Laboratory Manual

Electrical Circuits II Laboratory

EEE/ECE 204 (V1, V2)
EEE/ECE 203L (V3)

Department of Electrical & Electronic Engineering (EEE)

School of Engineering (SoE)
Brac University

Revision: July 2022

A. Course Objective:

The objectives of this course are to:

a. Introduce basic understanding of phasors and phasor diagrams to analyze voltage, current, power and
impedance for AC circuits.
b. Teach how to apply different network theorems to solve AC circuits in phasor domain.
c. Introduce the design and analyze the concept of series and parallel resonance circuits
d. Make understand the phase rotation and Wye/Delta connections for balanced and unbalanced 3-phase
systems
e. Introduce how to calculate AC power and power factor for single and three phase ac circuits.
f. Introduce computer simulations and extensive laboratory sessions to investigate each major topic.

B. Mapping of CO-PO-Taxonomy Domain & Level- Delivery-Assessment Tool:

Sl. CO Description POs Bloom’s Delivery Assessment

taxonomy methods and tools
domain/level activities
EEE 203 Electrical Circuits II
Apply different network theorems to
Lectures, Quiz, Assignment,
CO1 solve AC circuits in phasor domain and a Cognitive/ Apply
notes Exam
for non-sinusoidal inputs.
Analyze circuit problems on
Cognitive/ Lectures, Assignment,
CO2 resonance, power, and poly phase b
Analyze notes Exam
system for different types of loads
EEE 203L Electrical Circuits II Laboratory
Cognitive/ Apply,
Use simulation tool to investigate AC Lab Work, Lab
CO3 e Psychomotor/ Lab class
circuits in schematic level Exam, Project
Precision
Cognitive/
Construct and troubleshoot AC Understand, Lab Work, Lab
CO4 e Lab class
circuits using laboratory equipment Psychomotor/ Exam, Project
Precision
Demonstrate the findings of hardware Lab Reports,
Lab Class,
CO5 and software experiments through j Affective/Valuing Project
Lecture
reports Presentation

C. Tentative Marks Distribution:

Assessment Tools Weightage
Attendance 10%
Lab Work (Hardware, Software) 20%
Lab Report (Hardware, Software) 20%
Lab Exam (Hardware) 20%
Lab Exam (Software) 20%
Project 10%

1
D. Course Materials:

Text and Reference Books:

Sl Title Author(s) Publicatio Edition Publisher ISBN
. n Year
1 Introductory Robert.L. Boylestad 2012 12th ed. Pearson ISBN-0-13097417-XII
Circuit Analysis Education
2 Electric Circuits J.W.Nilsson and 2014 7th ed. Prentice Hall ISBN 978–0–07–
S.Riedel 352955–7

Other materials (if any)

a. Lecture notes
b. Lab hand-outs
c. Lab usage manual
d. Simulation tool

2
 Lab Safety and Security Issues
(Please modify this part as you feel appropriate for your lab)

1. Laboratory Safety Rules (General Guidelines):

The Department of EEE maintains general safety rules for laboratories. The guideline is attached in front of
the door in each of the laboratories. The written rules are as follows.

a. Closed shoes must be worn that will provide full coverage of the feet and appropriate personnel
clothing must be worn.
b. Always check if the power switch is off before plugging in to the outlet. Also, turn the instrument or
equipment OFF before unplugging from the outlet.
c. Before supplying power to the circuit, the connections and layouts must be checked by the teacher.
d. Voltage equal or above 50V are always dangerous. Therefore, extra precautions must be taken as
voltage level is increased.
e. Extension cords should be used only when necessary and only on a temporary basis.
f. Once the lab exercise is done, all equipment must be powered down and all probes, cords and
other instruments must be returned to their proper position.
g. In case of fire, disconnect the electrical mains power source if possible.
h. Students must be familiar with the locations and operations of safety and emergency equipment
like Emergency power off, Fire alarm switch and so on.
i. Eating, drinking, chewing gum inside electrical laboratories are strictly prohibited.
j. Do not use damaged cords or cords that become too hot or cords with exposed wiring and if
something like that is found, inform the teacher/LTO right away.
k. No laboratory equipment can be removed from their fixed places without the teacher/LTO’s
authorization.
l. No lab work must be performed without the laboratory teacher/lab technical officer being present.

2. Electrical Safety
To prevent electrical hazards, there are symbols in front of the Electrical Distribution Board, High voltage
three phase lines in the lab, Backup generator and substation. Symbols related to Arc Flash and Shock
Hazard, Danger: High Voltage, Authorized personnel Only, no smoking etc. are posted in required places.
Only authorized personnel are allowed to open the distribution boxes.

3. Electrical Fire:
If an electrical fire occurs, try to disconnect the electrical power source, if possible. If the fire is small, you
are not in immediate danger, use any type of fire extinguisher except water to extinguish the fire. When in
doubt, push in the Emergency Power Off button.

4. IMPORTANT:
Do not use water on an electrical fire.

3
 List of Activities

Week Activity Page Is this activity

used for any CO
assessment?

Yes No

1 Group Formation, Marks Distribution, Report Structure, Project 1

Requirement, Activity List, Course Outcome Assessment, Student
Feedback, Google Classroom etc.

