Why different cutoff frequencies for TE and TM in a medium?

In summary, in electro-magnetics class, it was explained that the cut-off frequencies of TE and TM waves on a co-axial cable are different, meaning that the propagation constants are imaginary below the cut-off frequency and real above it. This is significant because the properties of the medium and waves should not be confused, and the difference between phase and group velocities plays a role. The use case of having two separate cut-off frequencies is that the effective length and delay for each mode will be different, reducing the potential for distortion caused by multiple paths.
  • #1
tworitdash
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Today in my electro-magnetics class, we were told that the cut-off frequencies of TE and TM waves on a co-axial cable are different. As far as I understand, it says that if there is an electric field with one frequency projected on it and if we know that the problem can be simplified if we see it as a combination of one TE and one TM wave, as the wave travels inside the medium, it is treated differently because of two different cut-off frequencies.

The cut-off frequency I am referring here is the frequency below which the propagation constant is imaginary and above which the propagation constant is real. Imaginary propagation constant shows oscillating behavior. What is the significance of two separate cut-off frequencies for TE and TM, because we can visualize one wave as a combination of both? When I asked this, I got a good response, but I didn't get it properly.

The response says that the properties of medium and waves are different and shouldn't be confused with one another. It comes down to the difference between phase and group velocities. What is the use case of two separate cut-off frequencies?
 
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tworitdash said:
What is the use case of two separate cut-off frequencies?
The effective length of a guide (hence the delay) will be different for each mode. If you can use a guide which supports only one mode at the frequency you are using, there is only one path through it so there will be no 'multiparth' distortion.
 
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1. Why do TE and TM waves have different cutoff frequencies in a medium?

TE (Transverse Electric) and TM (Transverse Magnetic) waves have different cutoff frequencies in a medium because they have different polarization orientations. TE waves have their electric field perpendicular to the direction of propagation, while TM waves have their magnetic field perpendicular to the direction of propagation. This difference in polarization leads to different interactions with the medium, resulting in different cutoff frequencies.

2. How does the dielectric constant of a medium affect the cutoff frequency for TE and TM waves?

The dielectric constant of a medium affects the cutoff frequency for TE and TM waves because it determines how strongly the waves are affected by the medium. For TE waves, the electric field is perpendicular to the direction of propagation, so a higher dielectric constant will increase the electric field's interaction with the medium, resulting in a lower cutoff frequency. For TM waves, the magnetic field is perpendicular to the direction of propagation, so a higher dielectric constant will decrease the magnetic field's interaction with the medium, resulting in a higher cutoff frequency.

3. Can the cutoff frequency for TE and TM waves be the same in a medium?

No, the cutoff frequency for TE and TM waves cannot be the same in a medium. As mentioned before, TE and TM waves have different polarization orientations, leading to different interactions with the medium. This results in different cutoff frequencies for each type of wave. However, the difference between the two cutoff frequencies can be minimized if the medium has a very low or very high dielectric constant.

4. How does the geometry of the medium affect the cutoff frequency for TE and TM waves?

The geometry of the medium can affect the cutoff frequency for TE and TM waves in a few ways. Firstly, the shape and size of the medium can determine the propagation direction of the waves, which can affect the polarization and thus the cutoff frequency. Additionally, the geometry of the medium can also affect the dielectric constant, which as mentioned before, has an impact on the cutoff frequency for TE and TM waves.

5. Why is it important to consider the cutoff frequency for TE and TM waves in a medium?

It is important to consider the cutoff frequency for TE and TM waves in a medium because it determines the range of frequencies at which these waves can propagate through the medium. If the frequency of the wave is below the cutoff frequency, the wave will be completely attenuated and cannot travel through the medium. This information is crucial in designing and optimizing communication systems and other applications that use electromagnetic waves.

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