What is the attenuation below cut-off frequency for TE10?

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SUMMARY

The discussion centers on the attenuation of electromagnetic waves below the cut-off frequency for the TE10 mode in electric conductors. It establishes that below the cut-off frequency, the propagation constant becomes imaginary, indicating no wave propagation occurs in the medium. The conversation highlights the significance of finite conductivity in determining attenuation above the cut-off frequency using specific formulas, including the loss power equation and the surface current density. Terman's references provide empirical attenuation values for capacitive plates and magnetic coupling in conductive tubes.

PREREQUISITES
  • Understanding of electromagnetic wave propagation and cut-off frequencies
  • Familiarity with the TE10 mode in rectangular waveguides
  • Knowledge of Poynting vector and its application in calculating power loss
  • Basic concepts of skin depth and its effect on wave attenuation
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  • Research the TE10 mode in rectangular waveguides and its implications for wave propagation
  • Study the derivation and application of the Poynting vector in electromagnetic theory
  • Explore the concept of skin depth in conductors and its impact on high-frequency signal loss
  • Investigate empirical attenuation values for different geometries and materials in electromagnetic applications
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Electrical engineers, physicists, and researchers focused on waveguide design, electromagnetic theory, and signal integrity in conductive materials.

tworitdash
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It is not useful to talk about the attenuation below cut-off frequency, but I have this doubt about what happens to the wave below cut off for an electric conductor. As we know if we derive the propagation constant, it becomes imaginary saying that there should not be any wave propagating in the medium. The discussion ends here.

For frequencies above the cut-off, we consider the finite conductivity of the conductor to determine the attenuation based on the formulae below.

$$ P_{loss} = (1/2) \iint Rs(\vec{r}) \left| \vec{J_s}(\vec{r}) \right| ^ 2ds$$

$$ \vec{J_s}(\vec{r}) = \hat{n} \times \vec{H}_{PEC}(\vec{r}) $$

Where ##R_s## is a function of conductance and frequency. From the above equations with the poynting vector, we find the attenuation constant.

However, we do not consider the attenuation due to the lossy but conducting medium when the frequency is below the cut-off. Does it affect below the cut-off? If so, why and how can we compute it? What should be the ##\vec{H}_{PEC}## below the cut-off?
 
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I do not know how to calculate the loss due to the walls of the tube or the dielectric but the attenuation of the evanescent wave is in any case very high. Terman, in Radio Engineering, quotes 20.9dB per distance/radius for capacitive plates in a round copper tube. For magnetic coupling he quotes 33.3dB per radius/distance. He also gives a correction for skin depth.
 
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