Power Dividers & Couplers - 國立中興大學web.nchu.edu.tw/~ycchiang/MicroWave/Microwave_07.pdf · 2013-09-24 · Poweowe v de s & ect o a Coup e sr Dividers & Directional Couplers

Power Dividers & Couplers

1

Power Dividers & Directional Couplersowe v de s & ect o a Coup e s

Figure 7.1 (p. 309)Power division and combining (a) Power division (b) Power combining

• Passive microwave components for power division or power combining

Power division and combining. (a) Power division. (b) Power combining.

• Three-port networks: T-junctions and other power dividers (3dB or unequal)Four-port networks: directional couplers (arbitrary) and hybrids (equal)H b id j i i h h hif (90o 180o)• Hybrid junctions with phase shift (90o or 180o)

2

3-Port Networks (T-Junctions)3 o t Netwo s ( Ju ct o s)

SSS 131211

:networkport -3for matrix Scattering

unitary,

:lossless also isit If S

SSSSSSS

333231

232221

,1

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12

213

212

SS

SS

ijji SSS symmetric ,reciprocal:materials canisotropi no and passive isit If

0

,1

,2

232

13

2312

SS

SS

• 3-port network cannot be lossless,reciprocal, and matched at all ports. 0

,0

,0

1223

2313

SS

SS

SS

one of 3 conditions (lossless,reciprocal matched) need be

0:0 matched, are ports all If

1312 SSSii

.01312 SS

reciprocal, matched) need berelaxed, then a physicallyrealizable device is possible.

0

0

2313

2312

SSSSS

3


• Nonreciprocal, lossless matchednetwork: (Circulator)

,0

:solutions possible Two

312312 SSS

00

2321

1312

SSSS

S

,0

,1,

133221

133221

312312

SSS

SSS

03231 SS

unitary, :lossless isit If S .1

,or

312312

133221

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21

213

212

SS

SS

,0

,1

3231

232

231

SS

SS

.0

,0

,0

1312

2321

3231

SS

SS

SS

Figure 7.2 (p. 310) The two types of circulators and their [S] matrices.(The phase references for the ports are arbitrary.) (a) Clockwise circulation. (b) C t l k i i l ti

4

1312 (b) Counterclockwise circulation.


• Lossless and reciprocal networks:only two ports are realizably matched 0

:solution Possible SSSS

2312

1312

00

SSSS

S1

0

3313

23132313

SS

SSSS

332313 SSS

unitary, :lossless isit If S

,1

,12

232

12

213

212

SS

SS

,0

,1

2313

233

223

213

SS

SSS

.0

,0

,0

13331223

33231312

2313

SSSS

SSSS

SS

Figure 7.3 (p. 311) A reciprocal, lossless three-port network matched at ports 1 and 2

5

13331223 network matched at ports 1 and 2.

4-Port Networks (Directional Couplers)o t Netwo s ( ect o a Coup e s)

:networkport-4 matched reciprocal a

23341214

34142312

(7.12b) .0

(7.12a) ,0

SSSS

SSSS

00

242312

141312

SSSSSS

S 234

21223

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23341214

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:(7.12b)(7.12a)( )

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coupler ldirectiona 0SS

(7 10a)0equations 10

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S

224

212

213

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1

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:(7 10b)(7 10a)

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22

234

213

2412

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1

1

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:(7.10b)(7.10a)2

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3424

,

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6


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3412 SS

,0 :Coupler ricalAntisymmet The 2.

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0000

00

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2Coupler lSymmetrica The .1

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3

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log20log10(dB)Coupling

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PPC

000000

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1

144

3

log20log10(dB)Isolation

log20log10(dB)y Directivit

SDCPI

SPD

122

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2

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log20log10(dB)Isolation

PPT

SDCP

I

7

1P


010:Couplers Hybrid The

j

100

0012

1j

jj

S

010 j

0110hybrid) race-rat(or

:hybrid T-magic The

10011001

0110

21S

Figure 7.4 (p. 313) Two commonly used symbols for directional couplers and power flow conventions

011010012

8

couplers, and power flow conventions.


• Measuring Coupler DirectivitydB35 dB,20 hascoupler A DC

dB 50but dB, 55dB 30 having load awith

,p

CRLCD

RL

fli lthiDh

CDC

0

eVV j

i

lti lthiChC2 PP ic 110Dy directivit the

of valuenumerical theis D where

320dB

VVD

110Cfactor coupling

voltagenumerical theis C where

320dB

VVC

4V

9

1V


• Measuring Coupler Directivity

PPM c

D1D

2

Pm

P

D1

D12

max

max

mM

Pm

2D

D1min

:powersoutputmaximumandminimumThe

mM

1 thatrequires method This

1D

2

min CDC

:powersoutput maximum and minimum The

iPP

DRL dB,in or, D1

2

max CDC

iPP ,editors, Fox, J. andSucher M. :

ents Measureme Microwavof HandbookReference

10

1963 York, New Press, cPolytechni II, vol3ed,

The T-Junction Power Dividere Ju ct o owe v de

Figure 7.5 (p. 315) Various T-junction power dividers. (a) E plane waveguide T. (b) H plane waveguide T (c) Microstrip T junction

11

waveguide T. (c) Microstrip T-junction.


