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a) If a given directional antenna can receive 15 times the power of an isotropic antenna, what is
its gain in dBi?
b) If the gain of a directional antenna is 2.15 dBi and it received 1mW of power, how much
power would have been received by an isotropic antenna?

A If A Given Directional Antenna Can Receive 15 Times The Power Of An Isotropic Antenna What Is Its Gain In DBi B If The Gain Of A Directional Antenna Is 215 DB class=

Sagot :

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;

[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;

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

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