Transmission Line Theory Applied to Digital Systems
Transmission Line Design
11-13
term, T
1
, is the amount of time it takes for the waveform at A to switch to the
level at which the output transistor turns off. The fall time of the signal would
have been longer by an amount equal to:
if the termination resistor had been 70 Ω or less.
The reflected voltage waveform leaving point B at t = T
D
arrives at point A at t
= 2TD. The source impedance is very high initially (ρ
S
= + 1.0), with the output
transistor being in the off condition until the voltage at A falls to 0.32 V. Then,
the source impedance changes to 5 Ω (ρ
S
= - 0.82).
The following formula may be used to determine the point at which the
transistor turns on:
(9)
where V
1
is now the incident voltage approaching the source and ∆V
source
is
the change in voltage at the source necessary to turn the transistor on.
In this example the actual voltage change for this conduction to occur is
∆V
source
= 0.32 - 0.58 = - 0.26 V. Therefore, the voltage waveform approaching
the source (193 mV) can be broken into two signals V
11
= -0.13, and
V
12
= - 0.063 V. The reflected voltage due to V
11
is V’
11
= -0.13 V, and for V
12
,
the reflected voltage is V’
12
= (-0.82) (-0.063) = 0.052 V. The two reflected
voltages of opposite polarity at point A going toward point B are the reason for
the increased overshoot of short duration at point B, when t = 3T
D
+ (0.13 ÷
0.193) T
1
. Refer to Figure 11-6.
The steady state voltage reflection that occurs after t = 2T
D
+ T
1
is the sum of
-0.13 V and +0.052 V, equal to -78 mV as shown in Figure 11-5. The steady state
voltage reflection can be calculated using the relation:
(10)
T
′
1
1.16 0.305–
()
1.16 0.58–
()
----------------------------------
T
1
=
∆
V
source
V
1
ρ
S
V
1
+2
V
1
==
V
′ρ
S
2
∆
V
source
1
Z
o
R
o
2
--------+
2
------------------
ρ
S
1
V
1
∆
V
source
1
Z
o
R
o
2
--------+
2
------------------
–+=
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