Lattice Diagram for Transmission Line

[icesalmon]

Homework Statement

Figure for problems 1 and 2: Figure shows a transmission line system. The
effective dielectric constant of the TL is 9 and its length is 2 m. The source is a
DC voltage source. The other parameters are as follows: Vg = 10V, Zg = 20ohms Z0 = 40ohms ZL = 60ohms

Q: Calculate and plot the current at the center of the transmission line as a
function of time between 0ns and 70ns.

Relevant Equations

V = I*Z

The propagation speed of the wave is C/sqrt(9) = u_p if the length of the transmission line is 2m then every 10ns it will pass through the middle of the transmission line. But the switch in the circuit is opened after 5ns so after the current wave bounces off of the Load for the first time it will travel back to the generator and then bounce off of that and travel back towards the load again, but because of the open circuit I should be measuring 0A at 30ns, 50ns, and 70ns (the times at which the current wave would pass through the center of the transmission line) The solution for this problem shows non-zero amplitudes of the current wave at these times. I don't understand how this is possible.

 

[Joshy]

I'm not sure where I see the switch opening after 5 ns comment (maybe we're missing a part of the problem?), but this is one of many things the problem is trying to show you: RF electronics you have to of the signal as (standing) waves and so your open and short circuits might not be as intuitive as it was with low frequency or DC electronics. The real big takeaway is that things are even more complicated when both the source and the load are not matched. It's very common to focus a lot on the load, but if the source is not matched as well, then you need to account for that; this also happens between stages when items are cascaded.

The usual approach I see to this problem is you would draw two vertical lines representing the source and the load. You would show that the signal $V_0^{+}$ goes through the medium $Z_0$ and then it bounces back and forth changing because of the reflection coefficients $\Gamma_S$ and $\Gamma_L$. Did you try that? Were there any other equations that might be relevant for this problem?

 

[icesalmon]

I'm not sure where I see the switch opening after 5 ns comment (maybe we're missing a part of the problem?),

I apologize i must not have copied that portion of the problem, my posting of this was rushed and sloppy.

The usual approach I see to this problem is you would draw two vertical lines representing the source and the load. You would show that the signal $V_0^{+}$ goes through the medium $Z_0$ and then it bounces back and forth changing because of the reflection coefficients $\Gamma_S$ and $\Gamma_L$. Did you try that? Were there any other equations that might be relevant for this problem?

Yes i obtained this: Vg should be V₀ = V_g*Z₀/(Z_g+Z₀)