HP 54753A - Page 234

Transmission Line Theory Applied to Digital Systems
Transmission Line Design
11-6
(4)
By summing the incident voltage v
1
(equation 1), together with similar voltage
contributions from the various orders of reflection (due to ρ
L
and ρ
S
), a general
equation for total line voltage can be written, and used to develop practical
design information:
(5)
Note that as time progresses, the unit step function (u) brings successively
higher order reflection coefficient terms into v(x,t). Successive terms may be
positive or negative, depending on the resulting sign and so damped ringing can
occur. Equation 5 expresses the voltage at any point, x, on the line for any time,
t. The equation can be used graphically with a lattice diagram to find v(x,t).
Example 1
Figure 11-4 will be used to illustrate the lattice diagram method for finding
v(x,t) and the use of equation 5. The source impedance of the MECL III gate
is 5 Ω, resulting in a reflection coefficient at the source of - 0.82 for a line
impedance of 50 Ω.
ρ
S
R
o
Z
o
–
R
o
Z
o
+
------------------=
vxt
,()
v
A
t
()
ut t
pd
x
–
()ρ
L
ut t
dp
2
lx
–
()
–
()ρ
L
ρ
S
ut t
pd
2
lx
+
()
–
()
ρ
L
2
ρ
S
ut t
pd
4
lx
–
()
–
()ρ
L
2
ρ
S
2
ut t
pd
4
lx
+
()
–
()…
++
++ +
[
]
V
dc
+
=