Transmission Line Theory Applied to Digital Systems
Signal Propagation Delay for Microstrip and Strip Lines with Distributed or Lumped
Loads
11-17
An equation for maximum open line length for a strip line (using G-10 fiber glass
epoxy material) can be written in a similar fashion as follows:
(13)
Using the lattice diagram, it has been found that the rule of thumb used to derive
equations 12 and 13 should be modified for an open line because the incident
voltage doubles at the end of the line. This results in a faster risetime at the
receiving end of an unloaded line than at the driving end. An approximate value
of maximum open line length can be generated from equations 12 and 13 if the
risetime that is substituted into the equations is multiplied by an adjustment
factor, 0.75. This maintains an approximate overshoot and undershoot of less
than 35% and 12% respectively.
To demonstrate how equations 12 and 13 may be used, the maximum open line
length will be computed for a 50 Ω line with a fanout of one MECL 10K gate.
Using the equation t
pd
= Z
o
C
o
, the line capacitance, C
o
, is found to be
C = 2.96 pF/in for microstrip, and C
o
= 3.76 pF/in for strip line. For a fanout of
one, C
D
is equal to 5 pF when the device is in a socket. The risetime for MECL
10K is 3.5 ns which means that a value of t
r
= 0.75 X 3.5 = 2.6 ns should be used
in the equations. Solving equations 12 and 13, l
max
for a 50 Ω microstrip line
and l
max
= 6.2 inches for a 50 Ω strip line.
Equations 12 and 13 can be very useful in finding the approximate maximum
line length under various conditions. Suggested maximum open line lengths for
MECL 10K/10KH and MECL III are tabulated in tables Table 11-1, Table 11-2,
and Table 11-3 for various fanouts and line impedances. For these tables, line
lengths are chosen to limit overshoot to 3.5% of logic swing and undershoot to
12%. Note that the tables give the maximum line lengths for fanouts of 1, 2, 4,
and 8 for various types of lines with a wide range of characteristic impedances.
l
2
max
C
D
C
o
-------
l
max
7.1
t
2
r
–+ 0 (for strip lines)=
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