EE1427 Engineering Science Laboratory Guide
EE1427 ENGINEERING SCIENCE LABORATORY
TASKS
1.0 PREREQUISITES
In order to prepare for the experiments to be conducted in this laboratory
exercise, please familiarise yourself with the following:
http://www.staff.city.ac.uk/eleclab/scope/scope.htm
This link will enable you to familiarise yourself with oscilloscope
functions. While the scope featured is the old style cathode ray scope
(CRT), the functions are applicable to all types of scope.
http://www.staff.city.ac.uk/eleclab/TDS2000.pdf
This link contains the manual for the present TFT scopes in use in
CG04. Pay particular attention to “Understanding Oscilloscope
Functions”, “Operating Examples” and Application Examples”.
http://www.staff.city.ac.uk/eleclab/TandMSys/tandm.htm
Pay particular attention to the left half of the Test and Measurement
Unit, i.e. to the Frequency Generator and the Frequency Counter.
2.0 LAB REQUIREMENTS
For this lab, you will need a breadboard which should have been
purchased from the lab technician, along with the necessary tools
required for manipulating components and wires.
You will also need your lab book, in which you will record all your work,
which should include calculations, graphs and diagrams. After each
section, your lab book must be signed by the module leader.
It is also recommended that you bring with you a USB memory stick, as
you will need to save captured images from the oscilloscope, and use
them in your reports.
Finally, you will also need a degree of care and vigilance. The lab is a
dangerous place, so please adhere to the safety protocols that have
been laid out previously.
3.0 LAB TASKS
Week 1 – Task 1 Oscilloscope Familiarisation
Week 2 – Task 2 RCL Filter Circuits: Frequency and Time Domain Study
Week 3 – Task 3 RCL Filter Circuits: Resonance Study
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4.0 REPORT AND MARKS
This lab will contribute towards your final mark for the Engineering
Science module, so it is important that you try and get as higher mark as
possible. This can be achieved by the standard of work you will produce.
I expect a detailed typed up formal report in addition to the notes made
in your lab books as you carry out each procedure, with clearly labelled
circuit diagrams, graphs, calculations and I also want to see your work
backed up by relevant theory. My assistants and I will be monitoring you
closely throughout the duration of the lab, and I will take into
consideration the way you conduct yourselves in the lab when it comes
to marking your reports.
Finally, please feel free to ask questions if you become stumped, as I
and my assistants will only be too willing to help. However, we will not
give you any answers, nor will we construct circuits. All the best!
5.0 TASK 1 – OSCILLOSCOPE FAMILIARISATION
5.1 INTRODUCTION
The aim of the first task is to introduce the basic operational procedures
of the oscilloscope so you will learn how the “scope” functions and how
to set it up with the optimal operating settings in the most common
measurement and diagnostic conditions.
The “cathode ray oscilloscope” is one of the most versatile tools
available to an electrical engineer for investigating circuits, but have
been replaced in the lab with the modern “digital storage oscilloscope”.
Its great versatility demands a basic level of understanding on the part of
the user. Without sufficient understanding, a scope can be virtually
useless or even dangerous.
In order to help you develop a degree of familiarity with the scope and its
functions, the following procedures have been designed. They should be
followed so that familiarisation with the scope can be effectively gained.
For each of the aspects involved in this experiment, note down all your
observations in your lab books, as well as any parameters that you are
asked to measure.
5.2 EQUIPMENT REQUIRED
1 Tektronix TDS2002 Digital Storage Scope (Figure 5.1)
1 USB memory stick
BNC-BNC leads (Figure 5.2)
BNC-croc clipped leads (Figure 5.3)
Frequency Generator and Counter
Breadboard
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Figure 5.1
Figure 5.2
Figure 5.3
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5.3 INITIALISATION
The type of scope installed in the lab is the Tektronix TDS2002 digital
storage oscilloscope. These scopes are small, lightweight, benchtop
packages that can be used to take ground-referenced measurements. To
switch on the scope, push the button located to the left on the top
surface of the device. After a few seconds, the main scope screen will
appear which has a black background with dotted horizontal and vertical
lines.
