1 eeng 224 ideal filter magnitude responses h()h() cc lowpass filter h()h() cc highpass filter...
TRANSCRIPT
1Eeng 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 types of ideal filter functions.
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Actual Filter Magnitude Responses
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LOW-PASS 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 pass only frequencies from DC up to the cutoff frequency c.
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HIGH-PASS 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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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
0
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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 .
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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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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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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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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