Question

An antenna with an efficiency of 90% has a maximum radiation intensity of 0.5 W/Steradian. Calculate the directive gain of the antenna when the input power to the antenna is 0.4 W.
1. 18.23
2. 17.4
3. 11.2
4. 21.6

Answer 1

Correct Answer - Option 2 : 17.4

Directive Gain (D):

It is defined as the ratio of radiation intensity due to the test antenna to isotropic antenna (hypothetical antenna that radiates uniformly in all direction)

\(D = \frac{U}{U_0}=\frac{4\pi U}{P_{rad}}\)

Where,

U = radiation intensity due to test antenna, in watts per unit solid angle

U0  = radiation intensity due to an isotropic antenna, in watts per unit solid angle

Prad =total power radiated in watts

Since U is a directional dependent quantity, the directive gain of an antenna depends on the angle θ and Φ. If the radiation intensity assumes its maximum value then the directive gain is called the Directivity (D₀).

\(D_0=\frac{U_{max}}{U_0}=\frac{4\pi U_{max}}{P_{in}}\)

Calculation:

Given:

Efficiency, η = 0.90, U_max = 0.5 W/sr

Also, with Pin = 0.4 W, the radiated power will be:

P_rad = 0.4 × 0.9 = 0.36 W

∴ The directivity will be:

\(D= \frac{{4\pi \; \times \;0.5}}{{0.36}}\)

D = 17.46