Find the value of the attenuation constant due to the conduction losses and the distance travelled by the waveguide which is attenuated by
Answer to Problem 31P
The value of the attenuation constant due to the conduction losses
Explanation of Solution
Calculation:
Given that the complex permittivity is ,
Refer to Equation (12.57) in the textbook for the complex permittivity.
Compare the Equations (1) and (2).
Here,
Write the expression to calculate the cutoff frequency.
Here,
Write the expression to calculate the phase velocity of uniform plane wave in the lossless dielectric medium.
Here,
Substitute
Substitute
Simplify the above Equation.
Given that the operating frequency of the waveguide is
Write the expression to calculate the intrinsic impedance of a uniform plane wave in the medium.
Here,
Substitute
Write the expression to calculate the attenuation constant due to conduction losses for the
Here,
Write the expression to calculate the real part of the intrinsic impedance of the conducting wall.
Here,
Substitute
Simplify the above Equation.
Substitute
From the comparisons of Equations (1) and (2),
Rearrange the above Equation.
Substitute
Simplify the above Equation.
Write the expression to calculate the attenuation constant due to the dielectric losses.
Substitute
To calculate the distance over which the wave is attenuated by 30%,
Simplify the above Equation.
Rearrange the Equation.
Conclusion:
Thus, the value of the attenuation constant due to the conduction losses
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Chapter 12 Solutions
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