Lecture #4 Contentseee.guc.edu.eg/Courses/Communications/COMM603 Radio... · GUC (Dr. Hany Hammad)...

GUC (Dr. Hany Hammad) 2/14/2016

COMM (603) Lecture #3 1

© Dr. Hany Hammad, German University in Cairo

Lecture #4 Contents

• Three Port

• T-Junction Power Dividers.

• Resistive Dividers.

• The Wilkinson Power Divider.

• Four Port

• Branch Line Coupler.

• The Rate Race Ring

© Dr. Hany Hammad, German University in Cairo © Dr. Hany Hammad, German University in Cairo

Power Dividers (3 ports)

• T-junction.

• Resistive Dividers.

• The Wilkinson Power Divider.




The T-Junction Power Divider

All junctions are lossless (in absence of transmission line loss).

Microstrip T-junction (Layout)

Lossless T-junction Model (Transmission Line Model)

Model the discontinuity (fringing fields & Higher Modes)

021

111

ZZZjBYin If

021

111

ZZZYin 0B Then

50oZ 1001 Z

1002 Z

Quarter Wavelength matching sections can be used to convert back to 50 .

Microwave Engineering, 3rd Edition by David M. Pozar

Copyright © 2004 John Wiley & Sons


The T-Junction Power Divider

Summer 2007 Internship

http://www.facebook.com/photo.php?pid=1129771&id=736435197




Resistive Dividers

Z

inZ

0332211 SSS

1

00

01

3

2

323

32V

ZZ

ZVV

1

00

032

2

1

4

3

3VV

ZZ

ZVVV

011

101

110

2

1S

2

1233121 SSS dB 6

o

inZ

VP

2

1

2

1

in

oo

PZ

V

Z

VPP

4

1

8

1

2

1 2

1

2

121

32 Half the supplied power is dissipated in the resistors

inZ oZ

3

4

3

000

ZZZ

0000

3

2

323Z

ZZZZ




The Wilkinson Power Divider

• Lossless T-Junctions dividers suffers from the problem of not being matched at all ports + no isolation between output ports.

• Resistive divider can be matched at all ports but not lossless + no isolation between output ports.

• Wilkinson achieve matching at all ports + isolation between output ports (it is a lossy three port-network).

“Layout”

“TL Model”






Even-Odd Mode Analysis

Even Mode Analysis

Odd Mode Analysis

ogg VVV 232

ogg VVV 232

By Superposition

og VV 42

03 gV

Normalized

Symmetrical

Find Z and r to achieve the Matching Conditions?

Port 1

Port 2

Port 3




Even Mode Analysis

No Current Flow because same potential

ljZZ

ljZZZZ

L

Le

in

tan

tan

0

00

ZZ 0 2LZ

24

2

l

e

inZ

2

22

0 Z

Z

ZZ

L

e

in

If 2Z(Quarter Wavelength

Transformer)

1e

inZ (Matched)

00

22

2

2V

VVV se (Voltage Divider)

0x 4x

xjxj eeVxV )(

x

1

11)0( 01

jVVVV e

22

22

0

0

ZZ

ZZ

L

L

021)4

( VVjVjjVV e

1

0VjV

201 jVV e

ogg VVV 232

Finding eV1

Finding e

inZ






Odd Mode Analysis

ogg VVV 232 0

3

0

2 VV (Voltage Null in Center “Symmetry”)

ljZZ

ljZZZZ

L

Lin

tan

tan

0

00

0

)

4tan(

tan0

tan00

0

00

jZ

lZ

ljZZZin

(Open Circuit)

2

rZ o

in

inZ o

inZ

If 2r 1o

inZ

02 VV o

01 oV

(Voltage Divider)

(Non-going to port 1)

Finding o

inZ

Finding oV1




Input impedance port 1

Symmetry

ljZZ

ljZZZZ

L

Lin

tan

tan

0

00

20 Z

2

1

222

0 L

inZ

ZZ

24

2

l

1inZ

Finding inZ






The Wilkinson Power Divider

Summary:

011 S

03322 SS

(Zin=1 at port 1)

(Ports 2 and 3 matched for even and odd modes)

222

112112

j

VV

VVSS

oe

oe

(Symmetry due to reciprocity)

23113

jSS

(Symmetry of port 2 & 3)

03223 SS (Due to short or open at bisection)

When the divider is driven at port 1 and the outputs are matched, no power is dissipated in the resistors. Thus the divider is lossless when the outputs are matched; only reflected power from ports 2 and 3 is dissipated in the resistor. Since S23=S32=0, ports 2 and 3 are isolated.

001

001

110

2

jS


N-Way equal-split Wilkinson Divider

Fabrication problems for N 3 Microwave Engineering, 3rd Edition

by David M. Pozar Copyright © 2004 John Wiley & Sons




Four-way Corporate Power Divider




Couplers (4 ports)

• The Quadrature (90o) Hybrid (Branch Line Coupler)

• The 180o Hybrid (The rat race ring).




