An antenna can be modeled as an electric dipole of length 5 m at 3 MHz. Find the radiation resistance of the antenna assuming uniform current over the length.

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Question

This question was previously asked in

ESE Electronics 2011 Paper 1: Official Paper

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Answer 1

Concept:

The radiation resistance of the dipole antenna is given as:

\({R_{rad}} = 80{\pi ^2}{\left[ {\frac{{d\ell }}{\lambda }} \right]^2}\)

Where dℓ is the small length of the antenna.

λ = Wavelength.

Calculation:

dl = 5 m

f = 3 MHz

∴ \(\lambda = \frac{{3\; \times\; {{10}^8}}}{{3\; \times\; {{10}^6}}} = 100\;m\)

So radiation resistance of dipole antenna

\({R_{rad}} = 80\;{\pi ^2}{\left( {\frac{5}{{100}}} \right)^2}\)

R_rad = 1.97 ≃ 2 Ω