2 Experiment 1: Familiarization with the Alternating Current (AC) waves 5

3 Experiment 2: Verification of KVL in AC circuits 16

4 Experiment 3: Verification of KCL in AC circuits 20

5 Experiment 4: Familiarization with the Alternating Current (AC) waves 10,

and Verification of KVL and KCL in AC circuits using PSpice 18,
22

6 Experiment 5: Familiarization with Passive Filters 24

7 Midterm examination of theory courses

8 Experiment 6: Familiarization with Series Resonance in AC circuits 30

9 Experiment 7: Series Resonance - Bandwidth and Selectivity 37

10 Experiment 8: Familiarization with Passive Filters, Series Resonance 34,

in AC circuits and Bandwidth and Selectivity using PSpice 40

11 Hardware examination

12 Project submission 44 ✓

Updated by:
1. Dr. Abu S. M. Mohsin
2. Aldrin Nippon Bobby
3. Farzana Shabnam
4. Tasfin Mahmud
5. Dr. Soumitra Kumar

4
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 1

Name of the Experiment:

Familiarization with the alternating current (AC) waves

Objective:
In this experiment, we shall study some aspects of sinusoidal waveform, and correlate these with
practically measurable values such as- rms. value (also called effective value), phase angle and
time period. Also an exposure to simple ac circuit and some circuit elements are made. Try to
familiarize yourself with

• Oscilloscope
• How to measure peak value, phase angle and time period (or frequency) using
oscilloscope
• The methods of measuring rms. value both using oscilloscope and multimeter
• Difference between AC & DC setting of multimeter & oscilloscope
• Capacitor, resistor and breadboard

Introduction:
Any periodic variation of current or voltage where the current (or voltage), when measured along
any particular direction goes positive as well as negative, is defined to be an AC quantity.
Sinusoidal AC wave shapes are the ones where the variation (current or voltage) is a sine
function of time.
1

0.8

0.6

0.4
Vm

0.2
Voltage, v

-0.2

-0.4
T

-0.6

-0.8

-1
0 1000 2000 3000 4000 5000 6000
Time, t
Figure 1(a): AC Voltage waveform

Here, Time period = T, Frequency, f = 1/T

v(t) = Vm sin(2пft)

5
Effective value:

The general equation of rms. value of any function (voltage, current or any other physical
quantity for which rms. calculation is meaningful) is given by the equation,

1 𝑇
𝑉 = √𝑇 ∫0 𝑣 2 𝑑𝑡

Now, for sinusoidal functions, using the above equation we get the rms. value by dividing the
peak value (Vm) by square root of 2. That is,

1 𝑇
𝑉 = √𝑇 ∫0 ((𝑉𝑚 𝑠𝑖𝑛 𝑠𝑖𝑛 (2п𝑓𝑡) )2 𝑑𝑡

1 2п
𝑉 = √2п ∫0 ((𝑉𝑚 𝑠𝑖𝑛 𝑠𝑖𝑛 (Ѳ) )2 𝑑Ѳ

𝑉𝑚
𝑉=
√2

These rms values can be used directly for power calculation.

𝐼𝑚
Similarly, for currents, 𝐼 =
√2

1 𝑇
The formula for average power is given by, 𝑃𝑎𝑣𝑔 = ∫0 (𝑣𝑖)𝑑𝑡. And for sinusoids this leads
𝑇
to, 𝑃𝑎𝑣𝑔 = 𝑉 𝐼 𝑐𝑜𝑠(Ѳ). Here, V and I are rms values and Ѳ is the phase angle between voltage
wave and current wave. The phase angle is explained in the next section.

Phase Angle:

Phase difference between two ac sinusoidal waveforms is the difference in the electrical angle
between two identical points of the two waves. In figure 2, the voltage and current equations are
given as:

V = Vm sin(2пft)
I = Im sin (2пft - Ѳ)

6
Impedance:

For ac circuit analysis, impedance plays the same role as resistance plays in dc circuit analysis. It
can be stated fairly safely that the concept of impedance is the most important thing that makes
the ac analysis so much popular to the engineers. As you will see in your later courses, any other
periodic forms of time varying voltages or currents, are converted into an equivalent series
consisting of sines and cosines (much like any function can be expanded by the power series of
the independent variable using the Taylor series), only because the analysis of sinusoidal
voltages are very much simple due to the impedance technique.

What is impedance anyway? Putting it simply, it is just the ratio of rms voltage across the device
to the rms current through it. That is:

𝑉 𝑉𝑚
𝑍= =
𝐼∠Ѳ 𝐼𝑚 ∠Ѳ
Its unit is ohms.

Equipments:

1. Oscilloscope
2. Function generator (used as ac source)
3. Resistors : 1k, 220 Ω
4. Capacitor : 1 uf
5. Multimeter
6. AC ammeter
7. Switch : SPST
8. Breadboard

7
Circuit Diagram:

Procedure:

1. Connect the output of the function generator directly to channel 1 of the

oscilloscope as shown in figure 2. Set the amplitude of the wave at 10v peak to peak and
the frequency at 1 kHz, Select sinusoidal wave shape.

2. Sketch the wave shape observed on the oscilloscope. Determine the time period of
the wave and calculate the frequency.

3. Measure the voltage with an ac voltmeter.

4. Change the frequency to 500 Hz and note what happens to the display of the
wave. Repeat when the frequency is increased 2 kHz.

5. Construct the circuit as shown in figure 3. Measure the input voltage with
multimeter with ac voltage mode and the input current, with an ac ammeter. The ratio
between the voltage to the current gives the magnitude of the impedance Z.

6. Observe the wave shapes in channel 1 and 2 simultaneously. Find the frequency
of both the waves (are they equal to the supply frequency) and their amplitude from the
display. The phase difference is given by 360f.t degree, where ‘t’ is the time delay
between the two waves. Note that the voltage in channel 2 is the voltage across a
resistance and hence this is in phase with the current flowing in the circuit.

