Answer to Question #101365 in Electricity and Magnetism for NILAKSHA GHOSH

Question

Two identical pulses each of magnitude 12 V and width 2 us are incident at t = 0 on a lossless transmission line of length 400 m terminated with a load. If the two pulses are separated 3 µs (similar to the case of Figure 11.53) and u = 2 X 108 m/s, when does the contribution to VL(€, i) by the second pulse start overlapping that of the first?

Answer 1

When does the overlapping occur? It occurs at the moment when the front part of the pulse that is reflected overlaps the back part of the pulse that is traveling toward the load. Calculate the "length" of the pulses:

$$L_p=u\tau=2\cdot10^8\cdot2\cdot10^{-6}=400\text{ m}.$$

The distance between the fronts of the two pulses:

$$D_p=u\tau_s=2\cdot10^8\cdot3\cdot10^{-6}=600\text{ m}.$$

The time required for one pulse to pass the line:

$$\tau_\text{line}=\frac{L}{u}=\frac{400}{2\cdot10^8}=2\cdot10^{-6}\text{ s}.$$

So this is what happens: the first pulse reaches the line at t=0. Passes it at t=2 microseconds and its front starts reflecting. Then when we can easily draw the moment when these two pulses overlap, that is, when the two green vertical lines at the front of the reflected pulse hits the back of the incident pulse:

As we see from the drawing, the distance between the green lines is 600 m. The pulses travel toward each other with the speed of $4\cdot10^8$ m/s. The green lines will reach each other in

$$t_o=\frac{600}{4\cdot10^{-8}}=1.5\cdot10^{-6}\text{ s}.$$

Thus, the overlapping occurs at

$$t=t_0+4=5.5\space\mu\text{s}.$$