Electric Circuits II: (ELCT 401)

Instructors: Prof. Yasser Hegazy

Prof. Said Fouad

Lecture 1: Introduction

Course Outline

• Sinusoidal Steady State Analysis (AC Circuits)

• Power Calculations in AC circuits.

• Operational Amplifiers.

• Frequency Dependent Circuits

• Circuit Analysis in the Laplace Domain.

2

Study PlanWeek Topic Laboratories Tutorials

Remarks

Week I Introduction

Week II Circuit Elements in Phasor

Domain

Start of all Labs Start of All tutorials

Week III Circuit Analysis in Phasor Domain

Week IVLectures 4-5 AC Power

CalculationsWeek V

Week VI Operational Amplifiers

Midterm Exam ( no teaching )

Week VII Operational Amplifiers Applications

Week VIII Resonance

Week VIIII Filters No lecture for MCTR

Week X Circuit Analysis in “S” Domain No lectures for

IET and MET

Week XI Examples on “S” Domain

Week XII Revision

Course Activities

• Lectures

– Monday 2nd slot – H14 (MET II)

– Sunday 3rd slot – H14 (IET / MET I)

– Thursday 1st slot – H14 (MCTR I)

– Thursday 2nd slot – H14 (MCTR II)

• Tutorials.

One slot weekly, according to your schedule

• Laboratories.

One slot weekly, according to your schedule

4

Marking Scheme

• Assignments. 10 %

• Quizzes. 10 %

• Laboratories. 15 %

• Practical Project. 05 %

• Midterm Exam. 20 %

• Final Exam. 40 %

5

Resources

1.0 Text book

1. Electric Circuits Textbook by, Nilsson & Riedel. 10th Edition

• Chapters 5, 9 , 10 , 13, 14 and 15.

2. Charles K. Alexander and Matthew Sadiku, “Fundamentals of

Electric Circuits” 11th Edition, Mc. Graw Hill, 2017.

2.0 Lab manual

• Posted on the course webpage.

3.0 Webpage:

• All course information will be available online at

http://eee.guc.edu.eg/

6

Chapter I

Sinusoidal Steady State Analysis

“Alternating Current Circuits (A.C.)”

Objectives

• To review basic facts about sinusoidal signals.

• To introduce Phasors and convert the time domain

sinusoidal waveforms into Phasors.

• To develop the phasor relationships for the basic

circuit elements.

• To solve electric circuits in phasor domain.

8

Sinusoids

• A sinusoid is a signal that has the form of the sine or cosine

function.

• A general expression for the sinusoid,

whereVm = the amplitude of the sinusoidω = the angular frequency in radians/sФ = the phase

)sin()( tVtv m

Sinusoids

10

SinusoidsA periodic function is one that satisfies v(t) = v(t + nT), for all t and for all integers n.

HzT

f1

f 2

• Only two sinusoidal values with the same frequency can be

compared by their amplitude and phase difference.

• If phase difference is zero, they are in phase; if phase

difference is not zero, they are out of phase.

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:

12

rz

jrez

)sin(cos jrjyxz a. Rectangular

b. Polar

c. Exponential22 yxr

x

y1tanwhere

Phasor

• Transform a sinusoid to and from the time domain to the phasor domain:

(time domain) (phasor domain)

)cos()( tVtv m mVV

• 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.

Example:

Transform the following sinusoids to phasors:

i = 6 Cos(50t – 40o) A

v = –4 Sin(30t + 50o) V

Solution:

a. I A

b. Since –sin(A) = cos(A+90o);

v(t) = 4cos (30t+50o+90o) = 4cos(30t+140o) V

Transform to phasor => V V

406

1404

Example

Transform the sinusoids corresponding to phasors:

a.

b.

V 3010 V

A j12) j(5 I

Solution:

a) v(t) = 10cos(t + 210o) V

b) Since

i(t) = 13cos(t + 22.62o) A

22.62 13 )12

5( tan 512 j512 122

I

15

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

Have a Wonderful Semester