8
Data:

Table for Vs

Vsa (V) 𝑉𝑠𝑎 ∠ 𝑉𝑠

|𝑉𝑠| =
(Peak value from Oscilloscope) √2 (o)
(V)

Table for |I|

R VRa 𝑉𝑅𝑎 |𝑉𝑅 |

|𝑉𝑅 | = |𝐼| =
√2 𝑅
(Ω)(using multimeter) (V)
(V) (mA)

Table for ∠I

Sign (+/-) ∆t(ms) f(kHz) 360f∆t (o) ∠I (o)

(From (From
oscilloscope) oscilloscope)

Table for Z
|𝑉𝑠| ∠Z=∠Vs - ∠I (o)
|𝑍| = (kΩ)
|𝐼|

Report:

1. Compare the frequency of the wave determined from the oscilloscope in step 2 of
the procedure with the mentioned value on the function generator.

2. Calculate the rms value of the voltage observed in step 2 of the procedure and
compare with that measured in step 3.

9
 3. How does the time period vary when the frequency of the wave is changed in
step 4?

4. Calculate the magnitude of the impedance from the readings taken in step 5.

5. Find the magnitude and phase angle of the impedance from the readings taken in
step 5 and 6.

Experiment 1 (PSpice Simulation)

1. Go to the Start menu and locate the application “Schematics”

2. Now, set up the following circuit following the instructions given below-

3. Get the following parts by clicking the “Get new Part” button from the toolbar above, OR press
Ctrl+G.

In the box “Part Name” that appears, type in-

a) Vsin (for AC Voltage source)
b) R (Resistor)
c) C (Capacitor)
d) Gnd_earth- (for ground- i.e. a reference potential from which all voltages are measured)

10
4. Place the parts as shown in the first figure. To rotate a part, select the part and press Ctrl+R.
After that, connect each part using wires. To select wire, use the button from the toolbar above.

5. To change the parameter values (resistance for resistors, capacitance for capacitors, etc) simply
double click on the default value that is shown alongside the part, and enter the desired value in
the window that appears.

Pspice Schematics understands- n for nano

u for micro
k for kilo and so on.
So, to enter the capacitance value of 1 micro farad, enter “1u”.

6. Set up the AC voltage source by double clicking on it. In the window that appears, enter the
values as shown-

11
 DC=0
AC=0
VOFF=0
VAMPL=5 (if you want 10V peak to peak)
FREQ=1k

There is no need to change any other values.

7. Get the voltage markers using the button from the toolbar above, and place the markers above
the resistor (load) and the voltage source (Vsin).

8. Next, from the toolbar again, press on the ‘Setup Analysis’ button. In the window that appears,
click on the button ‘Transient’.

12
For ‘Print Step’, type in a very small value, e.g.- 1ns. (ns= nano seconds)

For ‘Final Time’, type in 4 ms (ms=millisecond). The final time tells the software when to stop the
simulation. We want to see the input and output waveshapes for 4 complete cycles of the input
sinusoid; the frequency of our sine wave source was kept at 1 khz, which gives the corresponding time
period to be= 1ms. Thus, to see 4 complete cycles, we need to enter (4x1=) 4 ms.

Press ‘OK’, and then press ‘Close’ to get back to the schematic design.

13
9. Go ahead and save the schematic in your desired directory, and press the button ‘Simulate’
from the toolbar above-

In a new window, you will be shown the simulation results as seen in the figure above. The red circle at
the bottom shows where you can find which waveshape is which. In this case, the green one is the input
waveshape, and the red one is appearing across the load, i.e. the resistor.

10. In the same window on the top ribbon, find and press the ‘Toggle cursor’ button.

Notice that as you click on the waveshapes, a cursor runs along the curve. Left clicking selects one
waveshape and its corresponding cursor, and right clicking selects the other. A small window with the
values of the cursors appear on the window which can be dragged around.

14
Position the two cursors, such that they both are at the adjacent zero crossings of the two waveshapes,
so as to be able to measure the time difference between them. The difference in the x axis appears on
the left hand column of the “Probe Cursor” window, beside ‘dif’.

Using this information and the formula 2*pi*f*t, find the phase difference between the two
waveshapes, where, ‘t’ is the time difference, ‘f’ is the source frequency, and ‘pi’ is equal to 3.142.

Change the source (from Vsin) frequency to 2 kHz, and then to 500 Hz, and for both the
frequencies obtain the output and input waveshapes together. Using the cursors, determine
the phase difference as well.
Include the schematic circuit design, the waveshapes for all the three frequencies and the
calculated phase differences in a new document and submit the hard copy. (See the file- “How
to submit Pspice Assignment” for submission guidelines).
Data:

Table for Vs

|Vs| (V) ∠ Vs (o)

Table for I

|𝐼| (mA) Sign (+/-) ∆t (ms) f (kHz) 360f∆t (o) ∠I (o)

Table for Z

|𝑉𝑠| ∠Z=∠Vs - ∠I (o)

|𝑍| = |𝐼|
(kΩ)

15
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 2

Name of the Experiment:

Verification of KVL in AC Circuits

Objective:

The objective of this experiment is to study RLC series circuit when energized by an ac
source. KVL in phasor form will also be verified.

