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
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