# Question 66a5c

Nov 27, 2017

Anetnna Efficiency: \eta \equiv P_{rec}/P_{"inc"} = A_e/A;#
${P}_{\text{inc}}$ - Incident power; $\setminus q \quad {P}_{r e c}$ - Received power;
${A}_{e}$ - Effective area; $\setminus \quad \setminus q \quad A$ - Actual physical aperture area.

#### Explanation:

When a receiver antenna of physical aperture area $A$ is held normal to a radiation of intensity $I$, the total power incident on the antenna is:

${P}_{\text{in}} = I . A$

But not all the incident radiation is received by the antenna. The received power is always less than the incident power. We can treat it as though we have an antenna of smaller effective aperture area ${A}_{e}$ that receives all that is incident on it. Suppose if the received power is ${P}_{r e c}$, then we can write it as,

${P}_{r e c} = I . {A}_{e}$

Antenna Efficiency is defined as the ratio of the actual received radiation power to the total radiation power incident on it.

$\setminus \eta \setminus \equiv {P}_{r e c} / {P}_{\text{inc}} = \frac{\setminus \cancel{I} . {A}_{e}}{\setminus \cancel{I} . A} = {A}_{e} / A$