Question

Which of the following is the radiation resistance of the Hertzian dipole?

(a) \(\frac{\eta_0 w^2 dl^2}{6\pi c^2}\)

(b) \(\frac{\eta_0 wdl^2}{6\pi c^2}\)

(c) \(\frac{\eta_0 w^2 dl^2}{3\pi c^2}\)

(d) \(\frac{\eta_0 w^3 dl^2}{3\pi c^3}\)

I have been asked this question in an internship interview.

Asked question is from Radiation topic in section Radiation, Baluns & Polarization of Antennas

Answer 1

The correct choice is (a) \(\frac{\eta_0 w^2 dl^2}{6\pi c^2}\)

To explain: Radiation resistance of a Hertzian dipole is \(R_{rad} = 80\pi^2(\frac{l}{\lambda})^2\)

By simplifying the options given above,

\(\frac{\eta_0 w^2 dl^2}{6\pi c^2} = \frac{120\pi(2\pi/\lambda)^2 dl^2}{6\pi} = 80\pi^2(\frac{l}{\lambda})^2\)