• Lossless Divider2:1: , 50

DividerPower junction -T The 7.1Ex

210 PPZ

1:2

0in

VP

Solution

32

21

31

21

2

in

20

2in

20

1

0in

PZVPP

ZVP

Z

752

3 1503

3232

0201

21

ZZZZ

ZZ

practicalnotis0

111 021

in

BjZZZ

BjY

666015075||50 50150||75

2in

Z

ports mismatchedith divider w losslessrange within added becan

practicalnot is 0

fBj

Bj

333.075150||5075150||50

666.015075||50

2

1

12

p 75150||50


• Resistive Divider1

00

01 3

2323

32 VZZ

ZVV

100

032

00

21

43

3

3323

VVZZ

ZVVV

ZZ

233121 dB 6 21SSS

011101110

21S

4 00

0 ZZZZ

21

in 21

011

ZVP

03

23

33

332211000

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in

0

21

0

21

32

0

41

812/1

21

2

PZV

ZVPP

Z

13

33 00

The Wilkinson Power Dividere W so owe v de

Figure 7.8 (p. 319) The Wilkinson power divider. (a) An equal-split Wilkinson power divider in microstrip form (b) Equivalent transmission line circuitmicrostrip form. (b) Equivalent transmission line circuit.

dividerport -3 isolation good and matched Lossy,

14


• Even-Odd Mode Analysis

Figure 7.9 (p. 319)

15

The Wilkinson power divider circuit in normalized and symmetric form.



7 8Figure22 rZ

2:excitation modeEven

7.8 Figure2 ,2

032 VVV

rZ

gg

2:excitation mode Odd

032

032

VVV gg

gg

0 ,4:ionSuperpositBy

302 VVV gg

gg

parameters S

Figure 7.10 (p. 320) Bisection of the circuit of Figure 7.9. (a) Even-mode excitation. (b) Odd d it ti

16

(b) Odd-mode excitation.


2:excitation modeEven

032 VVV gg 2

:excitation mode Odd

032

VV

VVVoo

gg

7.10(a) Figure as replaced O.C.2/hru current t no ,

22;

32 rVV ee

line. /4 intoseen O.C.7.10(b) Figure as replaced Ground

32

VV

1imatched,2 If

2

2;

22 ;in

ZVVZ

ZZ

ee

e

121:Finding

0 and ,2 If2

11

102

ZS

VVVr

i

oo

14/

1 since

2 ;in02

VVjVVeeVxV

ZVV

e

xjxj

ee

matched32,ports01port at 10

122

: Finding

3322

11

11

SSZS

ZS

in

in

11 10

1 4/

01

02

VjVVV

VVjVV

e

yreciprocit toduesymmetry 2

matched 3 2,ports0

22

112112

3322

j

jVVVVSS

SS

oe

oe

2 2222

01 VjV e

at C. O.or S.C. todue0

3 and 2 ports ofsymmetry 2

3223

3113

SS

jSS

17

bisection


Figure 7.11 (p. 321)g (p )Analysis of the Wilkinson divider to find S11. (a) The terminated Wilkinson divider. (b) Bisection of the circuit in (a).

18


• Example 7.2Split-equalan Design

frequency at 50 afor dividerpower Wilkingson

0f

7.702 0ZZ

Solution

1002 0ZR

Figure 7.12 (p. 322) Frequency response of an equal-split Wilkinson power divider. Port 1 is the input port; ports 2 and 3

h

19

are the output ports.


• Unequal Power Division and N-Way Wilkinson Dividers

Figure 7.13 (p. 322) A Wilkinson power divider in microstrip formpower divider in microstrip form having unequal power division.

PPK If 232

Figure 7 14 (p 323) An N way

K

KZZ 1 3

2

003

Figure 7.14 (p. 323) An N-way, equal-split Wilkinson power divider.Figure 7.15 (p. 324) Photograph of a four way corporate power divider network

KZR

KKZZKZ

1

)1(

0

2003

202

four-way corporate power divider network using three microstrip Wilkinson power dividers. Note the isolation chip resistors. Courtesy of M.D. Abouzahra, MIT

20

K

KZR 0 Lincoln Laboratory.

The Quadrature (90o) Hybride Quad atu e (90 ) yb d

• Branch-line Hybrid

010 j

001100010

21

jj

j

S

Figure 7.21 (p. 333) Geometry of a branch-line coupler.