The scope has two channels, (so that two signals can be displayed
simultaneously) Channel 1 (CH1) and Channel 2 (CH2). Channel 1 and
its related controls have a yellow designation. This also means that when
a signal is connected to the CH1 input, a yellow trace will appear.
Channel 2 is designated with the colour blue.
First, it is necessary for the yellow (CH1) trace to be visible in the centre
of the screen in order to initialise Channel 1. This is achieved by first
pressing the yellow CH1 MENU until in the bottom left of the main screen
you see yellow text saying “CH1” followed by a voltage value. If in the
same part of the screen you see blue text, (CH2, voltage value), press
the blue CH2 MENU button until this disappears. To initialise Channel 1,
press the AUTO SET button, which is located in the top right hand corner
of the scope controls. You should now see the yellow Channel 1
horizontal trace in the centre of the screen.
Can you initialise Channel 2 in the same way?
Next, you are to display a signal from the Function Generator on
Channel 1 of the scope screen. Connect a BNC-BNC (BNC stands for
Bayonet Neill Concelman) cable from Ch1 (Channel 1) of the scope to
the OUTPUT socket on the Function Generator, which is the lower of the
three BNC sockets on the far lower left of the workstation. On the
frequency generator, locate the 50Ω/600Ω switch, and make sure it is out
(50Ω selected). On the DISPLAY button, make sure F/G is selected,
which allows the frequency to be displayed on the digital readout of the
frequency counter (upper left quadrant). Select the sinusoidal function on
the generator and select the X100K frequency multiplier button. Use the
dial to obtain a frequency of 20kHz.
To the left of the scope control panel, there are five buttons that go from
top to bottom. On the right of the scope screen there are five parameters
that correspond to the five function buttons. If these five parameters are
not displayed, press the yellow CH1 MENU button in order to bring them
up. From top to bottom, the functions are:
i) Coupling – set this to AC by pressing the button to the right
ii) BW limit – set to off
iii) Volts/div – set to Coarse
iv) Probe – set to 1x
v) Invert – set to off
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Note that the coupling button, when set to Ground, displays a horizontal
line (yellow for CH1, blue for CH2) which can be moved vertically by
turning the VERTICAL POSITION dials. This function can be used to
select an alternative zero reference if desired. Experiment with this and
make a note in your lab books regarding your observations.
5.4 BASIC CONTROLS
Figure 5.4
Figure 5.4 shows the screen of the scope, and what the axes
represent. Use the SEC/DIV (seconds per horizontal division) dial and
VOLTS/DIV (volts per vertical division) dial for Channel 1 (yellow) of
the scope controls to obtain a trace on the scope of at least 2 periods
and by adjusting the AMP button on the frequency generator, obtain a
waveform that fills at least two-thirds of the screen. Make a note in your
lab book of the VOLTS/DIV and SEC/DIV settings which are located at
the bottom of the screen, and use them to visually measure the
waveform’s frequency and peak-to-peak voltage. Take the following
measurements:
(i)
Positive peak to ground voltage
(ii)
Negative peak to ground voltage
Adjust the VERTICAL POSITION, HORIZONTAL POSITION,
VOLTS/DIV and SEC/DIV buttons, and by observing the changes
made to the waveform on the screen, explain what these controls do in
your lab book.
Next press the MEASURE button, which is at the top of the scope
controls. Use the function buttons on the left of the scope controls to
set the “Source” to CH1 (top button). Press the second function button
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several times, and make a note of all the parameters that this button
cycles through.
5.5 DC OFFSET
Locate the OFFSET button on the Function Generator. Pull this button
to the “out” position, and turn the button clockwise and anticlockwise.