The Quadrature (90o) Hybrid (Branch Line Coupler)

010

001

100

010

2

1

j

j

j

j

S

Normalized Model Microwave Engineering, 3rd Edition

by David M. Pozar Copyright © 2004 John Wiley & Sons



oeB 2

1

2

11

Even

O

dd

oe TTB2

1

2

12

oe TTB2

1

2

13

oeB 2

1

2

14

Even Reflection Coefficient

Odd Reflection Coefficient

Even Transmission Coefficient

Odd Transmission Coefficient

Bi is the amplitude of

the wave emerging from port i







1

1

2

1

1

01

02

20

1

01

j

j

jj

j

jDC

BA

e

1

01

1

01

jY

jZ

lj

ljZZ

ljZZ

ZZY

ooL

Lo

oinoc

tan

tan

tan11

Op

en

Sh

un

t S

tub

14

tantan

l

1oZ

02

20

cossin

sincos

j

j

lljY

ljZl

o

o

48

2

l

TL

Secti

on

24

2

l

2

1oZ

Even

Mo

de





0211

21111

jj

jj

DCZZBA

DCZZBAS

oo

ooe

j

jjDCZZBAST

oo

e

12

1

211

2221





jljZljZZ

ljZZ

ZZY

ooL

Lo

oinoc

tan

11

tan

tan11

1

01

1

01

jYSh

ort

Sh

un

t S

tub

T

L

Secti

on

Od

d M

od

e

02

20

cossin

sincos

j

j

lljY

ljZl

o

o

1

1

2

1

1

01

02

20

1

01

j

j

jj

j

jDC

BA

o





0211

21111

jj

jj

DCZZBA

DCZZBAS

oo

ooo

j

jjDCZZBAST

oo

o

12

1

211

2221

02

1

2

11 oeB

22

1

2

12

jTTB oe

2

1

2

1

2

13 oe TTB

02

1

2

14 oeB

(port 1 is matched)

(half-power, -90o phase shift from port 1 to 2)

(half-power, -180o phase shift from port 1 to 3)

(no power to port 4)





(Input)

(Isolated)

(Output)

(Output)

01 B2

2

jB

2

13 B03 B










The 180o Hybrid

0110

1001

1001

0110

2][

jS

If input at port (1)

Amplitude will equally split at port (2) & (3) with same phase & Port (4) is isolated.

If input at port (4)

Amplitude will equally split at port (2) & (3) with 180o phase difference & Port (1) is isolated.

If input at ports (2) & (3)

The summation () will be at port (1). The difference () will be at port (4).

Div

ider

Co

mb

iner

(Ring Hybrid or “Rate Race Ring”)




The Rat Race Ring (Input port @ 1)

Even

O

dd

oeB 2

1

2

11

oe TTB2

1

2

12 oe TTB

2

1

2

14

oeB 2

1

2

13







1

01

1

01

1 jYoc2

tan1

j

Z

ljY

o

oc

Op

en

Sh

un

t S

tub

02

20

cossin

sincos

jlljY

ljZl

o

o

48

2

l

TL

Secti

on

24

2

l

Even

Mo

de

2

tan2

j

Z

ljY

o

oc

4

3

8

32

l

1

01

1

01

2 jYoc

12

21

12

01

02

20

12

01

j

j

jjjDC

BA

e





12

01

1

01

1 jYoc2tan

1

j

lZ

jY

o

oc

Sh

ort

Sh

un

t S

tub

02

20

cossin

sincos

jlljY

ljZl

o

o

48

2

l

TL

Secti

on

24

2

l

Od

d M

od

e

2tan2

j

lZ

jY

o

oc

4

3

8

32

l

12

01

1

01

2 jYoc

12

21

12

01

02

20

12

01

j

j

jjjDC

BA

o







222

2

1221

122111

j

jjj

jj

DCZZBA

DCZZBAS

oo

ooe

222

2

1221

2221

j

jjjDCZZBAST

oo

e

222

2

1221

122111

j

jjj

jj

DCZZBA

DCZZBAS

oo

ooo

222

2

1221

2221

j

jjjDCZZBAST

oo

o

02

1

2

11 oeB

22

1

2

12

jTTB oe

02

1

2

14 oe TTB

22

1

2

13

jB oe

(same Amplitude & Phase)

(matched) (isolated)



Even

O

dd

oe TTB2

1

2

11

oeB 2

1

2

12 oeB

2

1

2

14

oe TTB2

1

2

13







1

01

1

01

1 jYoc2

tan1

j

Z

ljY

o

oc

Op

en

Sh

un

t S

tub

02

20

cossin

sincos

jlljY

ljZl

o

o

48

2

l

TL

Secti

on

24

2

l

Even

Mo

de

2

tan2

j

Z

ljY

o

oc

4

3

8

32

l

1

01

1

01

2 jYoc

12

21

12

01

02

20

12

01

j

j

jjjDC

BA

e





12

01

1

01

1 jYoc

2tan1

j

lZ

jY

o

oc

Sh

ort

Sh

un

t S

tub

02

20

cossin

sincos

jlljY

ljZl

o

o

48

2

l

TL

Secti

on

24

2

l

Od

d M

od

e

2tan2

j

lZ

jY

o

oc

4

3

8

32

l

12

01

1

01

2 jYoc

12

21

12

01

02

20

12

01

j

j

jjjDC

BA

o







222

2

1221

122111

j

jjj

jj

DCZZBA

DCZZBAS

oo

ooo

222

2

1221

2221

j

jjjDCZZBAST

oo

o

222

2

1221

122111

j

jjj

jj

DCZZBA

DCZZBAS

oo

ooe

222

2

1221

2221

j

jjjDCZZBAST

oo

e

02

1

2

11 oe TTB

22

1

2

12

jB oe

02

1

2

14 oeB

22

1

2

13

jB oe

(same Amplitude & 180o phase difference)

(isolated) (matched)


Rate Race Ring






Rate Race Ring



Example 3

Design a 180o ring hybrid for a 50 system impedance and plot the magnitude of the S-parameters (S1j) from 0.5 fo to 1.5 fo, where fo is the design frequency.

Solution

7.702 oZ




Lecture #4 Contentseee.guc.edu.eg/Courses/Communications/COMM603 Radio... · GUC (Dr. Hany Hammad)...

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