Electric Circuits II: (ELCT 401)
Instructors:
Dr. Walid Omran
Dr. Wassim Alexan
Lecture 1: Introduction
Course Outline
• Sinusoidal Steady State Analysis (AC Circuits)
• Power Calculations in AC Circuits
• Three Phase Circuits
• Operational Amplifiers
• Frequency Dependent Circuits
• Circuit Analysis in the Laplace Domain
2
Course Activities
• Lectures
– Tuesday 3rd slot – (MET III)
– Tuesday 4th slot – (MET II)
– Thursday 1st slot – (MCTR)
– Thursday 3rd slot – (MET I / IET)
• Tutorials
One slot weekly, according to your schedule
• Laboratories
One slot weekly, according to your schedule
3
Grading Scheme
• Assignments
10 %
• Quizzes
10 %
• Laboratories
15 %
• Practical Project
05 %
• Midterm Exam
20 %
• Final Exam
40 %
4
Resources
Text books
• James Nilsson & Susan Riedel, “Electric Circuits,” 10th
Edition, Pearson Education, 2015.
• Charles K. Alexander & Matthew Sadiku, “Fundamentals of
Electric Circuits” 7th Edition, McGraw Hill Education, 2021.
Webpage:
• All course information will be available online on the CMS.
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Chapter I
Sinusoidal Steady State Analysis
“Alternating Current Circuits (A.C.)”
Objectives
• Review basic facts about sinusoidal signals.
• Introduce phasors and convert time domain
sinusoidal signals into phasors.
• Develop the phasor relationships for basic circuit
elements.
• Solve electric circuits in phasor domain.
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Sinusoids
• A sinusoid is a periodic signal that has the form of the sine or
cosine function.
• A general expression for the sinusoid,
𝑣 𝑡 = 𝑉𝑚 sin(𝜔𝑡)
where
Vm = amplitude of the sinusoid
ω = angular frequency in rad/s
T = time period
f = frequency in Hz = 1/T = ω/2π
Sinusoids
If the sin function is shifted by an angle Φ from the y-axis the
expression becomes:
v(t )  Vm sin( t   )
Where Φ is the phase shift or phase angle
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The Phasor
• A phasor is a complex number that
represents the amplitude and phase
of a sinusoid.
• It can be represented in one of the
following three forms:
a. Rectangular z  x  jy  r (cos   j sin  )
b. Polar
z  r 
c. Exponential z  re
j
where
r
x2  y2
  tan 1
y
x
Phasor Representation of Sinusoids
The sinusoid can be expressed by:
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Phasor Representation of Sinusoids
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Phasor Representation of Sinusoids
•
Transform a sinusoid to and from the time domain to the phasor domain:
v(t )  Vm cos(t   )
(time domain)
•
V  Vm 
(phasor domain)
Amplitude and phase difference are two principal concerns in the study of
voltage and current sinusoids.
•
Phasor will be defined from the cosine function in all our proceeding study.
•
If a voltage or current expression is in the form of a sine, it will be changed
to a cosine by subtracting from the phase.
Sinusoid-Phasor Transformation
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Trigonometric Identities
Example:
Transform the following sinusoids to phasors:
i = 6 Cos(50t – 40o) A
v = –4 Sin(30t + 50o) V
Solution:
a. I  6  40 
A
b. Since –sin(A) = cos(A+90o);
v(t) = 4cos (30t+50o+90o) = 4cos(30t+140o) V
Transform to phasor => V  4140  V
Example
Transform to the following phasors to the time domain:
a. V   10 30  V
b. I  j(5  j12) A
Solution:
a) v(t) = 10cos(t + 210o) V
b) Since
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I  12  j5  12  5  tan ( )  13 22.62 
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2
2
1
i(t) = 13cos(t + 22.62o) A
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Phasor
The differences between v(t) and V:
•
v(t) is instantaneous or time-domain representation
V is the frequency or phasor-domain representation.
•
v(t) is time dependent, V is not.
•
v(t) is always real with no complex term, V is generally
complex.
Note: Phasor analysis applies only when frequency is constant; when
it is applied to two or more sinusoid signals only if they have
the same frequency.
Phasor Domain Analysis Approach