Question

An antenna has radiation resistance of $68\Omega$, a load resistance of $10\Omega$ and a power gain of $16$. The directive gain of the antenna is
A. $15$
B. $16.02$
C. $17.08$
D. $18.35$

Answer 1

Hint:- The power gain or gain of an antenna shows how strong an antenna can send or receive signal in a specific direction. Power gain is the measure of an antenna's efficiency and directivity. The directivity of an antenna is the measure of concentration of an antenna's radiation pattern.

Complete step-by-step solution :Step I:
An antenna is supplied with some power and the strength of the electromagnetic field in the surrounding space is measured. The efficiency of an antenna is defined as the ratio of the power radiated to the power supplied to the antenna. It is denoted by $\eta$.
Given power radiation resistance of the antenna is $68\Omega$
Total power supplied to the antenna is given by $R + R(l) = 68 + 10$
Step II:
For the circuits that are made in the form of RLC series circuit, the formula of efficiency is written as
$\eta = \dfrac{R}{{R + R(l)}}$
$= \dfrac{{68}}{{68 + 10}}$
$= \dfrac{{68}}{{78}}$
$= 0.872$
Step III:
The formula used for power gain is written as
Power gain $= \eta .G$
Directive gain, $G = \dfrac{{Power Gain}}{\eta }$
$G = \dfrac{{16}}{{0.872}}$
$G = 18.35$
Step IV:
Therefore, the directive gain of the antenna is $18.35$.
Hence, Option D is the right answer.

Note:- When an antenna receives signal, gain of the antenna measures how well antenna picks up the waves scattered in the air. It then concentrates into an electrical signal. But while transmitting the signal, gain represents how well the antenna converts electrical input into the radio waves. The antenna’s increase their gain by concentrating signals over a smaller area. But if the gain of the antenna is increased only in one direction then it will reduce the gain in other directions.