Topic: Electromagnetics
Consider a standard rectangular and a circular waveguide having same dominant mode cut-off frequency, determine the ratio of area of circular waveguide to rectangular waveguide
- A. $\frac{1}{\pi}$
- B. $\frac{6.78}{\pi}$
- C. $\frac{0.69}{\pi}$
- D. $\pi$
Answer: B. $\frac{6.78}{\pi}$
Explanation: For circular waveguide $\lambda_c = \frac{2\pi r}{1.841}$.
For rectangular waveguide $\lambda_c = 2a$.
Equating them: $\frac{2\pi r}{1.841} = 2a \Rightarrow a = \frac{\pi}{1.841}r$.
For standard rectangular waveguide, $b = a/2$.
Ratio of Area = $\frac{\pi r²}{ab} = \frac{\pi r²}{a(a/2)} = \frac{2\pi r²}{a²} = \frac{2\pi r²}{(\frac{\pi r}{1.841})^2} = \frac{2\pi(1.841)^2}{\pi²} = \frac{2(1.841)^2}{\pi} \approx \frac{6.78}{\pi}$.