Circuit Diagram:

Figure 1 : KVL circuit

Equipments:

1. Multimeter
2. AC ammeter
3. Resistances – 22Ω (1piece) and 2.5kΩ(3 pieces)
4. Capacitor –1 uF (1 piece)
5. Inductor – 2.7 mH (1 piece)
6. Bread Broad
7. Wires for connection

16
Procedure:
1. Construct the circuit as shown in figure 1.
2. Observe the wave shapes for the voltages of VR, VL, and VC and fill up the
required table.
Data:

Table for Vs
Vsa (V) 𝑉𝑠𝑎 f (kHz) ∠Vs
|Vs| =
(Peak value from √2 (From oscilloscope) (o)
Oscilloscope) (V)

Table for VR
VRa (V) 𝑉𝑅𝑎 Sign (+/-) ∆t(ms) f(kHz) 360f∆t ∠VR
|V𝑅 | =
(Peak value √2 (From (From (o) (o)
from (V) oscilloscope) oscilloscope)
Oscilloscope
)

Table for VC
VCa (V) 𝑉𝐶𝑎 Sign (+/-) ∆t(ms) f(kHz) 360f∆t ∠VC
|V𝐶 | =
(Peak value √2 (From (From (o) (o)
from (V) oscilloscope) oscilloscope)
Oscilloscope
)

Table for VL
VLa (V) 𝑉𝐿𝑎 Sign (+/-) ∆t(ms) f(kHz) 360f∆t ∠VL
|V𝐿 | =
(Peak value √2 (From (From (o) (o)
from (V) oscilloscope) oscilloscope)
Oscilloscope
)

Table for V𝑅 + V𝐶 + V𝐿
|V𝑅 + V𝐶 + V𝐿 | ∠V𝑅 + V𝐶 + V𝐿
(V) (o)

17
 Experiment 2 (PSpice Simulation)

Set up the circuit:

● Construct the circuit for KVL in PSpice schematics as shown:

● For the sine wave source, set the amplitude to 5V, and the frequency to 2kHz.

Add Probes:

● Locate the probes for voltage and current on the toolbar at the top.

● Place the voltage probe across the source and the current probe on any one of the
components.

● This will allow us to examine the waveshapes of the source voltage and the current
through the circuit.

18
Setup Analysis:

● We wish to obtain the voltage the and current waveshapes as function of time. To do this,
go to “Analysis Setup”, and to “Transient”.
● Enter a stop time so that you are able to see 6 complete cycles of the input waveform.
● Finally, save and simulate the circuit.
● Use cursors to find the phase difference between the current and voltage. See whether
this matches with that obtained from your phasor diagram.

Data:

Table for Vs
|Vs| ∠Vs
(V) (o)

Table for VR
|V𝑅 | Sign ∆t f 360f∆t ∠VR
(V) (+/-) (ms) (kHz) (o) (o)

Table for VC
|V𝐶 | Sign ∆t f 360f∆t ∠VC
(V) (+/-) (ms) (kHz) (o) (o)

Table for VL
|V𝐿 | Sign ∆t f 360f∆t ∠VL
(V) (+/-) (ms) (kHz) (o) (o)

Table for V𝑅 + V𝐶 + V𝐿
|V𝑅 + V𝐶 + V𝐿 | ∠V𝑅 + V𝐶 + V𝐿
(V) (o)

19
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 3

Name of the Experiment:

Verification of KCL in AC Circuits

Objective:

The objective of this experiment is to study RLC series parallel circuit when energized
by an ac source. KCL in phasor form will also be verified.

Circuit Diagram:

Figure 1 : KCL Circuit

Equipments:

1. Multimeter
2. AC ammeter
3. Resistances – 22Ω (1piece) and 2.5kΩ(3 pieces)
4. Capacitor –1 uF (1 piece)
5. Inductor – 2.7 mH (1 piece)
6. Bread Broad
7. Wires for connection

20
 Procedure:

1. Construct the circuit of figure 1.

2. Observe the wave shapes for the currents of IR1, IR2, and IR3 and fill up the
required table .

Data:

Table for IR1

R1 VR1a (V) |V𝑅1 | |I𝑅1 | Sign (+/-) ∆t (ms) f(kHz) 360f∆t (o) ∠IR1 (o)
(Ω) (Peak 𝑉𝑅1𝑎 |𝑉𝑅1 | (From (From
= =
(using value from √2 𝑅1 oscilloscop oscilloscop
multimeter Oscillosco (V) (mA) e) e)
) pe)

Table for IR2

R2 VR2a (V) |V𝑅2 | |I𝑅2 | Sign (+/-) ∆t (ms) f(kHz) 360f∆t (o) ∠IR2 (o)
(Ω) (Peak value 𝑉𝑅2𝑎 |𝑉𝑅2 | (From (From
= =
(using from √2 𝑅2 oscillosco oscilloscop
multimeter Oscilloscop (V) (mA) pe) e)
) e)

Table for IR3

R3 VR3a (V) |V𝑅3 | |𝑉𝑅3 | Sign (+/- ∆t (ms) f(kHz) 360f∆t (o) ∠IR3 (o)
𝑉𝑅3𝑎 |I𝑅3 | =
(Ω) (Peak value 𝑅3 ) (From (From
=
(using from √2 (mA) oscillosco oscilloscope
multimeter Oscilloscop (V) pe) )
) e)

Table for IR2 + IR3

|IR2 + IR3| ∠ IR2 + IR3
(mA) (o)

21
 Experiment 3 (PSpice Simulation)

Set up the circuit:

● Construct the circuit for KCL in PSpice schematics as shown:

● For the sine wave source, set the amplitude to 2V, and the frequency to 2kHz.

Add Probes:

● Locate the probes for voltage and current on the toolbar at the top.

● Place the current probe on R2 and R3 as shown in the above figure.

