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EMLAB Chapter 8. Microwave Filters 1

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Page 1: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Chapter 8. Microwave Filters

1

Page 2: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Common filter responses

Low-pass filterHigh-pass filter

Band-pass filter Band-reject filter

Passive filter 2

Page 3: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Lumped element filter synthesis

1|||| 221

211 SS

2221 |)(||)(| HS

21111

*1111

211 |)(|1)()()()(|)(| HSSSSS

)(1

)(1)(

11

110

S

SZZin

Filter

H(s)

Filter

H(s)

+Vout

-

SR

LR+

Vin-

: conservation of energy

3

Page 4: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Example #1- 1st order low pass filter

2

1

2

1

22

1

1)(

p

V

VH

2

1

2

121111

1

|)(|1)()(

p

pHSS

1

111

1)(

pjpj

S

1p 1p

Pole 의 부호는 (–) 인 것을 선택한다(+) 인 것은 physically unrealizable

010

10

11

110

11

110

21

1,

21

1

1

)(1

)(1

Zpj

Z

p

jZ

pj

pj

pj

pj

ZS

SZZin

4

Page 5: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

V_ACSRC1

LL1

2V

1V

1

02

p

ZL

pF63.7

nH159

MHz10021

C

L

p

m1freq=dB(S(2,1))=-3.000

99.85MHz

1E6

1E7

1E8

1E9

1E10

1E5

2E10

-20

-15

-10

-5

-25

0

freq, Hz

dB(S

(2,1

))

Readout

m1

01

2

ZpC

Circuit realization

CC1

V_ACSRC1

0Z

0Z

5

Page 6: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Example #2 – 3rd order Butterworth filter

6

1

6

1

2

1

22

1

1

1

1)(

ps

p

V

VsH

6

1

6

121111

1

|)(|1)()(

ps

ps

sHsSsS

122

)(

1

2

1

3

1

3

1

3/4

11

3/2

1

3

111

ps

ps

ps

ps

eps

eps

eps

ps

sSjjj

1p 1p

1222

122

,

122

1222

122

122

)(1

)(1

1

2

1

3

1

1

2

1

1

2

1

1

2

1

3

13

11

2

1

3

1

3

11

2

1

3

1

11

11

0

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

ps

S

S

Z

Zin

1

12

1

1,

1

12

1

1

1

1

1

1

10

psp

sps

psp

sp

s

Z

Zin

6

Page 7: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

1

0

p

Z

01

2

Zp

1

0

p

Z

0Z

0Z

01

1

Zp

1

02

p

Z

01

1

Zp 0Z

0Z

pF8.31 pF8.31

nH159

m1freq=dB(S(2,1))=-2.873

99.85MHz

1E6

1E7

1E8

1E9

1E10

1E5

2E10

-70

-60

-50

-40

-30

-20

-10

-80

0

freq, Hz

dB(S

(2,1

))

99.85M-2.873

m1

pF7.63

nH6.79

nH6.79

Example #2 – 3rd order Butterworth filter 7

Page 8: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Low pass filter proto-types : Ladder type

1,1 01 Zp 로 정한 필터

Value of n

g1 g2 g3 g4 g5 g6 g7

1 2.000 1.000

2 1.414 1.414 1.000

3 1.000 2.000 1.000 1.000

4 0.7654 1.848 1.848 0.7654 1.000

5 0.6180 1.618 2.000 1.618 0.618 1.000

6 0.5176 1.414 1.932 1.932 1.414 0.5176 1.000

NNsV

VsH

22

2

1

22

1

1

1

1)(

Butterworth filter

8

Page 9: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Filter transformation1. Impedance transformation

000 1 RZZ

00

Inductor.

LRLsLRZsLZ

a

0

01

Capacitor.

R

CC

sC

RZ

sCZ

b

2. Frequency transformation

]/[frequency offcut ]/[1frequency offcut sradsrad c

cc

LLL

sZsLZ

a

Inductor.

c

c

CC

Cs

ZsC

Z

b

11

Capacitor. dB0

21S

dB3 10log

]/[1 sraddB0

21S

dB3 10log

]/[ sradC

FilterFilter

1

1

FilterFilter

0R

0R

9

Page 10: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Microstrip realization – Stepped impedance filter

