Answer: the required dimensions (a, b) are; ( a= 1.667 cm, b = 1.0714 cm )
Explanation:
Given the data in the question;
air-filled rectangular waveguide
μ₀ = C
m = 1 --- { for single mode operation}
f₀ = c/za {we have equation}
denote the f₀ = 9 GHz
f₀ = Carrier frequency
f₁₀ = 14 Ghz Range or cut off frequency
so we have to find;
a = c/2f₀ and b = c/2f₁₀
so
f₀ = 9 GHz
a = c/2f₀
a = (3 × 10⁸) / ( 2× 9 × 10⁹)
a = 0.01666 cm
a = 1.667 cm
f₁₀ = 14 GHz
b = c/2f₀
b = (3 × 10⁸) / ( 2× 14 × 10⁹)
b = 0.01071 m
b = 1.0714 cm
Therefore the required dimensions (a, b) are; ( a= 1.667 cm, b = 1.0714 cm )
