28 Multiline circuits
•
In this lecture we will extend the bounce diagram technique to solve
distributed circuit problems involving multiple transmission lines.
•
One example of such a circuit is shown in the margin where two distinct
TL’s of equal lengths have been joined directly at a distance
l
2
away
from the generator.
+

0
f
(
t
)
R
g
= 2
Z
1
R
L
=
Z
2
z
l
Load
Z
1
Z
2
= 2
Z
1
0
l
4
81
τ
g
=
Γ
g
=
Γ
12
=
1
3
τ
12
=
4
3
Γ
L
= 0
1
3
1
9
1
27
1
81
4
9
t
l/
2
v
2
= 2
v
1
v
1
–
The impulse response of the system can be found by first con
structing the bounce diagram for the TL system as shown in the
margin.
–
In this bounce diagram,
z
=
l
2
happens to be the location of ad
ditional reflections as well as transmissions because of the sudden
change of
Z
o
from
Z
1
to
Z
2
= 2
Z
2
.
These reflections and transmissions between line
j
and
k
— transmis
sion from
j
to
k
, and reflection from
k
back to
j
— can be computed
with
reflection coe
ffi
cient
Γ
jk
=
Z
k

Z
j
Z
k
+
Z
j
and
transmission coe
ffi
cient
τ
jk
= 1 +
Γ
jk
that ensure the voltage and current continuity at the junction
1
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–
Z
j
is the characteristic impedance of the line of the incident pulse,
while
–
Z
k
is the impedance of the cascaded line into which the transmitted
pulse is injected.
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 Summer '10
 KUDEKI
 Impedance, The Circuit, Electrical impedance, Transmission line, Impedance matching, Characteristic impedance

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