Example 8.6

10

Page 11: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

lYlZ

B

lZl

ZX

00

00

sin1

2

1

2tan

2

10 Z

10 Z

,0Z

lljY

ljZl

DC

BA

cossin

sincos

0

0

l

1Z

3Z

2Z

CZZ

C

DZZZ

C

AZZZ

1

1

1

123

12222

12111

00

03

02

01

1,

sin

12

tan

2tan

ZY

ljYZ

ljZZ

ljZZ

1l

Transmission line → T- network 11

Page 12: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Chevyshev filter

)(1

1)(

22

2

1

22

NTV

VsH

)()(2)(

34)(

12)(

)(

21

33

22

1

xTxxTxT

xxxT

xxT

xxT

nnn

12

Page 13: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

ssH

1

1)(

LPF-to-HPF transformation

dB0

y

dB3

dB/dec20

111

1)'(

s

s

s

sH

dB0

y

dB/dec20

치환로 '

1

ss

10log

1c

LPF→HPF

. 1 지점임되는이s. 1 지점임되는이s

1c

dB3

13

Page 14: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

RR1

V_ACSRC1

LL1

RR2

CC1

LPF→HPF

치환로 '

1

ss

Lss

LsL

1'

1

'1

1 LL1

11

1

LC

LsC

s

sC'

'1

CC1

LL1

CC1

RR2

V_ACSRC1

RR1

CC1

RR2

V_ACSRC1

RR1

11

1

CL

RR1

LL1R=

RR2

V_ACSRC1

14

Page 15: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

ssH

1

1)(

dB0

y

dB3

dB/dec20

''

1

1)'(

0

0

0

ss

BW

sH

dB0

y

dB3

dB/dec20

치환로 '

' 0

0

0

s

s

BWs

10log

LPF→BPF

지점되는이 1'

' 0

0

0

s

s

BWs

jBW

j

BWj

BWj

j

j

BW

js

12

2

2122

20

20

220

2

0

0

20

2

1

'

dB/dec20

2' 1'

LPF-to-BPF transformation

1c

frequencyCenter;210

js js 1j2j

15

Page 16: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

120

10

0

011

'

1'

'

'

LBW

s

sBW

L

s

s

BWLsL

LL1

'1

'

1

''

111200

0

0

sBW

Cs

BWC

ss

BW

CsC

치환로 '

' 0

0

0

s

s

BWs

LL1

CC1

CC1

RR1

V_ACSRC1

LL1

RR2 V_AC

SRC1

RR2R=50 Ohm

CC1

LL1

RR1

CC1

RR2

V_ACSRC1

RR1

CC1

LL1 R

R2V_ACSRC1

RR1

16

Page 17: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

ssH

1

1)(

dB0

y

dB3

dB/dec20

''

11

1)'(

0

0

0

ss

BW

sH

dB0

y

dB3

dB/dec20

치환로

''

1

0

0

0

ss

BW

s

10log010log

LPF→BPF

dB/dec20

LPF-to-BRF transformation

1c

2' 1'

지점되는이 1'

' 0

0

0

s

s

BWs

jBW

j

BWj

BWj

j

j

BW

js

12

2

2122

20

20

220

2

0

0

20

2

1

'

frequencyCenter;210

js js 1j 2j

17

Page 18: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

'1

'1

1

''

1

1

20

1

0

0

0

11

sBWLs

BWLss

BW

LsL

LL1

'

1'

1

'

'11 200

0

0

sCBWs

CBWs

s

BWCsC

치환로

''

1

0

0

0

ss

BW

s

LL1

CC1

CC1

RR1

V_ACSRC1

LL1

RR2

CC1

RR2

V_ACSRC1

RR1

CC1

LL1

RR2

V_ACSRC1

RR1

RR2

RR1

CC1

LL1

V_ACSRC1

18

Page 19: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Real capacitor characteristics

유효 영역

19

Page 20: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Real inductor characteristics

유효 영역

20

Page 21: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

8.5 Filter implementation

LjjZ )( ljLjZ tan)(

p

ll

tantan

Richard’s transformation

8

1tan 1

l

l때일

CjjZ

1

)( ljY

jZtan

1)(

0

21

Page 22: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Kuroda’s identities

22

Page 23: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Figure 8.36a (p. 409)Filter design procedure for Example 8.5. (a) Lumped-element low-pass filter prototype. (b) Using Richard’s transformations to convert inductors and capacitors to series and shunt stubs. (c) Adding unit elements at ends of filter.

Example 8.523

Page 24: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Figure 8.36b (p. 410)(d) Applying the second Kuroda identity. (e) After impedance and frequency scaling. (f) Microstrip fabrication of final filter.

24

Page 25: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Figure 8.37 (p. 411)Amplitude responses of lumped-element and distributed-element low-pas filter of Example 8.5.

25

Page 26: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Figure 8.38a/b (p. 412)Impedance and admittance inverters. (a) Operation of impedance and admittance inverters. (b) Implementation as quarter-wave transformers.