Make a note of what is happening on the screen of the scope as you
vary the DC offset. Next, press the yellow CH1 MENU button and
select DC coupling. Observe what happens when you adjust the
“offset” button of the frequency generator. Can you explain what is
being added to the waveform on the scope screen? Push the OFFSET
button back in once you have finished with this part of the experiment,
and reselect AC coupling on the scope.
5.6 USING TWO CHANNELS
Construct the circuit below on your breadboard. Vin is to be supplied by
the Function Generator. Use Channel 1 of the scope to measure an
input sinusoidal waveform of 25kHz with a peak to peak voltage of
7.5V.
C=100nF
i
+
Vin
+
18W
-
Vout
-
Figure 5.5
On the scope controls, press the blue CH2 MENU button in order to
allow two waveforms to be displayed at the same time using the
scope’s second channel, Channel 2. Waveforms displayed on Channel
2 are blue in colour, and any related parameters have blue text. Attach
a BNC cable to the Channel 2 input of the scope, and connect the two
crocodile clipped ends to measure the output of your circuit across the
resistor. Adjust the VOLTS/DIV for Channel 2 to obtain a suitable trace
on the screen. In your lab books, draw accurately what you see, not
forgetting to note down the SEC/DIV and VOLTS/DIV for both
channels. What is the overall peak-to-peak gain of the circuit, which is
a ratio of the output and input voltages? Using the following formula,
calculate this gain in decibels.
Gain in dB = 20 log10 (Vout/Vin)
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Next use the CH1 and CH2 MENU buttons to find the peak to peak
values of both waveforms, and use this to recalculate the gain. Then
press the red MATH MENU button. Press the Operation button in order
to select +. Describe what you see, and explain what is being displayed
on the scope. Do the same for when – is selected. Then press the
MATH MENU to switch off the red trace.
To save you from drawing what you see on the scope screen, the
Tektronix TDS2002 Digital Storage Scope comes with PC based
software via a serial link. Switch on your bench PC, and log in. Open
the “OpenChoice Desktop” program. Once the new window has
opened, hit the “Select Instrument” button, which should open a new
dialog box. Select “ASRL1::INSTR”, and then back in the main window
select “Get Screen”. After a few seconds, the image from the scope will
be downloaded onto the PC interface program. Once this has been
done, you can save the image onto a USB stick, or on the desktop
should you with to email it to yourself. This image should go in your
main report.
5.7 TRIGGER FUNCTIONS
The TRIGGER function controls allow the oscilloscope display to be
synchronised with the signal you want to investigate. To provide a
more stable trace on the scope screen, modern oscilloscopes have a
function called the trigger. When using triggering, the scope will pause
each time the sweep (which is the steady motion of the trace across
the screen) reaches the extreme right side of the screen. The scope
then waits for a specified event before drawing the next trace. The
trigger event is usually the input waveform reaching some userspecified threshold voltage in the specified direction (going positive or
going negative).
The effect is to resynchronise the timebase to the input signal,
preventing horizontal drift of the trace. In this way, triggering allows the
display of periodic signals such as sine waves and square waves.
Trigger circuits also allow the display of nonperiodic signals such as
single pulses or pulses that don't recur at a fixed rate.
Press the TRIG MENU button located on the right of the scope
controls. This activates the trigger functions which should appear on
the right side of the screen. Leave the “Type” on “Edge”. Switch the
source between CH1 and CH2 (ignoring Ext, Ext/5 and AC Line). Can
you describe what is happening?
Vary the TRIGGER LEVEL dial for both CH1 and CH2 sources.
Describe what happens and draw what you see.
Next, while still in the TRIGGER menu, switch the “Source” function to
“Ext” (for external). What can you see on the scope? Draw in your lab
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books what you see. Fetch another BNC-croc clips cable. Connect the
BNC end of this cable to the EXT TRIG (trigger input) socket on the
scope. Attach the crocodile clips to the input of your circuit. Draw what
is displayed on the scope screen. Does what you see on the screen
look familiar? Why?
