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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 ( )