Impedance and admittance inverter 26

Page 27: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

1

1

aC

g1aC

1g

2g

3g

1

10 g

1

1

aC

g2g1

3

3

aC

g3aC

3

3

aC

g1

LZ

1g

K

21

K

g KLZ

inZ inZ

L

L

in Zsg

KZ

Ksg

KZ

1

221

2

1

121

aCK

g

Low pass filter using admittance inverter

LZLin Z

KZ

2

K

C 값이 여러 가지이므로 제작하기 어려움 .하나의 C 값으로 통일 .

L, C 가 모두 필요하므로 제작하기 어려움 . L 을 제거 .

27

Page 28: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

LZ

2g2K

2aC2K

LZinZ inZ

La

La

La

in

ZK

sCK

K

ZKK

sCK

K

ZKK

sC

KK

Z21

222

21

22

21

222

21

21

21

2

22

21

1

aCK

L

2

1K 1K

L

in

Zsg

Z1

1

2

L

in

Zsg

Z1

1

2

2

221 ,1

aC

gKK

2aCLZ1

2

2

aC

g

2

2

aC

g1

28

Page 29: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

1aC

1

1

aC

g

1aC 1

1

aC

g1

3

3

aC

g

3aC 3

3

aC

g1

2aC1

2

2

aC

g

2

2

aC

g1

1

1

aC

g

1aC 21

21

aa CC

gg1

3aC 3

3

aC

g1

2aC 32

32

aa CC

gg

1

1

aC

g

1aC 21

21

aa CC

gg1

3

3

aC

g1

32

32

aa CC

gg

1aC1aL 2aL 3aL

LPF→BPF

120

11

1

10

0

01

,

'

'

aa

aa

aa

C

BWL

BW

CC

Cs

s

BWsC

치환로

29

Page 30: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Band pass filter implementation using resonators30

Page 31: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

Admittance inverter equivalents 31

Page 32: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

2

21S

Resonator coupling & resonant freq. split 32

Page 33: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

)(

1,

)(

121

m

r

m

rCCLCCL

C

C

CCCCL

CC

LC

CCCCL

CCCCC

CCLCCL

m

mm

m

mm

mm

mm

rr

02

21

))((

))((

/1/1

)(

1

)(

1

2102,10

11

gg

BW

CKC

Cm

Inter-resonant coupling - 등가 회로 33

Page 34: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

2aC1

1

aC

g

1aC 21

21

aa CC

gg1

3

3

aC

g1

32

32

aa CC

gg

3aC1aL 2aL 3aL

eKC

2,1K1

1L eKL

C

Inter-resonator coupling

2102,10

11

gg

BW

CK

120

11

1 ,a

aa

a C

BWL

BW

CC

약하게 coupling 시킨다 .

34

Page 35: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

C

1eK 1L

eKC

L2eK 2

eK

102

0

3 221

g

BW

C

L

KQ

BW

e

dB

100

3 2

g

BWBW dB

External Q

동일한 간격의 gap

35

Page 36: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

2100

1

gg

BW

약하게 coupling 시킨다 .

Gap 을 변화시키면서 resonant freq. 의 차이가Proto-type 에 의해 정해진 값이 나오게 한다 .

m1freq=dB(S(1,2))=-13.401

140.0MHz

m2freq=dB(S(1,2))=-5.794

143.6MHz

139 140 141 142 143 144 145 146 147 148138 149

-60

-40

-20

0

-80

10

freq, MHz

dB(S

(1,2

))

Readout

m1

Readout

m2dB

(S(1

,1))

Example – Inter-resonator coupling 36

Page 37: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

m1freq=dB(S(2,1))=-2.963

142.4MHz

m2freq=dB(S(2,1))=-0.001

141.9MHzm1freq=dB(S(2,1))=-2.963

142.4MHz

m2freq=dB(S(2,1))=-0.001

141.9MHz

139 140 141 142 143 144 145 146 147 148138 149

-30

-20

-10

-40

0

freq, MHz

dB(S

(2,1

))

142.4M-2.963

m1

141.9M-513.7u

m2dB

(S(1

,1))

100

3 2

g

BWBW dB

동일한 간격의 gap

Gap 을 변화시키면서 3dB bandwidth 가 Proto-type 에 의해 정해진 값이 나오게한다 .

dBBW3

Example – External coupling 37

Page 38: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

f0 맞추기

Coupling

계수 구하기

Qex 구하기

Filter design by simulator38

Page 39: EMLAB Chapter 8. Microwave Filters 1. EMLAB Common filter responses Low-pass filter High-pass filter Band-pass filter Band-reject filter Passive filter

EMLAB

12-pole hair pin filter39