Question

Assume two similar antennas for transmitting and receiving. If the operating frequency gets reduced by 3 times then the received power gets _______

(a) increases by factor 3

(b) decreases by factor 3

(c) increases by factor 9

(d) decreases by factor 9

This question was posed to me in unit test.

Query is from Friis Transmission Equation in chapter Antenna Parameters of Antennas

Answer 1

Right answer is (c) increases by factor 9

Explanation: From Friss transmission equation,

\(\frac{P_r}{P_t} = \frac{G_t G_r λ^2}{(4\pi R)^2} = \frac{G_t G_r c^2}{(4\pi Rf)^2}\)

\(\frac{P_{r1}}{P_{r2}} = \frac{f_2^2}{f_1^2} = \frac{(f/3)^2}{f^2} = \frac{1}{9}\)

Pr2=9Pr1