Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

Filter: H(s)

(Transfer Function)Input: Vi(s)

A device that alters the frequency spectrum of signals passing through itFilter:

Output: Vo(s)

Vo(s) =

(14.1, 14.2 in Razavi)

(Analog filters in this course)

Vi(s) x H(s)

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters(14.1, 14.2 in Razavi)

1 2

1 2

( )( ) ( )( )( ) ( )M M

N

a s z s z s zs p s p s p

11 0

11 0

M MM M

N NN

a s a s as b s b

poles, zerosN : filter order

Larger N sharper filter response

( )H s

M N

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

First-order filter 1 0

0

( )a s a

H ss

Pole, zero locations determine how magnitude and phase of H(j) change

Pole-zero diagrams

Bode Plot

0

0

( )a

H ss

1

0

( )a s

H ss

1 0

0

( )a s a

H ss

01

0

( )s

H s as

(Real poles and zeros)

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

Low Pass (LP) Filter

Circuit Implementation(Passive)

0

0

( )a

H ss

( )( )

o

i

V sV s

0

0a

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

High Pass (HP) Filter

Circuit Implementation

1

0

( )a s

H ss

( )( )

o

i

V sV s

0

1a

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

Assume |a0/a1| > 0

( )( )

o

i

V sV s

0

0a

1 0

0

( )a s a

H ss

1a

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

All Pass (AP) Filter: Phase change only

Delay in time domain: Delay line0

1 10

( ) , a <0s

H s as

| ( ) |H j ( )H j

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

( )( )

o

i

V sV s

01 1

0

( ) , a <0s

H s as

0

1a

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

Homework: Identify the filter type and determine the RC circuit.

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

Limitation of passive filters (RC filters): Fixed gain, Loading effect

Active filters ( )oV s

( )( )

o

i

V sV s

LP Filter

No loading effect

Gain control possible

( ) 1( ) 1

o

i

V sV s sRC

0

0

( )a

H ss

1RC0

0a 1

RC

0

0a

21

( ) 1iV sR

R sC

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

HP Filter

( )( )

o

i

V sV s

1

0

( )a s

H ss

( )( )

o

i

V sV s

1

sRCsRC

0 1

RC

1 1a 0

1a

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

1 2 1 2

1 2 1 2 1 2

( )( )

o

i

V s sR R C RV s sR R C C R R

( )( )

o

i

V sV s

1 2

01 2 1 2

R RR R C C

0

0a 01 1 2

1( )

aR C C

11

1 2

Ca

C C

1 0

0

( )a s a

H ss

1a

( |a0/a1| > 0 )

Electronic Circuits 2 (18/1) W.-Y. Choi

Lect. 22: First-Order Filters

V

V

11iV

sRC

2i oV V

1 11 2 2

oi

VV

sRC

11

o

i

V sRCV sRC

2 ( 1)2( 1) 2

oi

VsRCVsRC

1

1

sRC

sRC

11

sRCsRC

01

0

( )s

H s as

1( ) 1

1( ) 2o

i

sV s RCV s s

RC

11iV

sRC

01

RC

112

a

01

RC

1 1a