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Part 4 Frequency Response/section/1
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. .
صادق الكناني: التدريسي
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 صادق الكناني: التدريسي
TRANSFER FUNCTION
The 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
صادق الكناني: التدريسي
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.
2
1 1
1
2
1
1
2( ) 1 1
( )( )
( ) 21 1
k k
n n
jj jK j
zNH
D jj jp
صادق الكناني: التدريسي
Magnitude plot for a low-pass filter
TRANSFER FUNCTION of Low-pass RC Circuit
R=20 kΩ
C=1200 pF
At low frequencies At high frequencies
صادق الكناني: التدريسي
Frequency Response of the RC Circuit
2
1
1
( ) 1( ) Transfer Function
1( ) 1
Magnitude Response
Phase Res
1( )
1 ( )
( ) ( ) tan
1Where
ponse
o
o
o
o
s
H
H
V j CH
V j RCRC
C
j
R
a) Time Domain RC Circuit b) Frequency Domain RC Circuit
صادق الكناني: التدريسي
Drawing Frequency Response of RC Circuit
a) Amplitude Response b) Phase Response
2
1( )
1 ( )o
H
1( ) ( ) tan o
H
Low 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.
صادق الكناني: التدريسي
HIGH Pass Filter
صادق الكناني: التدريسي
s=j
صادق الكناني: التدريسي
Vx
0.5Vx
0.5Vx Vx
صادق الكناني: التدريسي
Phase plot for a low-pass filter
TRANSFER FUNCTION of Low-pass RC Circuit
At low frequencies At high frequencies
R=20 kΩ
C=1200
pF
صادق الكناني: التدريسي
TRANSFER FUNCTION of High-pass RC Circuit
Magnitude plot for a high-pass filter
At high frequencies At low frequencies
R=20 kΩ
C=1200 pF
صادق الكناني: التدريسي
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 kΩ
C=1200 pF
صادق الكناني: التدريسي
TRANSFER FUNCTION of a Band-pass RC Circuit
صادق الكناني: التدريسي