Theory of Electric Circuits II
Lecture #1: Resonant Circuits
Fall 2009
Department of Electronics and Communications Engineering,
Cairo University
© Mahmoud H. Ismail, 2009
Introduction
Series Resonance
Outline
1
Introduction
Course contents, references and course plan
Resonance Circuits: types and applications
2
S i R
Series
Resonance
Definition
Phasor diagram for the series resonant circuit
The quality factor of a resonant circuit
The detuning factor and narrow
narrow--band (near
(near--resonance)
operation
Introduction
Series Resonance
Course Contents
Series and Parallel Resonance Circuits
Applications on Passive Electric Filters
o LP, HP, BP, BS filters
o Double
D bl -tuned
Doublet
d filters
filt
Resonance in MutuallyMutually-Coupled Circuits
o Single
Single--tuned transformers
o Double
Double--tuned transformers
o Frequency response using Bode plots
Two–
Two
–port Networks
o Admittance, impedance, hybrid and transmission parameters
o Equivalent circuits
o Parameters conversions
o Inter
Inter--connection of two
two--ports (series, parallel and cascade)
o Two
Two--port networks embedded within a network
Introduction
Series Resonance
References
References:
1 Syed
1.
S d A.
A Nasar
N
Nasar,, “Electric
“El t i Ci
Circuits,”
it ” Schaum’s
S h
’ Solved
S l dP
Problems
bl
Series, Mcgraw
Mcgraw--Hill, New York, 1988
1988..
2. Richard C. Dorf
Dorf,, “Introduction to Electric Circuits,”
, John Wileyy &
Sons Inc., New York, 1993
1993..
3. Cunningham Stuller, “Circuit Analysis,” John Wiley & Sons Inc.,
New York,
York 1995
1995..
4. James W. Nilsson and Susan A. Riedel, “Electric Circuits,”
Addison--Wisley Publishing Company, New York, 1996
Addison
1996..
Important topics to be revised:
1. Analyzing circuits with D.C. and A.C. input signals.
2 Using loop and node analysis.
2.
analysis
3. Calculating input impedances and admittances of networks.
4. Calculations of maximum power transfer to a load.
5. Dealing with independent and dependent sources in ideal &
actual cases.
Introduction
Series Resonance
Tentative Course Plan
Instructors: Prof. Dr. Afaf Abdel
Abdel--Fattah,
Dr. Mahmoud H. Ismail
TA: ??
G
Grading:
di
20
20%
% Midt
Midterm, 10
10%
%Q
Quizzes,
i
70
70%
% Fi
Finall E
Exam.
8310..
Meeting times: Sunday, Lecture Hall 8310
Office Hours:
Hours:First 4-5 weeks, Saturday. 9:30 - 11:30 AM, later: Sunday 1
10:30 - 12:30 PM
Some Classroom Regulations
• Late arrivals
• Attendance in first lecture
Introduction
Series Resonance
Resonance Circuits
What is Electric Resonance?
o A resonance circuit is a combination of R
R, L and C elements
having a frequency response as shown.
o Radio and TV receivers have response
p
curves similar to the
one shown.
o Resonance occurs when the inductive and capacitive
reactances of the circuit are equal
equal.
o In other words, it occurs when the input impedance to a circuit
is p
pure real ((resistive).
)
o At resonance, the energy absorbed at any instant by one
reactive element is exactly equal to that released by the other
element.
l
t
o At resonance, energy pulsates from one reactive element to
y
requires
q
no reactive
the other. Once at resonance,, the system
power and the total apparent power is equal to the average
power dissipated in the resistive elements.
Introduction
Series Resonance
Resonance Circuits
Types of Resonance Circuits
L
R
R
+
V
C
I
C
-
I
V
L
Series Resonance
Parallel resonance
Introduction
Series Resonance
Series Resonance
Rs
+
-
L
Rl
Coil
Es
C
Introduction
Series Resonance
Series Resonance
Analysis
At resonance:
Current and voltages at resonance:
Voltage across coil
Voltage across capacitor
Voltage across resistor
Introduction
Series Resonance
Series Resonance
Phasor Diagrams
Imag
g
Imag
g
Real
Phasor diagram for the series
resonantt circuit
i it att resonance
Real
Power triangle for the series
resonantt circuit
i it att resonance
Introduction
Series Resonance
Series Resonance
The Quality Factor (Qs) at Resonance
•
The quality factor Q of a series resonant circuit is defined
as the ratio of the reactive power of either the coil or the
capacitor to the average power of the resistance at
resonance..
resonance
Introduction
Series Resonance
Series Resonance
Analysis II
Voltages
g at resonance in terms of quality
q
y factor:
Note that usually
Impedance in terms of quality factor:
: Detuning factor
Introduction
Series Resonance
Series Resonance
Analysis II (contd.)
Current in terms of quality factor:
•
Let
Fractional detuning factor, represents deviation
f
from
resonance freq.
f
•
For narrowband (near resonance) operation, i.e.,