Issue link: https://resources.pcb.cadence.com/i/1480209
Making use of this knowledge, we can easily predict the final voltage the output capacitor reaches before it gets disturbed by the reflected wave from the source end, for any given transmission line delay T d . We can use the basic capacitor RC charging equation, V final (1-e -2Td / Z0C ), where V final is the voltage the output end of the transmission line would have reached for an open-circuited transmission line. This idea can be further extended to predict the profiles for each step in the reflected waveform both at the transmission line input as well as output. To illustrate an example, let's consider a 1V step injected into a 50ohm Z0 transmission line with delay T d =70ps, with source resistance =200ohms and output capacitor 1pF. Here Vfinal expected is 0.4V just after step reaches the output end, for an open-circuited transmission line. Thus, we can predict that the final voltage the output capacitor reaches before it gets disturbed by the reflected wave from the source end is V final (1-e -2Td / Z0 C) = 0.4 (1-e -2*70ps/50*1pF ) =~375.6mV. (This is observed to match the simulation result for the output waveform for this case, as observed in the waveform in Figure 18.) The initial portion of the simulation waveforms for the load end voltage (green waveform), for a 1V step injected into a 50ohm Z0 transmission line with delay=70ps, with source resistance =200ohms and output capacitor 1pF, showing the capacitor voltage charging to V final (1-e -2Td / Z0C ) = 0.4 (1-e -2*70ps/50*1pF ) =~0.376V, before it gets disturbed by the reflection from the source side. Figure 18: Simulation result for output waveform When the Step Reaches the End of the Transmission Line (Transmission Line Terminated in an Inductor) An approach similar to the capacitor termination case can be taken for a transmission line terminated in an inductor L, too. Only here, the time constant is L/Z0 and the impedance initially starts off as an open circuit, and decays exponentially to zero, finally following a time constant of L/Z0. As shown in Figure 19, 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, with source resistance =200 ohms and output inductor, is 10nH. Figure 19: Simulation waveforms for load-end voltage and source-end voltage www.cadence.com 13 Accurately Modeling Transmission Line Behavior with an LC Network-based Approach