Power Divider

Microwave Engineering

CHO, Yong Heui

Basic properties

1. Power divider

 Division of power: scattering matrix

 Lossless system -

- Scattering matrix: unitary matrix





















































2 2

2

2 2

2

lossy

1 1

1 1 0



       

 Simple 3-port network

 Waveguide or microstrip line

 Lossless or all-port matched network



port at

2 1

in

jB Y Y Y

Y   

출처: RFDH.com

2:1 ratio power divider

 Find the output characteristic impedances so that the input power is divided in a 2:1 ratio when a

source impedance is 50 [Ohms]



0 2

0 1

2 3 3

Z Z

Z Z



 

1 3 2 0

22 11











S S

 S

1. Power divider

 Port impedance:

 Series resistance:

 All port matched network

 Lossy network

 ^Z

3

1 Z R 



















0 1

1

1 0

1

1 1

0 2 1

lossy



Wilkinson power divider

 All port matched network

 Lossy network

 Isolation port: 2 and 3

 Even-odd mode analysis: superposition























0 0

1

0 0

1

1 1

0

lossy 2 S j



1. Power divider

출처: RFDH.com

Simulation





 Multisection Wilkinson power divider



Directional coupler

 4 port network

 Input①, through②, coupled③, and isolated④ port

 Waveguide or microstrip line

 Even-odd mode analysis



2. Coupler

 Quarter-wave length line

 Symmetric line

 Quadrature hybrid



factor coupling

a is where

, 0

1

1 4 1 3

2 1

2

V C V

V C V

C V j

V













Broadband directional coupler

 Multisection directional coupler

2. Coupler

Chip level PCB level

Cm Lm

Active line

Victim Line Zo

Zo

Zo

Zo Zo, tpd

Zo, tpd tr

1 2

3 4

 Signal switching

 Forward crosstalk

 Backward crosstalk



Lange coupler

 Tight coupling

 Edge-coupled lines

 Fabrication: narrow width and wire bonding

 MMIC (Monolithic Microwave Integrated Circuit)



2. Coupler

 90° hybrid

 3dB coupler

 Symmetric port

 Even-odd mode analysis



















 

0 1

0

0 0

1

1 0

0

0 1

0

2 1

j

j j

j



Ring (rat race) hybrid

 180° hybrid

 3dB coupler

 Asymmetric port

 Even-odd mode analysis





















 



0 1

1 0

1 0

0 1

1 0

0 1

0 1

1 0

2 S j



3. Hybrid