Now attach the crocodile clips from the trigger input BNC cable to the
output of your circuit (across the resistor). Draw and explain what you
see.
Can you explain the triggering function based on what you have
observed?
LAB BOOKS MUST BE SIGNED AT THIS POINT
6.0 TASK 2 – RCL CIRCUITS: FREQUENCY AND TIME
STUDY
6.1 INTRODUCTION
In this task, you will investigate the performance of some basic filter
circuits. Filters to select different frequency ranges are widely used in
electronics, communications, control systems etc. A common example
is the tone control provided in audio systems. This is a filter circuit
which can be adjusted to emphasise or reduce different frequencies
and so give different qualities to the music.
SIGNAL INPUT
FILTER CIRCUIT
SIGNAL OUTPUT
Figure 6.1
The engineering properties of a filter can be represented in the
frequency domain which shows how the attenuation (or AC voltage
ratio) varies with frequency. The AC voltage ratio is a complex quantity
and is usually represented in its polar form i.e. magnitude and phase
angle.
Time domain representation is also possible. This shows the relation
between the input and output time waveforms when a transient signal
(e.g. step or ramp waveform) is applied at the input.
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6.2 CR FILTER CIRCUIT – FREQUENCY DOMAIN RESPONSE
Theory
Figure 6.2 shows the circuit configuration for a CR filter.
+ vc -
i
+
FILTER CIRCUIT
+
C
R
vin
-
vout
-
Figure 6.2
Kirchhoff’s Voltage Law for the circuit of Figure 6.2 states that
vin  vc  vout
The bar above the variables indicates that the voltages are complex
quantities having angles as well as magnitudes. Also lower case letters
(v, i) are used for quantities which vary with time, whereas upper case
letters (V, I) are used for quantities which DO NOT vary with time (e.g.
average, RMS, peak values).
Capacitors are affected by the type of current that goes through them.
It has a resistance (impedance) called ‘reactance’ and is dependant on
the frequency of the voltage across it. The reactance of the capacitor is
denoted by Zc, where
Zc 
1
jC
Ohm’s Law is also applicable
vc  i Z c
vout  i R
So the AC voltage ratio equation is given by
vout
jCR

vin 1  jCR
Putting CR = τ, where τ is the time constant, and expressing numerator
and denominator in their separate polar forms gives
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vout
  90

12
vin
1   2 2  tan 1 


This can be evaluated by ‘polar’ division i.e. divide magnitudes and
subtract angles. Note the special condition that arises when ω = 1/ τ.
This important frequency is called the critical frequency, fc, where
ωc = 2πfc = 1/τ
Circuit
Connect a C = 1.0μF capacitor (non-electrolytic, non-polarised) and
170Ω<R<230Ω (record these values in your log book) onto your
breadboard to resemble the circuit shown in Figure 6.2. Use an
appropriate cable to connect the Function Generator, from which you
should use the 50Ω BNC output. Use another cable to connect the
circuit output to CH2 of the scope, and another to display your input on
CH1.
Draw a table in your log books with six columns headed by:
Frequency (Hz)
Log10f
vin (V)
vout (V)
Gv (= vout/vin)
dB = 20log10Gv
dB
fc
log10f
-3 dB level
Take extra points here to
give accurate fc
Figure 6.3
Set the function generator to input a sinusoidal waveform into your
circuit, which you can verify on the oscilloscope, with a peak to peak
voltage between 2.5V and 3.0V. Vary the frequency from about 30Hz
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up to 30kHz, using a suitable scale. Record your results in tabular form
and immediately plot a control graph of log10f against 20log10Gv. Your
graph should be similar to that of Figure 6.3.
If you examine your control graph you will see that for some intervals
there is a need to take additional measurements to fill the gaps
between some sets of points, particularly when there are conditions of
special interest, such as the value for fc, i.e. the -3dB frequency. Do
this while the equipment is set up, and you may need to plot another
graph to find out if the new results are good enough.
