Transcript Chapter14-Lect4 - faraday - Eastern Mediterranean University

Chapter 14
Filter Circuits
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
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Ideal Filter Magnitude Responses
 Magnitude responses of different type of ideal filter functions.
H()
H()

c

c
Highpass Filter
Lowpass Filter
H()
H()
1
2
Bandpass Filter

1

2
Bandstop Filter
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Actual Filter
Magnitude
Responses
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LOWPASS FILTER
 A low pass filter is designed to pas only frequencies from DC up to the cutoff
frequency c.
1
V ( )
1
j C
H ( )  0


Vi ( ) R  1
1  j RC
j C
H (0)  1 and H ()  0
At the cutof or Rolloff frequency  c
H ( c ) 
1
1   c 2 R 2C 2

1
2
c 
1
RC
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LOWPASS FILTER
Regulator: (a) effect of spike in current on the input side; (b) noise reduction.
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HIGHPASS FILTER
 A high pass filter is designed to pass all the frequencies above its cutoff
frequency c.
V0 ( )
R
j RC


Vi ( ) R  1
1  j RC
j C
H (0)  0 and H ()  1
H ( ) 
At the cutof or Rolloff frequency  c
H ( c ) 
1
1   c 2 R 2C 2

1
2
c 
1
RC
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BANDPASS FILTER
 A bandpass filter is designed to pass all the frequencies within a band of
frequencies, 1 <  < 2
H ( ) 
V0 ( )
R

Vi ( ) R  j  L  1

C
H (0)  0 and H ()  1

1
LC
The Lower and Upper cutoff frequencies are 1 and  2
The center frequency o is given by o 
The Bandwidth is B= 2 -1
H (o )  1 and H (1 )  H ( 2 ) 
1
2
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BANDSTOP FILTER
 A Bandstop filter is designed to stop or eliminate all the frequencies within a
band of frequencies 1 <  < 2 .

j L  1
V0 ( )
C
H ( ) 

Vi ( ) R  j  L  1


C
H (0)  1 and H ()  1

1
LC
The Lower and Upper cutoff frequencies are 1 and  2
The center frequency o is given by o 
The bandwidth is B= 2 -1
H (o )  1 and H (1 )  H ( 2 ) 
1
2
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Active first-order low-pass filter
 Active filters use also active devices such as OP AMPs.
 Passive filters use only passive devices such as inductors and capacitors only.
Rf
H ( ) 
Zf
V0 ( )

Vi ( )
Zi
Zi  Ri , Z f  R f
Rf
1
H ( )  
Ri 1  jC f R f
jC f
Rf
1


jC f R  1
1  j R f C f
f
j C f
1
c 
Rf C f
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Active first-order High-pass filter
Zf
V0 ( )
H ( ) 

Vi ( )
Zi
Rf
H ( )  
Ri  1
1
Zi  Ri 
, Z f  Rf
jCi

j Ci
j Ci R f
1  jCi Ri
c 
1
Ci Ri
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Active Bandpass Filter
 A bandpass filter is obtained by cascading a LPF and a HPF together with an
inverting amplifier to provide the desired gain.
Active Bandpass Filter Block Diagram.
Frequency Response
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Active Bandpass Filter Example
 Three cascaded stages are used to realize the bandpass filter.
 A LPF cascaded with a HPF and an inverter stage.


jC2 R 
1





1

j

C
R
1

j

C
R
1 
2


Rf
jC2 R
1

Ri 1  jC1 R 1  jC2 R
Rf
Vo
H ( ) 

Vi
Ri
o
1
1
2 
, 1 
, o  12 , B  2  1 , Q 
RC1
RC2
B
H ( ) 
Rf
H (o ) 
j
1
Ri 1  j 1  j 

1 
2 


R f 2
Ri 1  2
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Active Bandreject Filter
 A bandreject filter may be constructed by parallel combination of a LPF and a
HPF filter and a summing amplifier.
Active Bandreject Filter Block Diagram.
Frequency Response
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Active Bandreject Filter Example

j C2 R 
1



1

j

C
R
1

j

C
R
1
2


j


Rf 
1 
1



j

Ri  1  j
1

1 
2

Rf
Vo
H ( ) 

Vi
Ri
2


j
2

(
j

)
1


1
11  
R f  



Ri  1  j 1  j  

 
 


2
1

 

Rf
  0 and    H ( ) 
Ri
  o  1 2
21
H ( o ) 
Ri 1   2
Rf
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Simplified Block Diagram of a Superheterodyne
AM Radio Receiver
The input signal is downconverted in frequency to an
intermediate frequency (IF) before amplification.
Good IF filters are required.
The signal is again downconverted in frequency after IF
amplification.
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Frequency Assignments for Touch-tone Dialing
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Three-way, crossover network with 6 dB per octave.
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Three-way, crossover network with 12 dB per octave
at cutoff.
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Detection Scheme for Touch-tone Dialing
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