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1Eeng 224
Chapter 14Filter Circuits
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.
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2Eeng 224
Ideal Filter Magnitude Responses
H()
c
Lowpass Filter
H()
c
Highpass Filter
H() H()
1 2 21
Bandpass Filter Bandstop Filter
Magnitude responses of different type of ideal filter functions.
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3Eeng 224
Actual Filter Magnitude Responses
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4Eeng 224
LOWPASS FILTER
0
2 2 2
1( ) 1
( )1( ) 1
(0) 1and ( ) 0
At the cutof or Rolloff frequency
1 1 1( )
21
i
c
c c
c
V j CH
V j RCRj C
H H
HRCR C
A low pass filter is designed to pas only frequencies from DC up to the cutoff frequency c.
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5Eeng 224
LOWPASS FILTER
Regulator: (a) effect of spike in current on the input side; (b) noise reduction.
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6Eeng 224
HIGHPASS FILTER
A high pass filter is designed to pass all the frequencies above its cutoff frequency c.
0
2 2 2
( )( )
1( ) 1
(0) 0 and ( ) 1
At the cutof or Rolloff frequency
1 1 1( )
21
i
c
c c
c
V R j RCH
V j RCRj C
H H
HRCR C
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7Eeng 224
BANDPASS FILTER
A bandpass filter is designed to pass all the frequencies within a band of frequencies, 1 < < 2
0
1 2
2 1
1 2
( )( ) (0) 0 and ( ) 1
1( )
1The center frequency is given by
The Lower and Upper cutoff frequencies are and
The Bandwidth is B= -
1( ) 1and ( ) ( )
2
i
o o
o
V RH H H
V R j L C
LC
H H H
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8Eeng 224
BANDSTOP FILTER
A Bandstop filter is designed to stop or eliminate all the frequencies within a band of frequencies 1 < < 2 .
0
1 2
2 1
1 2
1( )
( ) (0) 1and ( ) 11( )
1The center frequency is given by
The Lower and Upper cutoff frequencies are and
The bandwidth is B= -
1( ) 1and ( ) ( )
2
i
o o
o
j LV CH H HV R j L C
LC
H H H
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9Eeng 224
Active first-order low-pass filter
0 ( ) 1( ) ,
1( ) 1
f
f f fi i f f
i i f f ff
f
R
Z j C RVH Z R Z R
V Z j C j R CRj C
1 1( )
1f
ci f f f f
RH
R j C R R C
Active filters use also active devices such as OP AMPs.
Passive filters use only passive devices such as inductors and capacitors only.
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10Eeng 224
Active first-order High-pass filter
0 ( ) 1( ) ,
( )
1( )
1 1
fi i f f
i i i
f i fc
i i i iii
ZVH Z R Z R
V Z j C
R j C RH
j C R C RR j C
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11Eeng 224
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
2 11
o 2
i 1 2
2
1 2
21 2
2
1
1
1 2
1
2
2
1 1,
(
V 1( )
V 1 1
1
1 1
, , ,
( )1 1
)
f
i
f
i
oo
f
oi
i
f
R j C RH
R j C R j C R
R j C R
R j C R j C R
B QB
jR
Hj jR
RC RC
RH
R
Three cascaded stages are used to realize the bandpass filter.
A LPF cascaded with a HPF and an inverter stage.
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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
o 2
i 1 2
1
2 1
2
1 1 1
2 1
11 2
1 2
V 1( )
V 1 1
1
1 1
2 ( )1
1 1
0 and ( )
2( )
f
i
f
i
f
i
f
i
fo o
i
R j C RH
R j C R j C R
jR
j jR
j jR
j jR
RH
R
RH
R
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15Eeng 224
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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16Eeng 224
Frequency Assignments for Touch-tone Dialing
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17Eeng 224
Three-way, crossover network with 6 dB per octave.
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18Eeng 224
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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