11 hp filter
14
Lecture 11 CHAPTER 4: Active Filter 1
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Lecture 11
CHAPTER 4: Active Filter
1
Lecture 11
2. High Pass Filter
2
a) 1st OrderAV (dB)
AV(max)
AV(max) - 3
fc
0.1fc
0.01fc
AV(max) - 20
AV(max) - 40
+20dB/dec
f (Hz)
A high-pass filter is a filter that passes high frequencies well, but attenuates (or reduces) frequencies lower than the cutoff frequency
The actual amount of attenuation for each frequency varies from filter to filter
A high-pass filter is the opposite of a low-pass filter
It is useful as a filter to block any unwanted low frequency components of a complex signal while passing the higher frequencies
R1
R2
_
+Vin
+V
-V
RA
CA
Vo
Lecture 11
Analysis
It is high pass filter ifThe numerator has s
V+ = VR
3
Vo = 1+ V+
V+ = Vi
RA
1sCA
+RA
R1
R2
Vo = 1+
R1
R2
Vi
V+ = VisRACA
sRACA+1
V+ = VRA
AV = = 1+
R1
R2Vi
Vo
R1
R2
_
+Vin
+V
-V
RA
CA
Vo
sRACA
sRACA+1
sRACA
sRACA+1
Lecture 11
Analysis
At 0 < f < fc, high pass filter will attenuate the frequencies at roll-off of +20dB/decade because XCA is decreasing starts from ∞. When XCA=∞,
V+=VRA = 0
AV = 0
4
AV(max) = 1+ R1
R2
At f = fc, the gain is
0.707AV(max) or in dB,
AVdB(max)-3 where the
magnitude of the capacitive
reactance, XCA equals the
resistance of the resistor,
RA
At f > fc, high pass filter will
pass the frequencies
because XCA is
decreasing to 0. When
XCA= 0,
V+=VRA=Vi
1 2fcCA
= RA
fc =1
2RACA
AV (dB)
AV(max)
AV(max) - 3
fc
0.1fc
0.01fc
AV(max) - 20
AV(max) - 40
+20dB/dec
f (Hz)
Lecture 11
21
2
11 1 1 2 2 2
22
1 2 1 2 1 2 1 2
1
1 11
o
in
Rs
RV
V RRC RC R C
Rs s
R R C C R R C C
5
b) 2nd Order (Sallen-Key)
Vo
R1
R2
_
+Vin
+V
-V
RA
CACB RB
AV (dB)
AV(max)
AV(max) - 3
fc
0.1fc
0.01fc
AV(max) - 40
AV(max) - 80
+40dB/dec
f (Hz)
AV(max) = 1+ R1
R2
1 2 RARBCACB
fc = fAfB
1 2RACA
1 2RBCB
=
=
Lecture 11
6
R1=2.55k, R2=4.3k , RA=RB=1.6k, CA=CB=0.01F
Lecture 11
Higher Order High Pass Filter
7
Table for Butterworth response
3rd order system
4th order system
R1
R2
_
+Vin
+V
-V
RA
CACB RB
R1
R2
_
+Vin
+V
-V
RA
CACB RB
Vo
R3
R4
_
++V
-V
RC
CCCD RD
R3
R4
_
++V
-V
RC
CC
Vo
Lecture 11
3. Band Pass Filter
8
fo = fC1fC2 BW = fC2 – fC1
The band-pass filter allows frequencies between fC1 and fC2 (fC1<
f < fC2) to pass while effectively blocking all others.
AV (dB)
AV(max)
AV(max) - 3
fo 10fC20.01fC1
AV(max) - 20
+20dB/dec
f (Hz)fC1 fC2
-20dB/dec
fC1 < fC2
BW
(HP) (LP)
Cascaded Low Pass and High Pass Filter
Lecture 11
9
HP
R1
R2
A
_
+Vin
+V
-V
RA
CA
R3
R4
B
_
++V
-V
RB CB Vo
R1
R2
A
_
+ Vi
+V
-V
RA CA
R3
R4
B
_
++V
-V
RB
CB
Vo
LP
fcA < fcB
HP
LP
fcA > fcB
Lecture 11
10
RA=1k, RB=10k, R1=R2=R3=R4= 1k, CA=CB=0.01F
LP HPVi Vo
Lecture 11
11
Multiple-Feedback Band-Pass Filter
Vo
+
-Vin
+V
-V
RA
CA
Rf
CB
RB
fo = 1
2 (RA||RB)RfCACB
Q = foRf CACB
BW =Qfo
22
1
2
A B
o A
A Bin
f A B f C C
sV R C
R RV s sR C R R R C
Lecture 11
12
RA=3.18k, RB=352 , Rf=31.8k, CA=CB=0.01F
Lecture 11
4. Band Stop Filter
13
Vo
+
-Vin
+V
-V
R1
C2
Rf
C1
R3
R2
fo = 1 2 R1RfC1C2
Multiple-Feedback Band-Stop Filter
Lecture 11
14
State-Variable Band Stop Filter
_
+
Vin
Rf
R1 +V
-V
VoR2
LPfC1
HPfC2
fC1< fC2
