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where:
t ( )
v
A
v
(t) = voltage at point A,
A
x = the distance to an arbitrary point on the line,
l = the total line length,
t
= the propagation delay of the line in ns/unit distance,
pd
= l t
,
T
D
pd
u(t) = a unit step function occurring at t = 0, and
E
(t) = the source voltage at the sending end of the line.
S
When the incident voltage v
≠ Z
. The reflection coefficient at the load, ρ
v'
will occur if R
1
L
o
by applying Ohm's Law.
The voltage at the load is v
= v
/Z
, and i'
= -v'
/Z
1
o
1
1
source). Therefore,
v
v'
1
v
+
v'
=
-----
–
------ -
1
1
Z
Z
o
By definition
ρ
=
S
+ v
in equation 2, and substituting in the relation for ρ
Solving for v'
1
1
R
–
Z
ρ
L
o
=
----------------- -
L
R
+
Z
L
o
Similarly, the reflection coefficient at the source is:
Transmission Line Theory Applied to Digital Systems
Z
t ( )
o
=
E
----------------- -
s
Z
+
R
o
o
reaches the end of the long line, a reflected voltage
1
+ v'
which must be equal to (i
1
1
(the minus sign is due to v'
o
R
1
L
o
v'
reflected voltage
1
--------------------------------------- -
=
------ -
incident voltage
v
1
Transmission Line Design
, can be obtained
L
+ i'
) R
. But i
1
1
L
, travelling toward the
1
(2)
results in:
L
(3)
11-5
1
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