Topic: Electromagnetics
Two rectangular waveguide have dimensions of $1\text{ cm}\times0.5\text{ cm}$ and $1\text{ cm}\times0.25\text{ cm}$ respectively. Their respective cut-off frequencies will be
- A. 15 GHz and 30 GHz
- B. 30 GHz and 60 GHz
- C. 15 GHz and 15 GHz
- D. 30 GHz and 30 GHz
Answer: C. 15 GHz and 15 GHz
Explanation: The dominant mode for a rectangular waveguide is typically $TE_{10}$, and its cut-off frequency is determined only by the broader dimension 'a'. $f_c = \frac{c}{2a}$. For the first waveguide, $a_1 = 1 \text{ cm}$, so $f_{c1} = \frac{3 \times 10^8}{2 \times 10^{-2}} = 15 \text{ GHz}$. For the second waveguide, $a_2 = 1 \text{ cm}$, so $f_{c2} = \frac{3 \times 10^8}{2 \times 10^{-2}} = 15 \text{ GHz}$.