It is particularly important to locate fc, which is the frequency at which
the voltage ratio is 1/√2 (= -3.0dB) as its value will be needed later in
the experiment. Take additional measurements to focus in on that part
of the graph, at around -3.0dB. Plot a graph for this range and read off
the value for fc.
Deduce your values of fc and τ from the graph. These are related
directly to the product R  C, and as a consequence there is no need to
know the separate values of R and C. Later on in the experiment the
product RC will also be evaluated from the time domain tests, so you
must keep the same two components for consistency.
Calculations and Comments
Each part of the tests described above should be fully accounted for,
both in your lab books and in your final formal reports.
Explain the relation between the 1/√2 gain factor and the theory
explained above. Determine from your graph the gradient of the low
frequency asymptote in terms of the change in dB for a 10-times
change in frequency, i.e. the number of dBs per decade.
Explain the reasons for the performance of this circuit at low, mid and
high frequencies in terms of its function as an AC voltage divider and
the impedance values involved.
Explain whether or not this circuit can be used as a DC blocking circuit
(i.e. any DC component of the input does not reach the output).
Explain whether the circuit should be described as a high pass filter or
a low pass filter.
In order to use filter circuits in future designs, you will need to
appreciate the above points.
Phase Angle
In many situations (e.g. control systems stability studies) it is essential
to have information on the phase angle in time between vout and vin and
the way this angle varies with frequency.
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Set up the oscilloscope to display both the input and output waveforms
of your circuit (Figure 6.2) on two separate channels. Double check to
make sure that both channels are not in ‘inverted’ mode. Connect CH1
to display vin and CH2 to display vout. Adjust the amplitude button on
the frequency generator to obtain 4.3V<vin<8.5V peak (can you work
out the equivalent RMS values?). In conjunction with this, adjust the
CH1 VOLTS/DIV control so that the waveform fills most of the screen
vertically.
Set the frequency to fc, and take measurements to determine the
phase angle at fc. This can be achieved by taking into consideration
that one cycle of a waveform is equivalent to 360. If you have set up
your scope controls appropriately, and you know how many vertical
divisions equate to 360, then you can compute how much each
vertical division is worth in degrees. You can make use of the cursor
function on the scope to assist you in this. On the scope screen, the
waveform that peaks first is the waveform that leads, i.e. it peaks
earlier in time than the other waveform displayed. The opposite of lead
is lag.
Repeat the steps for fc/3 and 3fc. What do these two angles add up to?
Set the scope to measure RMS, and set the frequency generator to
fc/3. Measure and record the three RMS voltages in the circuit, vin, vc
and vout. An RMS (root mean square) voltage is a measure of how
effective the waveform is in producing heat in a resistance. The DC
voltage that causes the same heating in resistance R as an AC voltage
is the effective value (RMS value) of the AC voltage (likewise for
current).
Vrms = (√2/2)Vpeak
Can you explain carefully why vin  vc  vout , but Vin ≠ VC + Vout (RMS
values).
6.3 CR FILTER CIRCUIT - TIME DOMAIN RESPONSE
Theory
The circuit is now tested with one of the standard, non-sinusoidal signal
inputs using the facilities available on the function generator.
From KVL, vin = vc + vout, and differentiating gives
dvin dvc dvout


dt
dt
dt
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Also
i
vout
dv
C c
R
dt
Combining and setting CR = τ gives
dv 
 dv
vout    in  out 
dt 
 dt
If
dvout
dv
 in , then
dt
dt
vout  
dvin
dt
This is an important equation showing that under certain conditions vout
can be a measure, via τ, of the time differential of the input voltage.
Thus the filter can be described as a differentiating circuit. The
subsequent tests will require measurements of dvin/dt and dvout/dt (in
volts/sec) and vout so that τ can be determined, and the level of
approximation assessed. Compare this value of τ to the value
calculated earlier.
