Question

A) If a given directional antenna can receive 15 times the power of an isotropic antenna, what is

Answer 1

The gain of the directional antenna is calculated based on the comparison

with an hypothetical isotropic antenna.

• a) The gain in dBi of the isotropic antenna is approximately 11.76 dBi

• b) The power received by the isotropic antenna is approximately 0.61 mW

Reasons:

a) The number of times the power of the directional antenna is stronger than the  isotropic antenna, G = 15 times

The gain in dBi is given as follows;

$\displaystyle G = \mathbf{10^{\dfrac{G(dBi)}{10} }}$

Which gives;

$\displaystyle 15 = 10^{\dfrac{G(dBi)}{10} }$

$\displaystyle \dfrac{G(dBi)}{10} = \frac{ln(15)}{ln(10)}$

$\displaystyle G(dBi)} = 10 \times \frac{ln(15)}{ln(10)} \approx 11.76$

The power gain of the isotropic antenna, G(dBi) ≈ 11.76 dBi

b) When the gain of the directional antenna is 2.15 dBi and it received 1 mW of power, we have;

The number of times stronger the directional antenna is, is found as follows;

$\displaystyle G = 10^{\dfrac{2.15}{10} } \approx \mathbf{1.64}$

The 2.15 dBi directional antenna receives the signal approximately 1.64 times stronger than the isotropic antenna, therefore;

• $\displaystyle The \ power \ received \ by \ the \ isotropic \ antenna = \frac{1 \, mW}{1.64} \approx \underline {0.61 \, mW}$

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