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High-Speed Circuits and Systems Laboratory Electronic Circuits 2 Lect. 14: Second-Order Passive Filters (S&S 12.5) 2nd-order filter 2 1 2 1 0 2 1 1 0 () aS aS a Ts S bS b + + = + + 2 2 1 0 2 2 0 0 () ( / ) as as a Ts s Qs ω ω + + = + + 2 1 2 1 2 ( )( ) ( )( ) a s z s z s p s p = If p 1 , p 2 are real, Consider T(s) with complex poles 2 0 1 2 0 , 1 (1 / 4 ) 2 p p j Q Q ω ω =− ± Depending on zero locations, various filter characteristics! (Q > ½) 2nd-order filters can be easily made by cascading two 1st-order filters

Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

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Page 1: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters (S&S 12.5)

2nd-order filter 2 1

2 1 02 1

1 0

( )a S a S a

T sS b S b

+ +=

+ +

22 1 0

2 20 0

( )( / )

a s a s aT s

s Q sω ω+ +

=+ +

2 1 2

1 2

( )( )( )( )

a s z s zs p s p

− −=

− −If p1, p2 are real,

Consider T(s) with complex poles

201 2 0, 1 (1 / 4 )

2p p j Q

ω= − ± −

Depending on zero locations, various filter characteristics!

(Q > ½)

2nd-order filters can be easily made by cascading two 1st-order filters

Page 2: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

Second-order filter pole-zero diagrams

Page 3: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

LP Filter

At ω=ω0, |T| = |a0/ω02| Q

Larger Q More peaking

Page 4: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

How to realize passive second-order LP filter

Use LCR

Two zeros at s infinity

Page 5: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

How to realize passive second-order LP filter

o

i

V( )

VT s ≡

2

1 /(1 / ) (1 / )

LCs s CR LC

=+ +

2

1 2

ZZ Z

=+

1

1 2

YY Y

=+

1/(1 / ) (1 / )

sLsL sC R

=+ +

01LC

ω = 0 1Q CRω

=0

CQ CR RL

ω= =

20

2 200s s

Q

ωω

ω=

+ +

Page 6: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

HP Filter

Page 7: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

Same pole characteristics as LP Same natural modes

o

i

V( )

VT s ≡ 2

1 2

ZZ Z

=+

1

1 2

YY Y

=+ (1 / ) (1 / )

sCsC R sL

=+ +

2

2 (1 / ) (1 / )s

s s CR LC=

+ +

Two zeros at s=0

Page 8: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

BP Filter

Large Q Sharper response

3dB bandwidth

Page 9: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

o 1

i 1 2

V 1/( )V (1/ ) (1 / )

Y RT sY Y R sC sL

= = =+ + +

2

(1 / )(1 / ) (1 / )

s RCs s RC LC

=+ +

0CQ CR RL

ω= =

Page 10: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

Band-Rejection or Notch Filter

Page 11: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

1 2

1

1 1

sL sLsCZs LCsL

sC

⋅= =

++

2o 2

2i 1 2

2

V (1 / )( )V (1 / ) (1 / )

1

Z R s LCT s sLZ Z s s RC LCRs LC

+= = = =

+ + +++

Page 12: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

Low-Pass Notch Filter

21

2

1 2 1 2

(1 / )( ) 1 1

( ) ( )

s LCT s

s sC C R L C C

+=

+ ++ +

Page 13: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

High-Pass Notch Filter

21

21 2

(1 / )( )

(1 / ) [1 /( ) ]s L C

T ss s CR L L C

+=

+ +

Page 14: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

Page 15: Lect. 14: Second-Order Passive Filters (S&S 12.5)tera.yonsei.ac.kr/class/2006_1/lecture/Lect 14 Second...Electronic Circuits 2 High-Speed Circuits and Systems Laboratory Lect. 14:

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 14: Second-Order Passive Filters

2 20 0 0

2 2 2 20 0 0 0

( / ) 2( / )( ) 1

( / ) ( / )s s Q s Q

T ss s Q s s Q

ω ω ωω ω ω ω

− += = −

+ + + +

02 2

0 0

( / )122 ( / )

s Qs s Q

ωω ω

⎛ ⎞= −⎜ ⎟+ +⎝ ⎠