Procedures
The function generator provides three waveform options. The one with
the simplest time-differential is the ramp or sawtooth waveform. This
waveform is to be used as the filter input signal, with the addition of the
a-symmetry function (function generator controls) to give a waveform
such as Figure 6.4.
Vin
V1
time
0V
V2
T1
T2
Figure 6.4
Use the appropriate symmetry controls to make T2 ≈ 3T1, within a 20%
error.
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Use the 50Ω output from the function generator. You may encounter
adverse distortion, which may be overcome by placing a low value
resistor, Rp, directly across the function generator’s output, where
5Ω≤Rp≤6Ω, where in addition to ensure impedance matching, you must
also place a resistor of about 39Ω in series with your input signal. Ask a
member of staff if you are unsure about this.
For the next series of tests, you will need to select the ramp function on
the frequency generator, and pull the SYMMETRY button to the OUT
position, and adjust it so that T2 ≈ 3T1. The amplitude button should be
at about the 2 o’clock position.
Set the actual frequency to around fc/20. Connect the scope to display
vin and vout for the filter, and select DC coupling for both channels.
Draw a sketch of both waveforms in your log books, and also do not
forget to download the scope image onto the bench PC in order to put
the waveforms into your formal reports. Be careful with the time
alignment between vin and vout.
The shape of the output waveform should be approximately as shown
in Figure 6.5.
Vp
Vn
T1
0V
T2
Figure 6.5
Take the following measurements on the waveforms as follows:
For vin: measure V1, V2, T1 and T2 (Figure 6.4) and hence calculate
dvin/dt for both slopes of the input waveform.
For vout: this should be an asymmetrical square wave (Figure 6.5).
Carefully set the 0V ground level and then measure the positive
voltage (Vp) and the negative voltage (Vn). Also take observations by
using the scope MEASURE menus to estimate the gradient (i.e. volts
per sec) to confirm whether or not the condition
dvout
dv
 in
dt
dt
is reasonably valid.
Explain the reasons for the shape of the output waveform, shown in
Figure 6.5. Use the theory provided and data from the scope
waveforms to evaluate τ. Complete the following table.
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Table of τ values by different methods
τ value from positive slope conditions
τ value from negative slope conditions
τ value from frequency response (section 6.2)
LAB BOOKS MUST BE SIGNED AT THIS POINT
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7.0 TASK 3 – SERIES RESONANT CIRCUIT
7.1 BACKGROUND AND THEORY NOTES
These circuits include both capacitance and inductance. The
interactions between these two components have important
consequences for the circuit behaviour. Resistance is an inevitable
component of such circuits and arises in connection with losses in the
inductor and capacitor as well as effects in the source circuit. The size
of the overall, effective resistance affects the circuit’s behaviour.
Consider the circuit of Figure 7.1.
L
+
R
+
vin
C
vout
-
Figure 7.1
Applying the AC voltage divider rule gives
vout
ZC

vin
Z R  Z L  ZC
where the impedances for each component are denoted by their Z
terms.
Z R  R  j0
Z L  0  jL
ZC  0 
1
jC
The above equations are the rectangular forms of the impedances. The
impedance for R has just a real component, whereas those for C and L
are purely imaginary. Using the rectangular forms gives
vout
1

2
vin
1   LC  jCR


From the above expression, there will be one frequency, ωr, when
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 r L  1 C
r
which is called the resonant frequency. At this frequency
vout
vin

1
 r CR
An important aspect of an AC circuit is its Q-factor (Quality). In general
it is the ratio of the reactive component of a series circuit to the
resistive component, i.e. a very large reactive circuit has a large Qfactor. Considering a single reactive component at the resonant
condition
Q
r L
R

1 r C  
R
1
 r CR
Hence at resonance
vout
vin
Q
The ratio is called the voltage magnification and it can be quite large
(over 100) depending on the circuit and components.
