Radiated Power and Maximum Directivity of any Antenna: Theory and Matlab code.

## Introduction

The radiated power of an antenna refers to the amount of power that is actually emitted into the surrounding space, in the form of electromagnetic waves. This value is typically measured in watts.

The maximum directivity of an antenna is a measure of its ability to concentrate the radiated power in a specific direction, rather than dispersing it equally in all directions. This value is expressed in decibels (dB) and indicates the gain of the antenna compared to an isotropic radiator, which would have an equal amount of power in all directions. The higher the directivity, the more focused the antenna’s transmission will be in a specific direction.

## Software Required

Matlab Software offline Recommended or online software.

## Procedure

- Define the current distribution on the antenna: This can be done using a mathematical model or by measuring the current distribution on a physical antenna.
- Calculate the electric and magnetic fields: Use Maxwell’s equations to calculate the electric and magnetic fields generated by the antenna.
- Calculate the Poynting vector: The Poynting vector is the product of the electric and magnetic fields, and is a measure of the energy flow in a particular direction.
- Integrate the Poynting vector over a spherical surface: To obtain the radiated power, integrate the Poynting vector over a spherical surface that surrounds the antenna.
- Calculate the efficiency: The efficiency is the ratio of the radiated power to the input power to the antenna.
- Calculate the average power density: Divide the radiated power by the surface area of the sphere.
- Calculate the maximum power density: Determine the direction in which the radiated power is the highest, and calculate the power density in that direction.
- Calculate the directivity gain: Take the logarithm of the ratio of the maximum power density to the average power density, and express the result in dB.

## Algorithm

```
➢ START
➢ Set the phase degree range 0 to 180
➢ Phi degree=0:360
➢ Convert the degree values of radius
➢ Set elevation angles theta Ranges 0-180
➢ Theta_degree=0:180
➢ Convert the degree values to radius
➢ Setting up the integration step size
➢ Convert it into radiation pattern of an antenna using meshgrid
➢ U=[sin(theta).*sin(phi)].^2
➢ Calculating average pattern
➢ P_avg=sum(sum(u.*sin(theta)*dth*dph))
➢ Calculating directivity
➢ D=4*pi*max(max(u))/p_avg
➢ Directivity in
```

## Matlab code

```
% Radiated power and Directivity of an antenna:
close all;
clear all;
clc;
format long;
%Angle definition:
%Azimuth angle phi ranges between 0 to 360 degrees:
phi_degree = 0:360;
phi_rad = phi_degree * pi/180; %Converting degrees to radians
%Elevation angle theta ranges between 0 to 180 degres:
theta_degree = 0:180;
theta_rad = theta_degree* pi/180; %Converting degrees to radian
%integration step size:
dth=theta_rad (2) -theta_rad (1);
dph=phi_rad (2) -phi_rad (1) ;
[THETA, PHI] =meshgrid (theta_rad, phi_rad);
%Radiation pattern of an antenna:
U = (sin (THETA).*sin (PHI) ).^2;
%Performing nunerical integration to obtain
%average power radiated by the antenna:
P_avg=sum(sum (U.*sin(THETA)*dth*dph) );
%Note sum() is discrete time equivalent of integration
%use of sum() twice is to integrate w. r.t. theta and phhi
%Directivity:
%D=4*pi*P_max (theta, phi)/P_avg(theta, phi)
D=4 *pi*max(max (U) )/P_avg;
D_db = 10*log10(D);
fprintf('Average power radiated by the antenna is %f\n', P_avg);
fprintf('Directivity of the antenna is %f(dimensionless) and %f(in dB)\n',D,D_db);
surf(U);
```

## Code Output

```
Output in Command Prompt
Average power radiated by the antenna is 4.188790
Directivity of the antenna is 3.000000(dimensionless) and 4.771213(in dB)
```

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