● This will allow us to examine the waveshapes of the currents through the circuit.

22
Setup Analysis:

● We wish to obtain the current waveshapes as function of time. To do this, go to “Analysis

Setup”, and to “Transient”.
● Enter a stop time so that you are able to see 6 complete cycles of the input waveform.
● Finally, save and simulate the circuit.
● Use cursors to find the phase difference between the current and voltage. See whether
this matches with that obtained from your phasor diagram.

Data:

Table for IR1

|I𝑅1 | (mA) Sign (+/-) ∆t (ms) f (kHz) 360f∆t (o) ∠IR1 (o)

Table for IR2

|I𝑅2 | (mA) Sign (+/-) ∆t (ms) f (kHz) 360f∆t (o) ∠IR2 (o)

Table for IR3

|I𝑅3 | (mA) Sign (+/-) ∆t (ms) f (kHz) 360f∆t (o) ∠IR3 (o)

Table for IR2 + IR3

|IR2 + IR3| ∠ IR2 + IR3
(mA) (o)

23
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 5

Name of the Experiment

Passive Filters: Low Pass and High Pass Filters

Objective:
The purpose of this lab is to introduce students to Low Pass and High Pass Filters.

Apparatus:
• Resistance
• Capacitor
• Oscilloscope
• Oscilloscope Probe
• Signal Generator
• Signal Generator Probe
• Multi-meter
• Bread Board
• Wires for connection

Introduction:
A filter is a frequency-selective circuit. Filters are designed to pass some frequencies and reject
others.
Filter circuits depend on the fact that the impedance of capacitors and inductors is a function of
frequency. There are numerous ways to construct filters, but there are two broad categories of
filters:
• Passive filters are composed of only passive components (resistors, capacitors, inductors)
and do not provide amplification.
• Active filters typically employ RC networks and amplifiers (Op-Amps) with feedback
and offer a number of advantages.

24
There are four basic kinds of filters:
● Low-pass filter – Passes frequencies below a critical frequency, called the cutoff
frequency, and attenuates those above.

● High-pass filter - Passes frequencies above the critical frequency but rejects those below.

● Band-pass filter - Passes only frequencies in a narrow range between upper and lower
cutoff frequencies.

● Band-reject filter - Rejects or stops frequencies in a narrow range but passes others.

25
RC Low-pass filter cut-off frequency:

RC High-pass filter cut-off frequency:

• The cutoff frequency is the frequency at which capacitive reactance and resistance are equal (R
= Xc), therefore fc = 1/2𝜋𝑅C
• When our frequency response curve is given in terms of ‘voltage vs. frequency’:
1
‘’Cutoff frequency is the point at which the voltage level of the signal falls ‘’ or 0.707’’
2
times from its maximum value provided that the input signal amplitude remains same for all
frequencies.’’

26
• When our frequency response curve is given in terms of ‘Signal power vs. frequency’:
1
‘’Cutoff frequency is the point at which the power level of the signal falls ‘’ or 0.5’’ times
2
from its maximum value.’’

• When our frequency response curve is given in terms of ‘gain vs. frequency’:
1
‘’Cutoff frequency is the point at which the gain of the signal falls ‘’ or .707’’ times
2
from its maximum value.’’

• When our frequency response curve is given in terms of ‘gain (in dB) vs. frequency’:
‘’Cutoff frequency is the point at which the gain (dB) of the signal falls ‘’-3 dB’’ from its
maximum value.’’

Procedure:
1. Measure the values of the resistor and capacitor. Construct the circuit by connecting the
capacitor and the resistor in series. Connect the oscilloscope to measure the voltage
across the resistor.

2. Calculate the cutoff frequency from fc= ωc/2π =1/2πRC. This should be the frequency at
which the output power is equal to one half of the input power, or, equivalently, the
output voltage is equal to 0.707 of the input voltage. Record this number.

3. Set the input voltage, the voltage across the signal generator, to 2 volts zero to peak.

4. Measure the output voltage of the circuit over a frequency range of 1 kHz to 10 kHz in 1
kHz increments. You will need to adjust the input voltage back to 2 volts as you change
the frequency. Plot gain vs. frequency.

Low-pass Filter

27
 Table for theoretical cutoff frequency
R C 1
𝑓𝑐𝑡 =
(Ω) (µF) 2𝜋𝑅𝐶
(using (using (kHz)
multimeter) multimeter)

Table for practical cutoff frequency

f Via (V) Voa (V) 0.707Voa Via (V) 𝑓𝑐𝑝
(kHz) (Peak value (Peak value (V) (Peak value (kHz)
from from from
Oscilloscope) Oscilloscope) Oscilloscope)
0.1

Table for gain

f Via (V) Voa (V) 𝑉𝑜𝑎
𝐴𝑣𝑑𝐵 = 20 log
(kHz) (Peak value (Peak value 𝑉𝑖𝑎
from from (dB)
Oscilloscope) Oscilloscope)

High-pass Filter

28
 Table for theoretical cutoff frequency
R C 1
𝑓𝑐𝑡 =
(Ω) (µF) 2𝜋𝑅𝐶
(using (using (kHz)
multimeter) multimeter)

Table for practical cutoff frequency

f Via (V) Voa (V) 0.707Voa Via (V) 𝑓𝑐𝑝
(kHz) (Peak value (Peak value (V) (Peak value (kHz)
from from from
Oscilloscope) Oscilloscope) Oscilloscope)
10

Table for gain

f Via (V) Voa (V) 𝑉𝑜𝑎
𝐴𝑣𝑑𝐵 = 20 log
(kHz) (Peak value (Peak value 𝑉𝑖𝑎
from from (dB)
Oscilloscope) Oscilloscope)

Questions:

1. What would happen to the value of fc if the value of the capacitor C for the low-pass and
high-pass filters is increased?

