Course Notes for EE1266 Applications of fields and waves
Chapter 2: Lecture 2
1
NOTES for Transmission Lines II
This lecture covers Chapter 6.2 and 6.3
1. Line parameters for lossless T-line
2. Voltage reflection coefficient
3. Standing waves
4. Input impedance of the lossless line
1. Line parameters for lossless T-line
The practical T-lines are those with low-loss
'
'
'
'
C
G
L
R
ω
ω
<<
<<
In this case, we can simplify the line parameters and
characteristics of wave propagating on the T-line
Where μ and ε are the magnetic permeability and electrical
permittivity of
the insulating material separating the
conductors, c is the speed of the light, and λ is the wavelength
of the EM wave in T-lines.
When the phase velocity of a medium is independent of
frequency, the medium is called nondispersive. Given the
electric pulse consists of many frequency components,
nondispersive mean the shape of the pulse propagating on T-
line keep their shape.
r
p
r
p
f
u
C
L
c
u
C
L
Z
C
L
ε
λ
με
ω
π
ω
π
λ
ε
με
λ
π
με
ω
ω
β
α
0
0
2
'
'
2
1
'
'
2
'
'
0
=
=
=
=
=
=
=
=
=
=
=
Course Notes for EE1266 Applications of fields and waves
Chapter 2: Lecture 2
2
2. Voltage reflection coefficient
For a lossless T-line, the voltage and current expression is
( )
( )
z
j
z
j
z
j
z
j
e
Z
V
e
Z
V
z
I
e
V
e
V
z
V
β
β
β
β
0
0
0
0
0
0
−
−
+
−
−
+
−
=
+
=
To determine the ratio between forward and backward
voltage amplitudes, we need put the T-line in the context of a
circuit.
If we set the location of the load as z=0, we have
( )
( )
)
0
(
)
0
(
0
0
0
0
0
0
0
0
I
V
Z
Z
V
Z
V
I
V
V
V
L =
−
=
+
=
−
+
−
+
Solving the above equations, we obtain
3. Standing Waves
Now we have solved for the amplitude of reflected voltage in
term of the incoming one.
( )
(
)
( )
(
)
z
j
z
j
z
j
z
j
e
e
Z
V
z
I
e
e
V
z
V
β
β
β
β
Γ
−
=
Γ
+
=
−
+
−
+
0
0
0
So at any point along the T-line, the amplitude of voltage is
the superposition (not simple ad