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2 years ago

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

Engineering

1 answer:

Sauron [17]2 years ago

4 0

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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