2. What would happen to the value of fc if the input voltage is increased?

3. What would happen if you replaced the capacitors in the above circuits with inductors?

29
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 6

Name of the Experiment

Familiarization with Series Resonance in AC Circuits

Objective:
This experiment helps students understand the resonance phenomenon in R-L-C series circuits.

Apparatus:
1. Resistor
2. Capacitor
3. Inductor
4. Signal Generator
5. Oscilloscope
6. Multimeter

Introduction:

Resonance is a particular situation that may occur in an electric circuit containing both inductive
and capacitive elements. In a series RLC circuit resonance occurs when the resultant reactance is
zero. We know, the drop across the inductance leads the current by 900 whereas that across the
capacitor lags the current by 900. The two drops are opposite. If they are made equal as in figure
below, the inductive and capacitive voltage drops neutralize each other. So, the total voltage drop
is equal only to the resistive drop.

IXL

IR I

IXC

30
Inspecting the above figure it can be said that, during series resonance the applied voltage drop is
in phase with current and the power factor is unity.

Thus for series resonance,

IXL = IXC

That concludes, Inductive Reactance = Capacitive Reactance

 XL = XC
1
 2  fL = ………………………………………………………………(1)
2fC
Therefore, the series resonant frequency is,
1
fr =
2 LC
At resonant condition for a series circuit the following should be observed:

• The resultant impedance of the circuit is purely resistive in nature:

ZT = R + j (XL- XC) = R + j.0 = R

• Since the impedance is minimum the current in the series circuit will be maximum and
V
given as: Imax = s
R
• The circuit yields a unity power factor since the impedance is purely resistive.
• The average power absorbed by the circuit is maximum at this resonance: Pmax = Imax2 R

Practical considerations to be taken for the experiment:

• Due to loading effect the amplitude of the source voltage changes when we use different
capacitors. So one should check the amplitude every time a new capacitor is used & make
adjustment if necessary. Remember that we should keep same amplitude value
throughout the experiment.
• Since at resonance point the circuit current is maximum, the watt dissipation of the
resistor R must be checked against its wattage rating. It should be applicable also for the
inductor current rating. Besides the signal generator we are using must be capable of
delivering maximum current.
• In a series circuit containing R, L & C the voltage across the C can raise beyond the
supply voltage. So other circuit equipment those are subjected to VC must be able to
withstand that voltage.
• From the current vs. capacitance curve, it should be noted that the current is maximum at
resonance point and decreases beyond that. The shape of the curve (flatness) mostly
depends on the value of ‘R’. A large value of ‘R’ will give rise to a flat curve and it will
make difficult for us to measure the variation of current at different capacitor values. So
we should use a smaller value of ‘R’.

31
 • When measuring the phase angle between voltage & current we should check the
connection of the oscilloscope probes carefully. Each of the black crocodile clip
represents the ground of respective oscilloscope channel. But inside the oscilloscope
these two grounds are shortened. So when we use both the probes there is a great chance
that we short-circuit some parts of the circuit. We should always avoid this situation.

Circuit:

Procedure:

1. Connect the circuit as shown in the circuit diagram.

2. Adjust the voltage from the signal generator to 2 V (zero-peak).
3. Keep the frequency to some minimum value (say 10 Hz) and note the current.
4. Increase the frequency and for each frequency note the corresponding current.
5. Draw the resonant curve by taking (I) along y-axis and (f) on x-axis.

32
 Data Table:

R C L 1 𝑉𝑆𝑎 𝑓𝑆𝑃 𝑉𝑆𝑎 ∠𝑉𝑆

𝑓𝑆𝑇 = |𝑉𝑆 | =
(Ω) (µF) (mH) 2𝜋√𝐶𝐿 (V) (kHz) √2 (o)
(kHz) (V)

𝑓 𝑉𝑆𝑎 𝑉𝑅𝑎 𝑉𝑅𝑎 |𝑉𝑅 | Sign (+/-) ∆t(ms) 360f∆t (o) ∠I (o)
|𝑉𝑅 | = |𝐼| =
(𝑘𝐻𝑧) (V) (mV) √2 𝑅 (From
(mV) (mA) oscilloscope)

𝑓 |𝑉𝑆 | ∠Z=∠Vs - ∠I (o)

|𝑍| = (kΩ)
(𝑘𝐻𝑧) |𝐼|

Questions:

1. Write the effects of series Resonance in AC circuit.

2. Draw necessary graphs for the RLC Series circuit.
3. What will happen to the plot of the current vs. frequency if the value of the Resistor (R)
is varied?

33
 Experiment 6 (PSpice Simulation)

● Construct the circuit as follows and place a current marker to determine the
current flowing through the series circuit.

● For the voltage source, use VAC and set the parameters accordingly.

34
● From the “Analysis Setup”, select “AC sweep” to perform frequency sweep.

(N.B.: Choose suitable value for “Start Freq.” and “End Freq.” so that the plot
includes the resonant frequency. By setting a larger value in “Total Pts.”, the plot
can be made smoother but it may take longer time to simulate as well.)

● Press the “Simulate” button and the graph window will appear. To determine the
resonant frequency, the peak value of the graph should be marked.

● For the peak value, click on “Toggle cursor” and then click on “Cursor Peak”.
The cursor will move the peak of the graph. After that click on “Mark Label”
button and the co-ordinates of that point will be shown.

