Determine the dimensions (a, b) of an air-filled rectangular waveguide that providessingle mode operation over the frequency range from 9 GHz to 14 GHz.

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 )