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