Discussion
Consider a rectangular wave guide with dimensions 2.28 cm × 1.01 cm. What TE modes will propagate, if the driving frequency is 17 GHz ? And, to excite only one TE mode, what range of frequencies could be used ?
Answer: B
The single-mode range is 6.6 GHz to 13.2 GHz.
The cutoff frequencies of a rectangular guide with sides \(a = 2.28\) cm and \(b = 1.01\) cm are
\[ \begin{aligned} \nu_{mn} &= \frac{c}{2}\sqrt{\frac{m^{2}}{a^{2}} + \frac{n^{2}}{b^{2}}} \\ \nu_{10} &= \frac{3 \times 10^{10}}{2 \times 2.28} = 6.58\ \text{GHz} \\ \nu_{20} &= 13.2\ \text{GHz}, \quad \nu_{01} = 14.9\ \text{GHz} \end{aligned} \]
and \(\nu_{11} \approx 16.2\) GHz. At 17 GHz the TE10, TE20, TE01 and TE11 modes all propagate. Only TE10 propagates between its own cutoff and the next one, so the single-mode band is about 6.6 GHz to 13.2 GHz.
3.3 to 6.6 GHz lies below the lowest cutoff, where nothing propagates; 1.62 to 6.6 GHz is also below cutoff; and 66 to 132 GHz is ten times too high and full of higher modes.
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