STANDING WAVE DIAGRAM (PART 2: Matlab exercises)

1. GET THE MATLAB CODE

Following our previous post about the Standing Wave Diagram equations and parameters, we are going to study the 3 essential examples in this tutorial. They will show you the waves shape according to the transmission line characteristics. In order to get started, download the FREE code available in our Mathworks account.

This code allows us create a standing wave diagram according to transmission line parameters:

  • Wavelength
  • Transmission line length
  • Characteristic impedance
  • Load impedance

Note that the transmission line length is normally expressed as a function of the wavelength, being this one a parameter: the Matlab script also allows this possibility.

In addition to the wave plot, after running the Matlab code, we can see the following data in the Matlab prompt:

  • load reflection coefficient
  • maximum and minimum voltage values
  • standing wave ratio

We can also interact with the plot and mark the points we like in the wave, which values will appear in the Matlab prompt.

 

2. TRANSMISSION LINE ENDING IN A MATCHING IMPEDANCE

As we know, if ZL=Z0  there won’t be reflected wave, \rho (0)=0 and there is a matching in the line, S=1. This means that our voltmeter will measure the same amplitude on each point:

3. LINE ENDING IN AN OPEN-CIRCUIT AND A SHORT-CIRCUIT

We know that in both cases, the total voltage in the line will be a pure standing wave: the voltmeter won’t read anything if we place it in the nodes (every λ/2 along the line length).

Let’s have a look at the case when the load is in short-circuit. This will happen when  ZL=0, therefore, S=∞. In this examples, we suppose we don’t know the wavelength:

Now, for the open-circuit case, we insert a very high value for ZL (theoretically, it should be infinite) to see what happens:




 

4. WHEN THE REFLECTED VOLTAGE IS DIFFERENT FROM THE 0% OR THE 100% OF THE INCIDENT VOLTAGE

In this case, we will find that part of the energy is absorbed by the load and some other is reflected. Therefore, the slotted line will measure a voltage formed by the travelling wave and the standing wave (although this voltage is normally described only as a standing wave).

The ratio between the travelling wave and the standing wave is calculated as the maximum and minimum amplitude found by the voltmeter (this is the S we’ve seen above, also named VSWR). This factor offers a measure of the quality of the line.

In the previous cases, we’ve seen that when the load is matching, we have VSWR=1 and when the load totally reflects, VSWR=∞.

For the present case ZL will be different from Z0. For instance:

And these are the essential examples that you need to study to make sure you understand how the propagation through a transmission line works! We hope you found it useful 🙂

In our next post for the Microwaves Propagation section, we will analyse the distributed and lumped transmission line parameters.

As always, don’t hesitate to leave a comment below or reach us through email for any question or feedback!

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