##### Polar form for a Symmetrical Dipole of Finite Length: Matlab Script
Share Now...

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),
• 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.

## 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
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 directivity
➢ Directivity in dB
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);

D_db = 10*log10(D);

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 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

## Explore More Projects on Matlab

We the team Connect Kreations have started a Blog page which is eminently beneficial to all the students those who are seeking jobs and are eager to develop themselves in a related area. As the world is quick on uptake, our website also focuses on latest trends in recent technologies and project learning and solutions. We are continuously putting our efforts to provide you with accurate, best quality, and genuine information. Here we also have complete set of details on how to prepare aptitude, interview and more of such placement/ off campus placement preparation.

Connect Kreations is excited to announce the expansion of our services into the realm of content creation! We are now offering a wide range of creative writing services, including poetry, articles, and stories.

Whether you need a heartfelt poem for a special occasion, a thought-provoking article for your blog or website, or an engaging story to captivate your audience, our team of talented writers is here to help. We have a passion for language and a commitment to creating high-quality content that is both original and engaging.

Our services are perfect for individuals, businesses, and organizations looking to add a touch of creativity and personality to their content. We are confident that our unique perspectives and diverse backgrounds will bring a fresh and exciting voice to your project.

Thank you for choosing Connect Kreations for your content creation needs. We look forward to working with you and helping you to bring your vision to life!

The website is open to all and we want all of you to make the best use of this opportunity and get benefit from it..🤓

Share Now... Articles: 157