Question

A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in TE₁₁ mode. The minimum operating frequency is:
1. 6.25 GHz
2. 6.0 GHz
3. 5.0 GHz
4. 3.75 GHz

Answer 1

Correct Answer - Option 1 : 6.25 GHz

Concept:

Minimum operating frequency or the cut off frequency for a rectangular waveguide is given by:

\({f_c} = \frac{c}{2}\sqrt {\frac{{{m^2}}}{{{a^2}}} + \frac{{{n^2}}}{{{b^2}}}} \)

a = length of the waveguide

b = height of the waveguide

m,n = modes of operation

Calculation:

Given, a = 4 cm

b = 3 cm

The minimum frequency in TE₁₁ is nothing but the cut-off frequency calculated as:

\({f_c} = \frac{{3 \times {{10}^8}}}{2}\sqrt {\frac{1}{{{{\left( {4 \times {{10}^{ - 2}}} \right)}^2}}} + \frac{1}{{{{\left( {3 \times {{10}^{ - 2}}} \right)}^2}}}} \)

\(f_c= \frac{{3 \times {{10}^8}}}{{2 \times {{10}^{ - 2}}}} \times \frac{5}{{4 \times 3}} = 6.25 \times {10^9}Hz\)

f_C = 6.25 GHz