Electromagnetics Waves by German Leon

What we do that defines us

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A wavelength/4 transformer -or (2n+1) wavelength/4 –  is a classical circuit scheme which allow us to match a real impedance to a transmission line (TL). The transformer impedance is the geometric average of the real impedance and the TL impedance. What happens inside the transformer? In the transitory state, an imping wave flows to the transformer. Part of the energy flows to the load, and part goes back to the generator, that is a backward wave does exist inside the TL (t=6s). The wave inside the transformer arrives the load and part of it returns to the TL (t=14s). During this time, a quasi-standing wave is made in the TL. But at t=24s, the backward wave from the load “compensates” the reflection from the transformer, and a flowing wave is formed in the TL, that is, in the steady state, all the energy that comes from the generator goes to the transformer, and it will be consumed in the load.

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This simulation shows the behavior of a lossy transmission line (TL). A sinusoidal signal propagates through the TL and, due to the losses, the signal decays when it advances. If you stop the motion at t=8s and join the peaks with an imaginary line, a decreasing exponential can be sketched. Moreover, this TL is not matched. It is very difficult to see the backward wave because it has very low level. However, if you stop the motion at t=10 s, you can see that the waveform at the end of the line is different to the waveform at the beginning.

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This video represents the potential and the intensity of two different Transmission Lines (TLs) joined in cascade.   This simulation is made using the Finite Different Time Domain (FDTD) method, which allows us to visualize what happens when the time goes by.

What can we see? A step signal feeds the first TL and the line is excited by certain potential. At t=2s, the step arrives to the discontinuity between the two TLs. Two waves appear: one wave is generated in the second line to forward direction and another wave advances to the backward direction. The first TL has a bigger transmission speed than the second.  The wave in the second line arrives at t=8s  to a certain load and a backward wave is produced that come back to the discontinuity.

Let‘s look a little more inside. We can make some affirmations. Try to understand why:

–          The two lines are lossless.

–          The two lines have different transmission speed and different impedance.  The impedance of the first line is smaller than the second one.

–          The load at the end of the second TL has a real value smaller than the impedance of the second line

–          The generator is matched to the first TL.