PSpice Application Notes

We can now predict the nature of the voltage variation at the output. Now, making use of the knowledge that the capacitor provides an exponentially varying impedance at the output with a time constant Z0C, we can also predict how the voltage at the source end of the transmission line changes once the reflected waveform from the load reaches it. Since the impedance provided by the capacitor starts off at 0 ohms, at first, as the reflected wave reaches back to the source end, the voltage at the source end would go to whatever voltage it would have gone to upon receiving the first reflection from the load side, for a short-circuited transmission line. As the capacitive impedance increases exponentially with a time constant Z0C, the voltage at the source end would go to whatever voltage it would have gone to upon receiving the first reflection from the load side, for a transmission line terminated in a resistance R=the instantaneous impedance of the capacitor at that time. Thus, the voltage at the source end also follows an exponential RC charging profile with time constant=Z0C. Finally, since the impedance provided by the capacitor is infinity, i.e. open circuit, once it has charged to its final voltage, the voltage at the source end would go to whatever voltage it would have gone to upon receiving the first reflection from the load side, for an open-circuited transmission line. In this manner, source and load reflections continue until the output settles to the final value. The simulation waveforms for the load end voltage (green waveform) and source end voltage (red waveform), for a 1V step injected into a 50ohm Z0 transmission line with delay=300ps, is given in Figure 16. A zoomed version of the initial portion of these waveforms is presented in Figure 17. Source resistance used is 200ohms, and output capacitor is 1pF. Figure 16: Simulation waveform for the load-end voltage and source-end voltage Figure 17: First 1ns of the previous waveform zoomed One important thing we have to consider here is the transmission line delay T d . It is to be noted that the output capacitor starts charging only after a time period= T d after the instant of injection of the original step input into the transmission line. The total time available for the output capacitor to charge freely as per Z0C until the charging process gets disturbed by the reflected wave from the source end is equal to the time taken for the initial reflected wave from the load to reach the source and get reflected back to the load from the source, which equals a round dip delay time of 2*T d . www.cadence.com 12 Accurately Modeling Transmission Line Behavior with an LC Network-based Approach

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