Question

What is the gain of a Hertzian dipole over an isotropic antenna?

Answer 1

Hint :In order to solve the question, we first need to define the both types of the antenna, Hertzian dipole antenna and the isotropic antenna, then converting the gain for the Hertzian antenna into decibel, and relating it with the isotropic antenna, we can find its gain over the isotropic antenna.
The formula to convert the power gain to decibel is
 $ Power Gain\left( dB \right)=10\times \log \left( power gain \right) $
Gain for an isotropic antenna is $ 1 $ .

Complete Step By Step Answer:
The Hertzian dipole is a dipole antenna. It consists of an infinitesimally small current source acting in the free space, however a Hertzian antenna cannot truly exist but a very small dipole can be approximated as a Hertzian dipole. Now, an isotropic antenna is the one that emits the signal equally in all the directions, i.e. at the same distances the power transmitted by an isotropic antenna is the same whatever the direction may be.
The value of gain for an isotropic antenna is equal to $ 1.0 $ , that is , a unit gain.
Now for the Hertzian dipole, it has a gain of $ 1.64 $ ,
Converting this gain in the unit of decibel, we get
 $ \begin{align}
  & 10\times \log \left( power gain \right) \\
 & \Rightarrow 10\times \log \left( 1.64 \right) \\
 & \Rightarrow 10\times 0.2148 \\
 & \Rightarrow 2.148dB \\
\end{align} $
This is approximately equal to $ 2.15dB $ .
Therefore, the gain is $ 2.15dB $ over the isotropic antenna which is a unit dipole.

Note :
A dipole antenna is any one of the antennas that produce a radiation pattern approximating that of an electric dipole with a radiating structure supporting a line current which is so energized that the current has only one mode at each end. The Isotropic dipole is a unit dipole.