35
 ● The X co-ordinate represents the Resonant frequency, f0

Data:

Table for |𝑉𝑅 |

|𝑉𝑅 |𝑚𝑎𝑥 𝑓𝑆
(V) (kHz)

Table for |𝐼|

|𝐼|𝑚𝑎𝑥 𝑓𝑆
(mA) (kHz)

Table for |𝑍|

𝑅 𝑓𝑆
(Ω) (kHz)

Table for ∠Z
𝑓𝑆
(kHz)

36
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Experiment 7

Name of the Experiment

Series Resonance: Cut-off Frequencies, Bandwidth & Selectivity

Objective:
Students are expected to find the Q-factor and Bandwidth of Series RLC circuit.

Apparatus:
1. Resistor
2. Capacitor
3. Inductor
4. Signal Generator
5. Oscilloscope
6. Multimeter

Introduction:

In a series R-L-C circuit, resonance can occur when

Inductive Reactance = Capacitive Reactance

 XL = XC
1
 2  fL = ………………………………………………………………(1)
2fC
Thus it is possible to have resonance by varying the frequency ‘f’ while keeping L & C constant.
For a series circuit, we should observe the followings while we vary ‘f’ in order to have
resonance:

• The frequency at which the resonance occurs is known as resonant frequency ‘fr’. At this
frequency, the current is maximum and the voltage drop across ‘R’ is also maximum.

37
 Beyond this frequency, the current and as well as the VR drops which gives rise to a
profile as shown below:

• From the above profile, notice that the maximum value of voltage (representing the
maximum current value) occurs at the resonant frequency ‘fr’.
• The half power point is defined as the point that corresponds to the points at which
V
voltage is equal to m = 0.707Vm.
2
• The frequencies (f1 & f2) corresponding to the half power points represents the cut-off
frequencies for the circuit.
• The bandwidth of the circuit is defined as BW = f1 ~ f2.

In our experiment, we shall try to find the frequency response of the series R-L-C circuit and find
its bandwidth. We shall conduct the following studies on quality factor of the series circuit:

• Selectivity of a coil (Resistance & pure inductance) or series R-L-C circuit is represented
by the quality factor ‘Q’. The quality factor is defined as:

CenterFrequency f0
Q= = ………………………………………….. (2)
Bandwidth f1 ~ f 2

Here the center frequency f0 =fr

• From the definition of Q it is clear that for a particular f r, the smaller the value of (f1~f2),
the larger the value of Q. Hence larger value of Q represents sharp peak in the resonance
profile signifying that the circuit/coil is more selective to the particular frequency ‘fr’.

38
 Circuit:

Procedure:

1. Connect the circuit as shown in the circuit diagram.

2. Adjust the voltage from the signal generator to 2 V (zero-peak).
3. Keep the frequency to some minimum value (say 10 Hz) and note the current.
4. Increase the frequency and for each frequency note the corresponding current.
5. Draw the resonant curve by taking (I) along y-axis and (f) on x-axis.
6. Find the Resonant frequency, half-power frequencies, bandwidth and Q-factor.

Data Table:

C 𝐿 1
𝑓𝑆𝑇 =
2𝜋√𝐶𝐿
(µF) (mH)
(kHz)

R 𝑉𝑆𝑎 𝑓𝑆𝑃 𝑉𝑅𝑎𝑚𝑎𝑥 0.707𝑉𝑅𝑎𝑚𝑎𝑥 𝑉𝑆𝑎 𝑓𝐶𝐿 𝑉𝑆𝑎 𝑓𝐶𝐻 𝐵𝑊 = 𝑓𝐶𝐻 − 𝑓𝐶𝐿 𝑓𝑆𝑃
𝑄𝑆 =
𝐵𝑊
(Ω) (V) (kHz) (V) (V) (V) (kHz) (V) (kHz) (kHz)

39
Question:

1. Derive the relation between Q-factor and Bandwidth in a Series Resonant circuit.
2. A Series RLC circuit has the following parameters:
R = 10Ω, L = 0.014H, C = 100uF. Compute the following:
a. Resonant frequency in rad/sec.
b. Q-factor of the circuit
c. Bandwidth
d. Upper and lower cut-off frequencies
e. Maximum value of voltage appearing across the capacitor if the applied voltage is
v(t) = 2 sin (1000t).

Experiment 7 (PSpice Simulation)

● Construct the circuit as follows and place a current marker to determine the
current flowing through the series circuit.

● For the voltage source, use VAC and set the parameters accordingly.

40
● From the “Analysis Setup”, select “AC sweep” to perform frequency sweep.

(N.B.: Choose suitable value for “Start Freq.” and “End Freq.” so that the plot
includes the resonant frequency. By setting a larger value in “Total Pts.”, the plot
can be made smoother but it may take longer time to simulate as well.)

● Press the “Simulate” button and the graph window will appear. To determine the
resonant frequency, the peak value of the graph should be marked.

41
● For the peak value, click on “Toggle cursor” and then click on “Cursor Peak”.
The cursor will move the peak of the graph. After that click on “Mark Label”
button and the co-ordinates of that point will be shown.

The X co-ordinate represents the resonant frequency, f0

42
 ● For the cut-off frequencies, determine the value of 0.707 Imax and then mark those
corresponding points to determine the lower (f1) and upper (f2) cut-off frequencies.

● Use the equations to determine Bandwidth and Q-factor.

