E E 2415

Lecture 162nd Order High Pass, Low Pass and Band Reject Filters

2nd Order Low Pass Filter (1/8)

Vin

~

R jL

-jC

+

Vo-

~

2nd Order Low Pass Filter (2/8)

2nd Order Low Pass Filter (3/8)

1

2

2

90 tan

1

os

os

oo

so

QH Q

Q

2nd Order Low Pass Filter (4/8)

Two Poles

2nd Order Low Pass Filter (5/8)

2nd Order Low Pass Filter (6/8)

Slope is -40 db/decade

2nd Order Low Pass Filter (7/8)

0.01 0.1 1 10 10080

60

40

20

0

20Bode Plot for 2nd Order Low-Pass

Frequency: Multiples of o

Gai

n in

db

G 10( )

G 2( )

G 1( )

2nd Order Low Pass Filter (8/8)

0.01 0.1 1 10 100190

170

150

130

110

90

70

50

30

10

10Phase Plot for 2nd Order Low-Pass

Frequency: Multiples of o

Deg

rees

P 10( )

P 2( )

P 1( )

2nd Order High Pass Filter (1/8)

Vin

~

R

jL

-jC

+

Vo-

~

2nd Order High Pass Filter (2/8)

2nd Order High Pass Filter (3/8)

2nd Order High Pass Filter (4/8)

Two Zeros at origin

Two Poles

2nd Order High Pass Filter (5/8)

2nd Order High Pass Filter (6/8)

Slope is 40 db/decade

2nd Order High Pass Filter (7/8)

0.01 0.1 1 10 10080

60

40

20

0

20Bode Plot for 2nd Order High-Pass

Frequency: Multiples of o

Gai

n in

db

G 10( )

G 2( )

G 1( )

2nd Order High Pass Filter (8/8)

0.01 0.1 1 10 10010

10

30

50

70

90

110

130

150

170

190Phase Plot for 2nd Order High-Pass

Frequency: Multiples of o

Deg

rees

P 10( )

P 2( )

P 1( )

2nd Order Band Reject Filter (1/4)

Vin

~ ~

R

jL

-jC

+

Vo

-

2nd Order Band Reject Filter (2/4)

2nd Order Band Reject Filter (3/4)

0.01 0.1 1 10 100-40

30

20

10

0

Bode Plot for 2nd Order Band Reject

Frequency: Multiples of o

Gai

n in

db

G m 10( )

G m 2( )

G m 1( )

2nd Order Band Reject Filter (4/4)

0.01 0.1 1 10 100100

50

0

50

100Phase Plot for 2nd Order Band Reject

Frequency: Multiples of o

Deg

rees

P 10( )

P 2( )

P 1( )