5.7 Cascaded lines

We can use bounce diagrams to handle somewhat more complicated problems as well.

Arnold Aggie decides to add an additional ethernet interface to the one already connected to hiscomputer. He decides just to add a "T" to the terminal where the cable is connected to his "thin-net" interface, and add on somemore wire. Unfortunately, he is not careful about the coaxial cable he uses, and so he has some $75\Omega$ TV co-ax instead of the $50\Omega$ ethernet cable. He ends up with the situation shown here . This kind of problem is called a cascaded line problem because we have two different lines, one hooked up after the other. The analysis issimilar to what we have done before, just a little more complicated is all.

We will have to do a little more thinking before we can draw out the bounce diagram for this problem. The driverfor ethernet cable coming to Arnold's computer can be modeled as a 10V (open circuit) source with a $50\Omega$ internal impedance. Since the source does not (initially) know anything about how the line it is driving isterminated, the first signal $V_1^{+}$ will be the same as in our initial problem, in this case just a +5V signal headed down the line.

Let's focus on the "T" for a minute .

In order to completely solve this problem, we also need to know $V_{T1}^{+}$ , the transmitted wave as well. Since says $V_{T1}^{+}$ is just the sum of the incident and reflected waves on the first line