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NETWORK THEORYNETWORK THEORY
LECTURE 2SECTION-D:TYPES OF FILTERS AND THEIR CHARACTERISTICSD:TYPES OF FILTERS AND THEIR CHARACTERISTICS
Example of First Order Filter
0 dB
3
Example of First Order Filter - Passive* Low Pass Filter
00
0
2
2/1
2
001
0
0
0
log20,For
01,For
1log10
1
1log20)(T
0a
thfilter wi pass) (loworder first a of form thehas This
1
1
1
)/1(11
1
11
1
1
)()()(
T
dBT
dBin
a
RCwhere
ssRC
s
sRCsC
R
sCRZ
ZsVsVsT
o
o
o
C
C
i
o
20 log (R2/R1)
Example of First Order Filter
For
For
T
a
This
where
T
V_= 0
Io
I1 = Io
4
Example of First Order Filter - Active* Low Pass Filter
01
20
121
20
2
1
2
2/1
21
2
01
201
2
0
0
1
2
0
1
2
2
1
2
21
2
1
2
1
2
11
2
log20log20,For
0log20,For
1log10log20
1
1log20log20)(T
0a
thfilter wi pass) (loworder first a of form thehas This
1
1
1
)/1(11
1)1(
)/1(1
)()()(
RRT
RRfordBRRT
RR
RRdBin
RRa
CRwhere
sRR
sRR
CRsR
RCsRR
RR
sCRR
ZRRIZRI
sVsVsT
o
o
o
CCo
i
o
Gain Filter function
Second-Order Filter Functions
o
o
bsbsasasasT
1
21
22)(
* Second order filter functions are of the form
which we can rewrite as
where o and Q determine the poles
* There are seven second order filter types:Low pass, high pass, bandpass, notch,Low-pass notch, High-pass notch andAll-pass
20
02
12
2)(
sQ
s
asasasT o
0
02121 1
22,,
Qj
Qpp PP
5
Filter Functions* Second order filter functions are of the form
* There are seven second order filter types:Low pass, high pass, bandpass, notch,
241 Q
js-plane
o
x
x
Qo
2
This looks like the expression for the new poles that we had for a feedback amplifier with two poles.
Ch. 12 Active Filters Part 1
Second-Order Filter Functions
Low Pass
High Pass
Bandpass
a1= 0, a2= 0
a0= 0, a1= 0
a0= 0, a2= 0
)(sT
Ch. 12 Active Filters Part 1 6
Order Filter Functions
20
02
12
2
sQ
s
asasa o
Second-Order Filter Functions
Notch
Low Pass Notch
High Pass Notch
a1= 0, ao = ωo2
a1= 0, ao > ωo2
a1= 0, ao < ωo2
20
02
12
2)(
sQ
s
asasasT o
All-Pass
7
Order Filter Functions
Passive Second Order Filter Functions
8
Passive Second Order Filter Functions
* Second order filter functions can be implemented with simple RLC circuits
* General form is that of a voltage divider with a transfer function given by
* Seven types of second order filters High pass Low pass Bandpass Notch at ωo
General notch Low pass notch High pass notch
20
02
12
2
)()()(
sQ
s
asasasVsVsT o
i
o
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