Data:

R |𝐼|𝑚𝑎𝑥 𝑓𝑆 0.707|𝐼|𝑚𝑎𝑥 𝑓𝐶𝐿 𝑓𝐶𝐻 𝐵𝑊 = 𝑓𝐶𝐻 − 𝑓𝐶𝐿 𝑓𝑆𝑃

𝑄𝑆 =
(Ω) (mA) (kHz) (mA) (kHz) (kHz) (kHz) 𝐵𝑊
220
470

43
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Project

Consider a filter having the following circuit:

Here, 𝑉𝑖n is a sinusoidal ac voltage source having a voltage of 10 𝑉 ∠0°. Now, do the tasks given below:

1. Define a filter. [Marks: 1]

2. Identify, with reasons, whether the filter mentioned above is passive or active. [Marks: 1]

3. Simulate the abovementioned filter in PSpice. Now, get the followings done:

a. Construct the circuit in PSpice. [Marks: 1]

b. Mention the values of the simulation parameters. [Marks: 1]

c. Illustrate the |𝑉𝑜| versus 𝑓 plot. [Marks: 2]

44
 d. Also illustrate the Gain (dB) versus 𝑓 plot (marking cut-off frequencies). [Marks: 2]

e. Complete the following data table: [Marks: 6]

The maximum Resonant The value of The cutoff The bandwidth Selectivity
value of |𝑉𝑜| frequency, 𝑓 the quantity frequencies (𝑘𝐻𝑧)
(𝑉) (𝑘𝐻𝑧) that identifies (𝑘𝐻𝑧)
the cutoff
frequencies

4. Identify, with reasons, whether the aforementioned filter is low-pass, high-pass, band-pass, or band-
stop. [Marks: 2]

5. Define pass-band and stop-band and determine the corresponding values for this filter. [Marks: 3]

6. Explain the circuit operation of this filter in brief. [Marks: 3]

Deliverables:

• A Report should be submitted.

The Report should include:

1. Cover Page [Marks: 1]

2. Answer to the assigned tasks [Marks: 22]

3. Discussion [Marks: 2]

• A Presentation is required.

For the Presentation, the following marking scheme would be followed:

1. Proper explanation of the workings [Marks: 5]

2. Organization of slides [Marks: 3]

3. Presentation skill [Marks: 3]

4. Response to questions [Marks: 4]

Study Material:

Refer to the following book:

Title: Introductory Circuit Analysis
Chapter: Decibels, Filters and Bode Points
Author: Robert L. Boylestad
Publisher: Pearson Education Ltd.

45
 Brac University
Department of Electrical & Electronic Engineering (EEE)
EEE203L – Electrical Circuits II Laboratory

Appendix

Oscilloscope

It shows the graph of a voltage. The x axis shows time and the y axis shows voltage.

The screen – It looks like a graph paper. The horizontal line at the middle is the x axis. The vertical line at
the middle is the y axis.

The CAL terminal – It may be used to check if the probes are functional or not.

The FOCUS knob – The focus should be such that the trace is thin and the readings are sharp.

The INTEN knob – The brightness of both the trace and readings should be low.

The channels – The oscilloscope has 2 channels. They are channel 1 and 2. Each channel can show a
graph. The screen can show 1 channel at a time or both simultaneously.

The probes – The oscilloscope has 2 probes. Each goes with a channel. Each has 2 terminals. One
terminal looks like pen and another terminal is a clip. The pen terminal is for + terminal of the voltage and
the clip terminal is for - terminal of the voltage. The clip terminals of both probes are joined together
internally. Each pen terminal has a switch with 2 options. They are ×1 and ×10. The ×1 option should be
selected for the general purpose.

The GND button – The voltage reading is 0 V when the probes are not connected to the circuit. It is shown
as a horizontal line. Each channel has a button to bring up the zero-line.

The AC/DC button – Each channel has two types of input coupling. They are ac and dc. The ac coupling
shows only the ac voltage component of the input. The dc coupling shows everything.

The CH1 and CH2 button – Each channel can be turned on or off.

The VOLTS/DIV knob – It selects the vertical scale of the screen for each channel. The channels can have
different scales. If both are shown simultaneously on the screen, they should have the same scale.

46
The ALT/CHOP/ADD and INV button – The ALT/CHOP/ADD button works when both channels are shown
simultaneously on the screen. The ALT option should be selected for the general purpose. If the graphs
flickers much, the CHOP option should be selected. The INV button can be long pressed to invert channel
2. Channel 1 cannot be inverted. Inversion shifts the zero-line automatically.

The VERTICAL POSITION knob – It shifts the zero-line up or down for each channel. It is used for the
purpose of viewing only.

The TIME/DIV knob – It selects the horizontal scale of the screen for both channels.

The MAIN/ALT/DELAY button – The MAIN option should be selected for the general purpose.

The HORIZONTAL POSITION knob – It shifts the zero-line left or right for both channels. It is used for the
purpose of viewing only.

The TRIGGER LEVEL knob – The value should be 0 V for the general purpose.

The MODE button – The ATO option should be selected for the general purpose.

The SOURCE button – The CH1 option should be selected when channel 1 or both channels are shown on
the screen. The CH2 option should be selected when channel 2 is shown on the screen.

The COUPLING button – The AC option should be selected for the general purpose.

Showing two graphs simultaneously – Let us consider the following circuit.

If 𝑣1 and 𝑣2 are to be shown, then the channels should be connected the following way.

47
If 𝑣2 and 𝑣3 are to be shown, then the channels should be connected the following way. Channel 2 should
be inverted.

If 𝑣1 and 𝑣3 are to be shown, then the channels should be connected the following way.

48