Discussion
A 6 cm × 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25. The range of frequencies over which single mode operation will occur is :
Answer: B
Single-mode operation occurs for 2 GHz \(\lt f \lt\) 3 GHz.
In a guide filled with a dielectric of index \(n\), waves travel at \(v = c/n = 2.4 \times 10^{8}\) m/s. The cut-off frequencies are \(f_{mn} = \frac{v}{2}\sqrt{(m/a)^{2} + (n/b)^{2}}\) with \(a = 6\) cm and \(b = 4\) cm:
\[ \begin{aligned} f_{10} &= \frac{2.4 \times 10^{8}}{2 \times 0.06} \\ &= 2\ \text{GHz} \\ f_{01} &= \frac{2.4 \times 10^{8}}{2 \times 0.04} \\ &= 3\ \text{GHz} \end{aligned} \]
Between these only TE10 propagates. The other ranges do not match these cut-offs; without the dielectric the window would be 2.5 to 3.75 GHz, which is not offered either.
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