1. Power dividers are microwave components that divide input power between output ports. Common types include T-junction, Wilkinson, and multi-section broadband dividers. T-junction dividers can be lossless or lossy. Wilkinson dividers provide isolation between output ports. 2. Directional couplers are 4-port networks that divide power between through and coupled ports. They use quarter-wave length lines and even-odd mode analysis. Voltage ratios define coupling factors. Multisection designs provide broadband operation. 3. Hybrids like the quadrature and ring hybrids are 90 or 180 degree hybrids based on symmetric/asymmetric port designs and even-odd mode analysis to provide specific scattering

1. Power Divider
Microwave Engineering
CHO, Yong Heui

2. Microwave Engineering
1. Power divider
Basic properties
  Division of power: scattering matrix
 Lossless system
[ ][ ] [ ][ ]
T *
- V+ V+ = V− V−
T *
- S

c
0 α 1−α 2 
  a
S lossy =

α
1−α 2
β
1−α 2 − β 2
1−α 2 − β 2 
β  t

 
 t
e
r
i
3-port networks 5-port networksn
2
g
EM Wave Lab

3. Microwave Engineering
1. Power divider
T-junction power divider
  Simple 3-port network
 Waveguide or microstrip line
 Lossless or all-port matched network
Yin = jB + Y1 + Y2 at Y0 port
출처 : RFDH.com
3 EM Wave Lab

4. Microwave Engineering
1. Power divider
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]
 Z1 = 3Z 0  S11 = 0
3 2
Z2 = Z0 S 22 = −
2 3
1
S33 = −
3
4 EM Wave Lab

5. Microwave Engineering
1. Power divider
T-junction resistive power divider
  Port impedance: Z0
1
 Series resistance: R = Z0
3
 All port matched network
 Lossy network
0 1 1 
1
 S lossy = 1 0 1 
2
1 1 0
 
5 EM Wave Lab

6. Microwave Engineering
1. Power divider
Wilkinson power divider
 

All port matched network
Lossy network
 Isolation port: 2 and 3
 Even-odd mode analysis: superposition
출처 : RFDH.com
0 1 1 
j 
 S lossy =− 1 0 0
2 
1 0 0
 
6 EM Wave Lab

7. Microwave Engineering
1. Power divider
Broadband divider
  Multisection Wilkinson power divider
 Simulation
 Fabrication
7 EM Wave Lab

8. Microwave Engineering
2. Coupler
Directional coupler
  4 port network
 Input①, through②, coupled③, and isolated④
port
 Waveguide or microstrip line
 Even-odd mode analysis
8 EM Wave Lab

9. Microwave Engineering
2. Coupler
Voltage ratio
  Quarter-wave length line
 Symmetric line
 Quadrature hybrid
V2
= − j 1− C 2
V1
V3
=C
V1
V4
= 0, where C is a coupling factor
V1
9 EM Wave Lab

10. Microwave Engineering
2. Coupler
Broadband directional coupler
  Multisection directional coupler
10 EM Wave Lab

11. Microwave Engineering
2. Coupler
Crosstalk
  Signal switching
 Forward crosstalk
 Backward crosstalk
1 A c tiv e lin e Z o , tp d
Zo 2
Zo
Cm
Lm
tr
3
Zo 4
V ic tim L in e Z o , tp d Zo
Chip level
PCB level
11 EM Wave Lab

12. Microwave Engineering
2. Coupler
Lange coupler
 

Tight coupling
Edge-coupled lines
 Fabrication: narrow width and wire bonding
 MMIC (Monolithic Microwave Integrated Circuit)
출처 : RFDH.com VGA (Variable Gain Amplifier)
12 EM Wave Lab

13. Microwave Engineering
3. Hybrid
Quadrature (branch line) hybrid
 

90° hybrid
3dB coupler
 Symmetric port
 Even-odd mode analysis
0 j 1 0 
 j 0 0 1
−1  
 S=
2 1 0 0 j 
 
 0 1 j 0
출처 : RFDH.com
13 EM Wave Lab

14. Microwave Engineering
3. Hybrid
Ring (rat race) hybrid
 

180° hybrid
3dB coupler
 Asymmetric port
 Even-odd mode analysis
0 1 1 0
 0 − 1
− j 1 0 
 S=
2 1 0 0 1
 
0 − 1 1 0
출처 : RFDH.com
14 EM Wave Lab