(a)
Find the value of the dimensions of an air-filled rectangular waveguide.
(a)
Answer to Problem 7P
The value of the dimensions
Explanation of Solution
Calculation:
Given that the cutoff frequency
For
Write the expression to calculate the cutoff frequency for the
Here,
Given waveguide is air-filled, therefore the phase velocity
Therefore the Equation (1) becomes,
Rearrange the above equation.
Substitute
For
Write the expression to calculate the cutoff frequency for the
Here,
Substitute
Rearrange the above equation.
Substitute
Conclusion:
Thus, the value of the dimensions
(b)
Find the value of the cutoff frequencies of the next three higher TE modes in an air-filled rectangular waveguide.
(b)
Answer to Problem 7P
The value of the cutoff frequencies
Explanation of Solution
Calculation:
From part (a), the dimension of the waveguide is in form of
The condition
Write the general expression to calculate the cutoff frequency for the waveguide.
Substitute
Substitute
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
For
The integers are
Therefore, the Equation (3) becomes,
Therefore, the next three higher TE modes are
Conclusion:
Thus, the value of the cutoff frequencies
(c)
Find the value of the cutoff frequency for the
(c)
Answer to Problem 7P
The value of the cutoff frequency
Explanation of Solution
Calculation:
For
Write the general expression to calculate the cutoff frequency for the waveguide.
Write the expression to calculate the phase velocity of uniform plane wave in the lossless dielectric medium.
Here,
Substitute
Substitute
Conclusion:
Thus, the value of the cutoff frequency
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