Polar form for a Symmetrical Dipole of Finite Length: Matlab Script
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Polar form for a Symmetrical Dipole of Finite Length: Matlab Script. This Experiment include finding of:

  • MATLAB program to compute the: (a) Maximum directivity (dimensionless and in dB),
  • Radiation resistance (Rr),
  • Normalized current distribution,
  • Directivity pattern (in dB) in polar form,
  • Normalized far-field amplitude pattern (H theta, in dB) in Polar form for a Symmetrical Dipole of Finite Length.

Introduction

The polar form of a symmetrical dipole of finite length is given by:

E(θ, φ) = (μ0 / 4π) * (L / r) * [(cos(θ/2))^2 * sin(θ)] * (cos(m * φ) – cos(θ))

where:

  • E(θ, φ) is the electric field at a point in space.
  • μ0 is the vacuum permeability.
  • L is the length of the dipole.
  • r is the radial distance from the dipole.
  • θ is the polar angle.
  • φ is the azimuthal angle.
  • m = 2πL / λ is the number of wavelengths along the length of the dipole, with λ being the wavelength of the electromagnetic wave.

This expression is derived by assuming that the dipole is a current-carrying wire of finite length and that the electric field is calculated far from the dipole, so that the approximation of a point dipole can be used.

The polar form of a symmetrical dipole of finite length describes the electric field produced by the dipole at a given point in space. It is a mathematical expression that takes into account the polar angle (θ) and the azimuthal angle (φ) of the point relative to the dipole.

The polar form is derived by considering the dipole as a current-carrying wire of finite length, and by assuming that the electric field is calculated far from the dipole, so that the approximation of a point dipole can be used.

The expression for the polar form of a symmetrical dipole of finite length is given by:

E(θ, φ) = (μ0 / 4π) * (L / r) * [(cos(θ/2))^2 * sin(θ)] * (cos(m * φ) – cos(θ))

where:

  • E(θ, φ) is the electric field at a point in space.
  • μ0 is the vacuum permeability, a constant that relates the magnetic field to the current.
  • L is the length of the dipole.
  • r is the radial distance from the dipole.
  • θ is the polar angle, the angle between the vector connecting the point to the dipole and the positive z-axis.
  • φ is the azimuthal angle, the angle between the projection of the vector connecting the point to the dipole onto the x-y plane and the positive x-axis.
  • m = 2πL / λ is the number of wavelengths along the length of the dipole, with λ being the wavelength of the electromagnetic wave.

The expression shows that the electric field produced by the dipole depends on several factors, including the length of the dipole, the distance from the dipole, and the orientation of the point relative to the dipole.

Software Required

Matlab Software Recommended or online matlab.

Procedure

Algorithm

ALGORITHM:
➢ START 
➢ Read length of diploe L
➢ Assign eta values (eta=120*pi)
➢ Initialize Io value IO=1
➢ Setting theta value in radians:
o Theta =(1:180)./pi/180
➢ Setting up step size
➢ Calculating Radiation intensity
o U=eta*(abs(IO)^2/(8*pi))*((cos(cl*pi)*cos(theta))cos(l8pi)./sin(theta))
➢ Calculating max radiation intensity by max keyword
➢ Calculating radiation power 
o Prad=sum(u.*sin(theta)*dth*2*pi)
➢ Calculating directivity
o D=(4*pi*umax)/prad
➢ Directivity in dB
➢ Calculating radiating resistance
o Pr=(2*pi)/abs(io^2)
➢ Calculating current and distribution 
➢ Calculating of electrical field pattern
➢ Initialize theta, r, lambda and calculate k values and E values
➢ Polar plot (theta, abs(E))
➢ Stop

Matlab Code

clear all; close all; clc;
L = input('\n Length of dipole in wavelength:');

eta = 120*pi;

I0 = 1;
theta = (1:1:180)*pi/180;

dth = theta(2)-theta(1);

U = eta*(abs(I0)^2/(8*pi^2))*((cos((L*pi)*cos(theta))-cos(L*pi))./sin(theta)).^2;

UMAX=max(U);

Prad = sum(U.*sin(theta)*dth*2*pi);

D = (4*pi*UMAX)/Prad;
D_db = 10*log10(D);

Rr = (2*Prad)/(abs(I0)^2);

Z=linspace(-L/2,L/2,1000);
I=sin(2*pi*(L/2-abs(Z)));
figure(1),plot(Z, abs(I));
xlabel('Z^2{\prime}/\lambda','fontsize',12);
ylabel('Normalized current distribution','fontsize',12);

theta = (1:1:360)*(pi/180);
r=10;

lambda=0.3;
k=(2*pi)/lambda;

L=lambda/2;
E=1i*eta*I0*exp(-1i*k*r)*(1/(2*pi*r))*((cos(k*L*cos(theta)/2)-cos(k*L/2))./sin(theta));
figure(2),polarplot(theta, abs(E));

fprintf('\n Maximum radiated power: %fwatts\n',Prad);
fprintf('\n Maximum directivity: %f(dimensionaless)\n',D);
fprintf('\n Maximum directivity: %f(dbi)\n',D_db);
fprintf('\n Radiation resistance: %fohms\n',Rr);

Code Output

Wave form output


Command Window Output


Wave form 2 Output


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