Concept explainers
(a)
Find the value of the phase constant, phase velocity, group velocity and intrinsic impedance of the air-filled rectangular waveguide.
(a)
Answer to Problem 21P
The value of the phase constant
Explanation of Solution
Calculation:
Given dimensions
Write the expression to calculate the cutoff frequency.
Here,
Given waveguide is air-filled, therefore the phase velocity
Substitute
Substitute
Write the expression to calculate the phase constant of the waveguide.
Here,
Substitute
Substitute
Write the expression to calculate the phase velocity.
Substitute
Substitute
Write the expression to calculate the group velocity.
Substitute
Substitute
Write the expression to calculate the intrinsic impedance for the free space.
Here,
Substitute
Conclusion:
Thus, the value of the phase constant
(b)
Find the value of the phase constant, phase velocity, group velocity and intrinsic impedance of the rectangular waveguide with a material.
(b)
Answer to Problem 21P
The value of the phase constant
Explanation of Solution
Calculation:
Write the expression to calculate the phase velocity of uniform plane wave in the lossless dielectric medium.
Here,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Write the expression to calculate the intrinsic impedance for the medium.
Here,
Substitute
Simplify the above Equation.
Conclusion:
Thus, the value of the phase constant
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Chapter 12 Solutions
Elements of Electromagnetics
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