010 j


Figure 7.22 (p. 334)Circuit of the branch-line hybrid coupler in a normalized form

21

coupler in a normalized form.


22

Figure 7.23 (p. 334) Decomposition of the branch-line coupler into even- and odd-mode excitations.(a) Even mode (e). (b) Odd mode (o).


B oe ,21

21

1

TTB oe

11

,21

21

2 jj

jjDCBADCBA

e

0211211

B

TTB oe

,11

,21

21

4

3

j

jjDCBATe

1

21

21122

jjBA

T

B

ee

oe

11012001

: and Solving

,224

jj

jjj

jDCBA

e

ShuntTrans4/Shunt

11

21

101

02

20 101

jYjY line

Shunt Trans. 4/Shunt

23


11

: and solving Similarly,

jBAToo

012

jDC

o

o

t h di1t0

12

1

B

jTo

o2

1

shift phase 90 power,-half2

matched is 1port 0

jB

B

4

o3

4port power to no0

shift phase 180 power,-half2

1

B

BFigure 7.24 (p. 336) Photograph of a microstrip quadrature hybrid prototype

oo

4

20~10by lengthened armsshunt :effectsity Discontinuonmultisecti 20%~10 :BWlengthbranch 4/

pp

microstrip quadrature hybrid prototype. Courtesy of M.D. Abouzabra,MIT Lincoln Laboratory.

24


• Example 7.5 line-branch 50 aDesign

parameter S plot the andjunction, hybrid quadrature

.1.5 to0.5 from magnitudes

0

0

S l tif

f

@4/:lengthbranch The

f

Solution

35 450:impedancesbranch The

@ 4/

0

0

Z

f

Figure 7.25 (p. 337) S parameter magnitudes versus frequency for the branch line coupler of Example 7 5

35.422

0

25

the branch-line coupler of Example 7.5


Figure The transformation of admittance through even and oddadmittance through even- and odd-mode two-port networks.

26


Figure The transformation of admittance at 0.9f0.

27

Coupled Line Directional CouplersCoup ed e ect o a Coup e s

Figure 7.26 (p. 337) Various coupled transmission line geometries. (a) Coupled stripline (planar, or edge-coupled). (b) Coupled stripline (stacked, or broadside-coupled). (c) Coupled microstrip.

28


• Coupled Line Theory Assume TEM propagation

(a)

Figure 7.27 (p. 337)A three-wire coupled (b)A three-wire coupled transmission line and its equivalent capacitance network

Figure 7.28 (p. 338) Even- and odd-mode excitations for a coupled line, and the resulting equivalent capacitance networks. ( ) E d i i (b) Odd d i i

( )

29

network. (a) Even-mode excitation. (b) Odd-mode excitation.


• Coupled Line Theory Example 7.6Symmetry 2211 CC stripline, coupled broadside For the

circuitedopen y effectivel ::

12CModeEven . and

WSolution

bWSW

10

2211

LCLZ

CCC

ee

e

Fd/m 2

Fd/m

011

2211

bWC

CCdWC

r

WSbZ e 200

22:

0

CCCCCModeOdd

CvCC epeee

Fd/m 012

11

SWC

Sbr

W

Z

W

o

r

112

12

00

1

22

0

12221211

CvZ

CCCCC

o

o

11

Fd/m 2 011

SbWCC r

e

SSb

W r2

static-quasinumerical,:linesTEM-quasimapping conformal :lines TEM

:C

Cv op Fd/m 11 22 01211

SSbWCCC ro

30

staticquasi numerical, :lines TEMquasi


31


32


2 20inin

oe ZZZZZ

11

11

1

1in

M dEIIVV

IVZ oe

oe

let weIf

22

000

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0inin0in

oe

oe

ZZZ

ZZZZZZZZ

24312431

tan , , ,

:

jZZVVVVIIII

ModeEveneeeeeeee

tantan

00

000in

000

oe

eoe

e

oe

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ZZ

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tan

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ee

e

e

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e

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00

000in

00

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o

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ZZ

j

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0

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:

,

ModeOddZZ

VIZZ

ZVV ee1e

e1

inin

010in

00

oeoeoe

eo

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000i

24312431

tan , , ,

jZZZZ

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oo

oooooooo

tan 00in

0in

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in011333

ee

oeoeoe

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ZZZZVVVVVV

0in0

000in

,

tan

ZZVI

ZZZVV

jZZZZ

oo1o

oo

1

oo

tan

tan2

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000

00

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oo

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ee

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33

0in0in0 ZZZZ o1o1 tan2 0000in oe

o ZZjZZZ


000

0003 tan2

tan ZZjZ

ZZjVVoe

oe

00

00

2ZZZZZC

oe

oe

00

02

tan

21

CjVV

ZZZC

oe

22444

203

0tan1VVVVV

jCjVV

oeoe

Figure 7.33 (p. 344) Coupled and through port voltages (squared) versus frequency for the coupled line coupler of

2

2

0222

22444

sincos11

jCCVVVV oe

(squared) versus frequency for the coupled line coupler of Figure 7.31.

