Transient Response of Transmission Lines (Part I)

 

In our previous posts series on this section, Distributed Element Model in Transmission Lines, we analyzed the transmission lines as a function of the z coordinate, in the instant of time, t.

Following that study, we move onto the transient response analyzing what happens when there is a sudden change in the conditions of the line. In order to fully study this new block, we will see the following 4 posts:

  1. Reflection coefficient at the load and at the source
  2. Standing wave ratio (SWR)
  3. Analysis of behavior of the voltage waves in the line: open circuit and short circuit cases
  4. Two solved exercises explained

After this block is finished, we’ll be ready to study and learn how to use the Smith Chart

Ready? Let’s have a look at the first point:

Reflection coefficient at the load and at the source

Let be the following transmission line of length l:


Load reflection coefficient

The load reflection coefficient is the ratio between the reflected and the incident voltage waves at the load (z=0):

Source reflection coefficient

The reflection coefficient is very useful to define the boundary conditions of the transmission line load and source.

As above, the source (also named generator) reflection coefficient is the ratio between the reflected and the incident voltage waves at the load (z=l):

Also, the transmission coefficient at the generator is the ratio between the transmitted and the incident voltage waves at the load (z=l):

The following graph shows the Voltage vs. transmission line length for the incident wave from the generator. As you can observe, the voltage decreases with the distance:

 

Ready for more?

We hope this post was useful as an introduction to the transient state of transmission lines, and you are ready now for the following points:

2.Standing wave ratio (SWR)

3. Analysis of behavior of the voltage waves in the line: open circuit and short circuit cases

4. Two solved exercises explained

Don’t forget to compare this analysis with the Distributed Elements analysis that we did previously, to make sure you have a comprehensive knowledge of the subject. Of course, as always, any question or comment, just write it in the comments section or contact us 🙂

 

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