The maximum value of the voltage ratio occurs at the resonant
frequency. The voltage ratio will reduce at higher and lower
frequencies and the proceeding practical tests will measure this. An
important measure of the pattern of reduction is the bandwidth Δf,
which is the frequency change between the half power points. These
are identified by the two frequencies f1 and f2 at which the voltage ratio
has fallen to 1/√2 (i.e. -3.0 dB) of the maximum (as P is directly
proportional to v2, this corresponds to half power). When Q is above
about 10 a simple expression for Δf can be developed, i.e.
f2 – f1 = Δf = fr/Q
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7.2 CIRCUIT DIAGRAM
L
+
Rs
+
vin
C
vout
-
Figure 7.2
Figure 7.2 shows the circuit that you are to construct on your
breadboards. However Rs is the combination of Rp (the resistance
placed across the function generator terminals and the input series
resistance) and the 50Ω internal resistance of the function generator,
so you do not have to physically put a resistance into your circuit, but
you have to calculate Rs and include it in any future calculations.
Connect up the circuit as shown, using L = 10mH and C = 147nF
(constructed from using 100nF and 47nF non-polarised capacitors).
Calculate the theoretical resonant frequency, and note this in your lab
books.
7.3 TEST PROCEDURE – FREQUENCY RESPONSE
Set the function generator to sinusoidal. Set the DC offset control to
zero, and ensure that the SYMMETRY controls are disengaged. Select
the 0dB button and set the amplitude to about mid range. Connect the
50Ω output across Rp to provide the input to your circuit.
Use the appropriate cables and scope controls to measure both input
and output voltages.
Observe the magnitude of the output voltage and hence adjust the
frequency to resonant condition, which should be around 3.9kHz. If
component tolerances make the resonant frequency greater than 4kHz,
then it is suggested that you increase the total capacitance by an
additional 22nF to reduce the resonant frequency.
Take measurements covering at least the frequency range fr ±20%. At
each frequency setting take measurements of vin, vout and f.
Calculate the voltage ratio in dB for each frequency. Plot a control
graph of frequency versus dB gain, and check that you have not taken
too many or too few values. The graph should resemble that of Figure
7.3.
Dr. Daniel Nankoo
18 of 20
EE1427 Engineering Science Laboratory Guide
Volt ratio dB
100%
3.0dB
70.7%
f1
fr
f2
Frequency (Hz)
Figure 7.3
Use the graph to deduce values for f1, f2 and fr. Use a suppressed zero
for the frequency axis, i.e. do not show f = 0.
7.4 TEST PROCEDURE – STEP RESPONSE
Keep the same circuit as shown in Figure 7.2, but now set the
frequency to about fr/50, and the input waveform to be a square wave
with an amplitude of about 0.4V. Display vin on CH1 and vout on CH2.
Make good quality sketches in your lab book, and use the scope
controls to establish the best possible traces. Take the appropriate
readings in order to determine the ringing (which is comparable to the
way a bell rings after it has been struck).
The oscillatory component can be represented by the product
t
e
d
 cos d 
where ωd = 1/√(LC) and τd = 2L/R. Calculate these.
7.5 COMMENTS AND CONCLUSIONS
Determine the voltage magnification, resonant frequency
bandwidth. Deduce Q from voltage values and frequency values.
and
Research circuits where resonance is of importance, and explain why
resonance is needed in such circuits.
LAB BOOKS MUST BE SIGNED AT THIS POINT
Dr. Daniel Nankoo
19 of 20
EE1427 Engineering Science Laboratory Guide
8.0 WHAT NOW?
I would like a formal typed up report of the work carried out throughout this
lab. You must include clear calculations, diagrams, tables, graphs, a table
of contents, page numbers and appropriate headings. Explain each of the
theorems covered, and please also mention what you have gained from
doing this lab, and what would you like to have done if you had been given
extra time.
Please leave your completed reports by the end of week 9 in the general
office.
Dr. Daniel Nankoo
20 of 20