Download Lecture Notes - Transfer Function and Frequency Response File

Chapter 14
Frequency Response
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.
Huseyin Bilgekul
Eeng 224 Circuit Theory II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
Eeng 224
‹#›
FREQUENCY RESPONSE
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.
Eeng 224
‹#›
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 ( )
H( )  Voltage gain  o
Vi ( )
H( )  Transfer Impedance 
Vo ( )
Ii ( )
I o ( )
Ii ( )
H( )  Transfer Admittance 
I o ( )
Vi ( )
H( )  Current gain 
Eeng 224
‹#›
TRANSFER FUNCTION of Low-pass RC Circuit
R=20 kΩ
C=1200 pF
At low frequencies
At high frequencies
Magnitude plot for a low-pass filter
Eeng 224
‹#›
TRANSFER FUNCTION of Low-pass RC Circuit
R=20 kΩ
C=1200
pF
At low frequencies
At high frequencies
Phase plot for a low-pass filter
Eeng 224
‹#›
TRANSFER FUNCTION of High-pass RC Circuit
R=20 kΩ
C=1200 pF
At high frequencies
At low frequencies
Magnitude plot for a high-pass filter
Eeng 224
‹#›
TRANSFER FUNCTION of High-pass RC Circuit
R=20 kΩ
C=1200 pF
Magnitude plot for a high-pass filter
At high frequencies
At low frequencies
Phase plot for high-pass filter
Eeng 224
‹#›
TRANSFER FUNCTION of a Band-pass RC Circuit
Eeng 224
‹#›
Frequency Response of the RC Circuit
a) Time Domain RC Circuit
b) Frequency Domain RC Circuit
1
V ( )
1
jC
H ( )  o


Transfer Function
Vs ( ) R  1
1  j RC
jC
1
H ( ) 
Magnitude Response
2
1  ( )
o
 ( )  H ( )   tan 1
Where o 
1
RC

o
Phase Response
Eeng 224
‹#›
Drawing Frequency Response of RC Circuit
Low Pass Filter
H ( ) 
1
1  (
o
)2
a) Amplitude Response
 ( )  H ( )   tan 1

o
b) Phase Response
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.
Eeng 224
‹#›
HIGH Pass Filter
Eeng 224
‹#›
TRANSFER FUNCTION
 The transfer function H() can be expressed in terms of its numerator polynomial
N() and its denominator polynomial D().
N ( )
H ( ) 
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
 j 2 1

j

j





K ( j ) 1 
1



   
z

1
k
k 



N ( )


H ( ) 

2
D( )

1  j  1  j 2 1   j  

p1  
 n   n  



1
Eeng 224
‹#›
s=j
Eeng 224
‹#›
0.5Vx
Vx
0.5Vx
Vx
Eeng 224
‹#›