E E 2415
Lecture 17Op Amp FiltersLow Pass and High Pass
1st Order Low Pass Filter (1/5)
f
jC
fR
ccV
ccV
gR
gV
oV
1o
f fR C
Half-Power Frequency
1st Order Low Pass Filter (2/5)
1
1
ff f
ff f
g
jRC RjRC R
HR
1
f f f
g
f f
jR C R
H jRC R
1
11
o
f fo
og g
o o
jjR RH
R Rj jj
1st Order Low Pass Filter (3/5)
1
2tan
1
f
g
o
o
RR
H
No Zeroes; 1 pole at o
2
0
20
1
f
g
RR
G Log
Gain in decibels
If Rf = 50 kW and Rg = 5 kW
1st Order Low Pass Filter (4/5)
0.01 0.1 1 10 10030
20
10
0
10
20Bode Plot for 1st Order Low-pass OpAmp
G m ( )
1st Order Low Pass Filter (5/5)
0.01 0.1 1 10 10080
100
120
140
160
180Phase Plot for 1st Order Low-Pass OpAmp
P ( )
1st Order High Pass Filter (1/5)
g
jC
fR
ccV
ccV
gR
gVoV
1
og gR C
Half-Power Frequency:
1st Order High Pass Filter (2/5)
1
1 1
f
f g g o
og
g g o
Rj
R R RH jR jj
C R
1
2
3 tan21
1
f
f g oo
g o
oo
Rj
R RH
R j
1st Order High Pass Filter (3/5)
2
0
20
1
f
g o
RR
G Log
Gain in decibels
If Rf = 50 kW and Rg = 5 kW
Zero at Origin, pole at o
13 tan2 o
P
Phase shift
1st Order High Pass Filter (4/5)
0.01 0.1 1 10 10030
20
10
0
10
20Bode Plot for 1st Order Low-pass OpAmp
G m ( )
1st Order High Pass Filter (5/5)
0.01 0.1 1 10 100180
200
220
240
260
280Phase Plot for 1st Order Low-Pass OpAmp
P ( )
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