223 1

:long 4 ,2For

CjVCV

j

CCZZ

CCZZ oe

11

11

0000

3400

1 , CjV

CV


• Example 7.7coupledsection -single dB 20 aDesign

thi kil2fd t05.0tan GHz, 3 , 50 ,2.2

cm,32.0 stripline.in coupler line

00

fZb

r

0 110

s. thicknesmil2 of conductorscopper

20/20 CSolution

55.2811

0.110

00

CCZZ

C

e

23.45111

00

CCZZ

C

o

306.0/ ,809.0/1.67 ,0.82 00

bSbWZZ orer

35

cm 098.0 cm, 259.0 SW

The Lange Couplere a ge Coup e

Figure 7.38 (p. 349) The Lange coupler. (a) Layout in microstrip form. (b) The unfolded Lange coupler.

36


Figure 7.39 (p. 350) Equivalent circuits for the unfolded Lange coupler. (a) Four wire coupled line model (b) Approximate two wire coupled line model

37

(a) Four-wire coupled line model. (b) Approximate two-wire coupled line model.


Figure 7.40 (p. 350) Effective capacitance networks for the unfolded Lange coupler equivalent circuits of Figure 7.39. (a) Effective capacitance for the four-wire model. (b) Effective capacitance for the two-wire modelfor the two-wire model.

C:asedapproximatbecan

and different, are linesfour theof inex4

inex4

6 mo

e

CCCCCCC

m

m

CCCCCC

ex

exexin

:as edapproximat becan

44

44

inex4

1 ,1

opo

epe

mo

CvZ

CvZ

38


mo

e

CCCCC

ex

ex

2

0000

20000

440 33 ZZZZZZZZZZZ

oeeo

oeoeoe

oeee

CCCC 43

20

2044

0000

3 ZZZZC oeoe

oeeo

eooo

oee

CCCCCC

CC

4

4

3

0020

20

00

44

44

23 ZZZZZZC

oeoe

oe

oe

oe

eo

oe

ZZZZ

CC

00

0

2

0 1128934 Z

CCCCCZ e

eo

eeo

eoe

ZZZZ

ZZZ

Z

00

000

004 3

0

2

0 1128934 Z

CCCCCZ o

ooe

o ZZZ

Z 000

4 3

39

The 180o Hybride 80 yb d

10010110

j

011010012

jS

Figure 7.41 (p. 352)Symbol for a 180° hybrid junction.

Figure 7.42 (p. 353)Photograph of a microstrip ring hybrid.

Courtesy of M. D. Abouzahra, MIT Lincoln Laboratory

40


Figure 7.43 (p. 353) Hybrid junctions. (a) A ring hybrid, or rate-race, in microstrip or stripline form. (b) A tapered coupled , p p ( ) p pline hybrid. (c) A waveguide hybrid junction, or magic-T.

41


42


43


,21

21

1port at waveIncident

1B oe

,2

j

je

,21

21

4port at waveIncident

1 TTB oe

,2

j

je

,21

21

,22

2

1

TTB oe

oe

,2

j

jTe

,21

21

,22

2

1

B oe

oe

,2

j

jTe

11

,21

21

3B oe

,2

jT

jo

11

,21

21

3 TTB oe

,2

jT

jo

: and Solving

,21

21

4

T

ΤΤB

ee

oe,0

,2

1

jB

To

: and Solving

.21

21

4

T

B

ee

oe,0

,2

1

jB

To

1221

g

jj

DCBA

e

ee

,22

j

jB

1221

g

jj

DCBA

e

ee

,22

j

jB

1221

jj

DCBA

j

o

e

.0

,2

4

3

B

jB

1221

jj

DCBA

j

o

e

.0

,2

4

3

B

jB

44

jo jo


• Example 7.9 afor hybrid ring180 aDesign o

parameters theof magnitude the

plot and impedance, system 50ygg

S.1.5 to0.5 from )( 001

Solution

ffS j

:linesion transmisring theof 7.43a, Figure toreferenceWith

0Z

70.72 0Z

Figure 7.46 (p. 357) S parameter magnitudes versus frequency for the ring hybrid of Example 7.9

45

Documents

Power Dividers & Couplers - 國立中興大學web.nchu.edu.tw/~ycchiang/MicroWave/Microwave_07.pdf · 2013-09-24 · Poweowe v de s & ect o a Coup e sr Dividers & Directional Couplers