Question

Which of the following expression is correct for radiation efficiency?

(a) \(\eta_r=\frac{R_r}{R_l}\)

(b) \(\eta_r=\frac{R_r}{R_r-R_l}\)

(c) \(\eta_r=\frac{R_r}{R_r+R_l}\)

(d) \(\eta_r=\frac{R_l}{R_r+R_l}\)

I got this question during an interview.

My doubt stems from Directive Gain in division Antenna Parameters of Antennas

Answer 1

Right option is (c) \(\eta_r=\frac{R_r}{R_r+R_l}\)

Explanation: Radiation efficiency is defined as the ratio of power radiated to the total input power to the antenna. Total input power is the sum of the radiated power Pr  and the ohmic losses Pl.

\(\eta_r = \frac{P_r}{P_{in}} = \frac{P_r}{P_r+P_l} = \frac{R_r I_{rms}^2}{I_{rms}^2 R_r+I_{rms}^2 R_l} = \frac{R_r}{R_r+R_l} \)