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1Eeng 224
Chapter 14Frequency Response
Huseyin BilgekulEeng 224 Circuit Theory II
Department of Electrical and Electronic Engineering Eastern Mediterranean University
Chapter Objectives: Understand the Concept of Transfer Functions. Be Familiar with the Decibel Scale. Learn how to make Bode Magnitude and Phase plots.
Learn about series and parallel resonant RLC circuits. Know Different Types of Passive and Active Filters and their
Characteristics. Understand the use of scaling in circuit analysis. Be Able to use PSpice to obtain frequency response. Apply what is learnt to radio receiver and touch-tone
telephone.
2Eeng 224
What is Frequency Response of a Circuit?
It is the variation in a circuit’s
behavior with change in signal
frequency and may also be
considered as the variation of the gain
and phase with frequency.
FREQUENCY RESPONSE
3Eeng 224
TRANSFER FUNCTIONThe transfer function H() of a circuit is the is the frequency dependent ratio of the phasor output Y() to a phasor input X().
Considered input and output may be either the current or the voltage variable.
4 types of possible transfer functions.
Y( )H( )
X( )
= H( ) |
)(V
)(V gain Voltage )(H
i
o
)(I
)(V ImpedanceTransfer )(H
i
o
)(I
)(I gain Current )(H
i
o
)(V
)(I AdmittanceTransfer )(H
i
o
4Eeng 224
Magnitude plot for a low-pass filter
TRANSFER FUNCTION of Low-pass RC Circuit
R=20 kΩC=1200 pF
At low frequencies At high frequencies
5Eeng 224
Phase plot for a low-pass filter
TRANSFER FUNCTION of Low-pass RC Circuit
At low frequencies At high frequencies
R=20 kΩC=1200 pF
6Eeng 224
TRANSFER FUNCTION of High-pass RC Circuit
Magnitude plot for a high-pass filter
At high frequencies At low frequencies
R=20 kΩC=1200 pF
7Eeng 224
TRANSFER FUNCTION of High-pass RC Circuit
Magnitude plot for a high-pass filter
Phase plot for high-pass filter
At high frequencies At low frequencies
R=20 kΩC=1200 pF
8Eeng 224
TRANSFER FUNCTION of a Band-pass RC Circuit
9Eeng 224
Frequency Response of the RC Circuit
2
1
1( ) 1
( ) Transfer Function1( ) 1
Magnitude Response
Phase Res
1( )
1 ( )
( ) ( ) tan
1Where
ponse
o
o
o
o
s
H
H
V j CH
V j RCR C
C
j
R
a) Time Domain RC Circuit b) Frequency Domain RC Circuit
10Eeng 224
Drawing Frequency Response of RC Circuit
a) Amplitude Response b) Phase Response
2
1( )
1 ( )o
H
1( ) ( ) tan
o
H
Low Pass FilterLow Pass Filter
The frequency value of o is of special interest.
Because output is considerable only at low values of frequency, the circuit is also called a LOW PASS FILTER.
11Eeng 224
HIGHHIGH Pass Filter Pass Filter
12Eeng 224
TRANSFER FUNCTION The transfer function H() can be expressed in terms of its numerator polynomial N() and its denominator polynomial D().
( )( )
( )
NH
D
The roots of N()=0 are called ZEROS of H() (j=z1, z2, z3, ….).Similarly The roots of D()=0 are called POLES of H() (j=p1, p2, p3, ….). A zero as a root of the numerator polynomial, results in a zero value of the transfer function. A pole as a root of the denominator polynomial, results in an infinite value of the transfer function.
21 1
1
2
1
1
2( ) 1 1( )
( )( ) 21 1
k k
n n
jj jK j zNH
D jj jp
13Eeng 224
s=j
14Eeng 224
Vx
0.5Vx
0.5VxVx