The gain of the directional antenna is calculated based on the comparison
with an hypothetical isotropic antenna.
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;
[tex]\displaystyle G = \mathbf{10^{\dfrac{G(dBi)}{10} }}[/tex]
Which gives;
[tex]\displaystyle 15 = 10^{\dfrac{G(dBi)}{10} }[/tex]
[tex]\displaystyle \dfrac{G(dBi)}{10} = \frac{ln(15)}{ln(10)}[/tex]
[tex]\displaystyle G(dBi)} = 10 \times \frac{ln(15)}{ln(10)} \approx 11.76[/tex]
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;
[tex]\displaystyle G = 10^{\dfrac{2.15}{10} } \approx \mathbf{1.64}[/tex]
The 2.15 dBi directional antenna receives the signal approximately 1.64 times stronger than the isotropic antenna, therefore;
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