wave guides and tranasmission lines

1. EEE194RF_L5 2
Lossless Transmission Line Model
• Line representation
)(
)(
0
CjG
LjR
Z
ω
ω
+
+
=Characteristic impedance:
Note: R, L, G, C are given per unit length and depend on geometry
Lossless implies:
R = G = 0!

2. EEE194RF_L5 3
Transmission Line Parameters for different line types
2-wire coax
σδπa
1
)
2
(1
a
D
ch−
π
µ
R
L
G
C
)
11
(
2
1
ba
+
πσδ
parallel-plate
))2/((1
aDch−
πσ
))2/((1
aDch−
πε
σδw
2
w
d
µ
d
w
σ
d
w
ε
)ln(
2 a
b
π
µ
)/ln(
2
ab
πσ
)/ln(
2
ab
πε

3. EEE194RF_L5 4
Microstrip line
1/),
4
8ln(
2
/ 00
0 <+= hW
h
W
W
h
Z
effεπ
εµ
])/1(04.0)/121[(
2
1
2
1 22/1
hWWhrr
eff −++
−
+
+
= −εε
ε

4. EEE194RF_L5 5
What is a voltage reflection coefficient?
0
0
0
ZZ
ZZ
L
L
+
−
=Γ
Reflection coefficient
at the load location
)(10 ∞→=Γ LZ
)0(10 →−=Γ LZ

5. EEE194RF_L5 6
Standing Waves
)()( djdj
eeVdV ββ −++
−=
)2/cos()sin(2),( πωβ += +
tdVtdv

6. EEE194RF_L5 7
Standing wave ratio
||1
||1
||
||
||
||
0
0
min
max
min
max
Γ−
Γ+
===
I
I
V
V
SWR
SWR is a measure of mismatch of the
load to the line
SWR=1 (matched) or SWR ∞→ (total mismatch)
match