This document discusses transmission line models and parameters. It defines transmission line parameters such as characteristic impedance and explains that lossless transmission lines have resistance and conductance values of zero. It provides the parameter equations for different common transmission line types including coaxial cable, parallel plates, and microstrip lines. It also defines the voltage reflection coefficient and explains how it is used to characterize impedance mismatches and standing waves on transmission 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