• That is,
2ܴܵ - ܼ0 - ܴܵ
ܼ0
+
ܴܵ
ρ =
{
}
• Thus,
ܴ
ܵ
– ܼ0
ܴ
ܵ
+ ܼ0
ρ = (
)
-VI
When the Step Reaches the End of the Transmission Line (Transmission Line Terminated
in R=Z0)
The source resistance is 200ohms. As seen in the simulation waveform below (Figure 10), the final output across
the 50ohm load R=Z0 (the green waveform) directly goes to the final voltage= 0.2V after about 320ps from the
input step edge at t=100ps (the red waveform). No reflection is observed.
NOTE: In an actual transmission line, the rise time of V
out
will be much smaller than as seen in the waveform in
Figure 10, and will almost look like a vertical edge, because the unit inductance and capacitance values are much
smaller than the ones used in the LC model here.
Also, some amount of ringing is noted here both at the transmission line input point and at the load, due to
the ultra fast rise time of the step inserted and the non-infinitesimally small values of L, C we have used in this
simulation.
Figure 10: Simulation waveform for a transmission line terminated with R=Z0
When the Step Reaches the End of the Transmission Line (Transmission Line Terminated
in R>Z0)
The source resistance is 200ohms. Here, the output of the transmission line is terminated with R>Z0 =75 ohms. As
seen in the simulation waveform below in Figure 11, the final output across the 75ohm load (the green waveform)
as well as the voltage right at the input of the transmission line (the red waveform) arrives at a final settled voltage
of around 272.73mV after a series of reflections.
Figure 11: Simulation waveform for a transmission line terminated with R>Z0
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8
Accurately Modeling Transmission Line Behavior with an LC Network-based Approach
