Topic: Electromagnetics
What is the value of the major cross-sectional dimension(width) of a rectangular waveguide with dominant $TE_{10}$ mode propagation, if its cut off frequency is 10 GHz?
- A. 15 mm
- B. 30 mm
- C. 7.5 mm
- D. 45 mm
Answer: A. 15 mm
Explanation: For the dominant $TE_{10}$ mode in a rectangular waveguide, the cutoff frequency is $f_c = \frac{c}{2a}$.
Given $f_c = 10\text{ GHz} = 10 \times 10^9\text{ Hz}$ and $c = 3 \times 10^8\text{ m/s}$.
$a = \frac{c}{2f_c} = \frac{3 \times 10^8}{2 \times 10 \times 10^9} = \frac{3 \times 10^8}{20 \times 10^9} = 1.5 \times 10^{-2}\text{ m} = 15\text{ mm}$.