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ECE 329
Homework 12
Due: Wed, Dec 8, 2010, 5PM
1.
A T.L. with characteristic impedance
Z
0
= 50
Ω
and length
l
= 0.2
λ
is terminated with a load
Z
L
= 100
Ω
.
a)
Using a Smith Chart, determine (i) the load reflection coefficient
Γ
L
, (ii) the generalized
reflection coefficient
Γ
(
d
) at
d
=
l
and (iii) the input impedance
Z
(
l
) at the generator end.
Hand in your marked Smith Chart.
Hint
: Start by finding the normalized load impedance
z
L
=
Z
L
/
Z
0
on the Smith Chart. Express
Γ
L
and
Γ
(
d
) as complex numbers in polar form
−
i.e.,
as
θ
Γ∠
.
b)
Using
Z
(
l
) from part (a), determine the voltage phasor
V
(
l
) at the generator end if the
generator has an open circuit voltage phasor
V
g
= 10 V and Thevenin impedance
Z
g
= 50
Ω
.
c)
Given the result of (b), determine
V
+
such that
( ) ( )
jd
L
Vd V e
e
ββ
+−
=+
Γ
.
d)
What is the load voltage phasor
V
(0) given the result of (c)?
e)
What is the corresponding load current
I
(0)?
2.
A lossless T.L. having a characteristic impedance of 50
Ω
is terminated by a load of unknown
impedance
Z
L
. Measurements of the voltage amplitude along the line reveal a “standing wave
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 Spring '08
 Kim
 Impedance

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