, to linearly move
the electron beam across the screen.
This is achieved by using a ramp signal.
96
Tr
Ts
Cont’d
 During time
right.
the beam moves from left to Ts
97
 During time beam quickly moves back to Tr
the left to start another sweep
 During this period, the control grid is gated
off to avoid retrace patterns
 For measurement or display of signals with
different frequencies, sweep rate must be
adjustable
98
Oscilloscopes with special features
a) Dual trace oscilloscope
99
Channel 1
Pre-amp
1
Electronic
switch
Channel 2
Vertical
amplifier
To rest of
scope
Pre-amp
2
100
How it works
 The two input are electronically switched into
a common vertical amplifier.
 The selection switch on the scope has
positions marked 1, 2, Alt. and chopped.
 In the positions 1 or 2, the selected signal is
displayed and the other switched off.
101
 In the alternate position, the two signals both
appear on the screen and the electronic
switch switches between them.
Cont’d
Switching rate is synchronized with the sweep
rate
This position is preferred when high frequencies
are involved.
102
In the chopped position, switching rate is
independent of the sweep rate
As a result each signal has portions missing while
the other is being displayed.
The chopped mode is preferred by low
frequencies where the Alt. mode gives a flicker.
b) Storage oscilloscopes
In these types , it is possible to retain the CRT
display for an extended time.
103
This makes it possible to make realtime observations of one-time events.
There are two types of storage
scopes.
i. Analogue type – which uses a specially
designed cathode ray tube.
ii. Digital type – uses the standard CRT and
digital memory. `
104
Cont’d
a. Analogue storage scope:
Here, the tube is modified so that it
contains: i. The normal electron gun (called the
writing gun), whose electron beam passes
through the focus electrode and the deflection
plates
105
ii. Two electron guns (called flood guns) whose
flood beams flood the CRT screen.
Analogue storage
 The write gun writes the image (from
vertical amplifier) on the storage target.
 The written portions of the target are
bombarded by low energy electron and
106
The written image is stored.
Disadvantages of analogue scope:
i. When power is lost, image is also lost. ii.
The image is not sharp and fades with time.
iii. Tube is complicated and expensive
Digital storage oscilloscope
Advantages:
107
i. Stored traces are bright and sharply defined
ii. Traces can be stored indefinitely or iii.
written to some external data storage device iv.
and reloaded when needed
v. Allows comparison of a trace acquired from
a system under test to a known standard
trace from a known - good system.
108
Cont’d
vi. Digital scopes can analyze waveforms and
provide numerical values as well as displays.
vii. These numerical values typically include:
 Averages
 Maxima and minima
 Root mean square values
 and frequency
109
viii.Trace can be manipulated after acquisition e.g. a
portion of the trace can be magnified to
observe details.
110