How Do You Sketch Voltage and Current Waveforms for a Coaxial Transmission Line?

[tim9000]

Homework Statement

As seen in picture: A coaxial transmission line has a characteristic impedance of 50 Ω, propagation
velocity of 200m/μs, length of 400m, and is terminated by a load resistance, RR =
16.7 Ω. At the sending end the line is connected to a pulse generator that has an
internal resistance of 150 Ω and produces a 40 V, 1 μs long pulse at time, t=0. Sketch
the sending end voltage and current waveforms for 0≤t≤15 µsec.

Homework Equations

The Attempt at a Solution

I'm not sure how to approach this, I'm assuming it has something to do with the inductance and capacitance found from Z = Sqrt(L/C), does anyone have any thoughts?
Thanks

 

[rude man]

IMO this is a very difficult assignment. It would be so even if the input were an infinite-duration pulse, in which case a lattice diagram could be used. Not sure if this type of diagram could be adapted for a finite-duration pulse (duration < L/v). Should in theory but wouldn't want to try it.

The basic idea of course is that
1. the outgoing wave V and I moves with velocity v, I = V/Z_0;
2. the returning wave V' and I' are related by the load reflection coefficient;
3. the returning wave, added to the ingoing wave, force a new V and I at the source, which will depend on the source impedance;
etc.

This keeps going until the input pulse goes back to zero V.

 

[tim9000]

thanks

I see, thanks anyway.
Though what does the internal resistance of the pulse generator have to do with it?

 

[rude man]

I see, thanks anyway.
Though what does the internal resistance of the pulse generator have to do with it?

The 150 ohm source resistance determines the fraction of the reflected pulse (back to the source) sent back out again as a new pulse in the +x direction. Us your experssion for the reflection coefficient with Z_0 = 50 ohms and Z_L = 150 ohms.

 

[HalfLostAndSearching]

for the question and the sketch provided. From the given information, we can calculate the characteristic impedance of the coaxial transmission line using the formula Z = √(L/C), where L is the inductance per unit length and C is the capacitance per unit length. This gives us Z = √(200m/μs / 400m) = 50 Ω.

Next, we can use the formula for the propagation velocity to find the time it takes for the pulse to travel from the sending end to the load. This gives us t = 400m / 200m/μs = 2 μs.

Now, to sketch the voltage and current waveforms at the sending end for 0≤t≤15 μsec, we can use the following steps:

1. At t=0, the pulse generator produces a 40 V, 1 μs long pulse. This means that for the first 1 μs, the voltage at the sending end will be 40 V and the current will be 40 V / 50 Ω = 0.8 A.

2. From t=1 μs to t=2 μs, the pulse travels along the transmission line towards the load. During this time, the voltage and current will remain constant at 40 V and 0.8 A respectively.

3. At t=2 μs, the pulse reaches the load and is reflected back towards the sending end. This causes a change in the voltage and current waveforms.

4. From t=2 μs to t=4 μs, the reflected pulse travels back towards the sending end. During this time, the voltage and current will remain constant at -40 V and -0.8 A respectively.

5. At t=4 μs, the reflected pulse reaches the sending end and is absorbed by the internal resistance of the pulse generator. This causes the voltage and current to drop to 0 V and 0 A respectively.

6. From t=4 μs to t=15 μs, the voltage and current will remain at 0 V and 0 A respectively as there are no more pulses being generated.

Based on these steps, the sending end voltage and current waveforms for 0≤t≤15 μsec can be sketched as shown below:

[Insert sketch here]

Note that the voltage and current waveforms will repeat after every 2 μ