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(Î¸, Ď†) = (ÎĽ0 / 4Ď€) * (L / r) * [(cos(Î¸/2))^2 * sin(Î¸)] * (cos(m * Ď†) – cos(Î¸))

where:

- E(Î¸, Ď†) is the electric field at a point in space.
- ÎĽ0 is the vacuum permeability.
- L is the length of the dipole.
- r is the radial distance from the dipole.
- Î¸ is the polar angle.
- Ď† is the azimuthal angle.
- m = 2Ď€L / Î» is the number of wavelengths along the length of the dipole, with Î» 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 (Î¸) and the azimuthal angle (Ď†) 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(Î¸, Ď†) = (ÎĽ0 / 4Ď€) * (L / r) * [(cos(Î¸/2))^2 * sin(Î¸)] * (cos(m * Ď†) – cos(Î¸))

where:

- E(Î¸, Ď†) is the electric field at a point in space.
- ÎĽ0 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.
- Î¸ is the polar angle, the angle between the vector connecting the point to the dipole and the positive z-axis.
- Ď† 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 = 2Ď€L / Î» is the number of wavelengths along the length of the dipole, with Î» 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:
âž˘ START
âž˘ Read length of diploe L
âž˘ Assign eta values (eta=120*pi)
âž˘ Initialize Io value IO=1
âž˘ Setting theta value in radians:
o Theta =(1:180)./pi/180
âž˘ Setting up step size
âž˘ Calculating Radiation intensity
o U=eta*(abs(IO)^2/(8*pi))*((cos(cl*pi)*cos(theta))cos(l8pi)./sin(theta))
âž˘ Calculating max radiation intensity by max keyword
âž˘ Calculating radiation power
o Prad=sum(u.*sin(theta)*dth*2*pi)
âž˘ Calculating directivity
o D=(4*pi*umax)/prad
âž˘ Directivity in dB
âž˘ Calculating radiating resistance
o Pr=(2*pi)/abs(io^2)
âž˘ Calculating current and distribution
âž˘ Calculating of electrical field pattern
âž˘ Initialize theta, r, lambda and calculate k values and E values
âž˘ Polar plot (theta, abs(E))
âž˘ 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

## Explore More Projects on Matlab

- Microwave and Antenna Various Matlab CodesMicrowave and Antenna Various Matlab Codes. Some of the Projects are below. Polar form for a Symmetrical Dipole of Finiteâ€¦ Read more: Microwave and Antenna Various Matlab Codes
- Multiple Input Multiple Output(MIMO) using MatlabIntroduction Multiple Input Multiple Output(MIMO) using Matlab. Multiple Input Multiple Output (MIMO) is a technology used in wireless communication systemsâ€¦ Read more: Multiple Input Multiple Output(MIMO) using Matlab
- Pulse Width Modulation(PWM) working Principal using MatlabIntroduction Pulse Width Modulation(PWM) working Principal using Matlab. PWM stands for Pulse Width Modulation. It is a type of digitalâ€¦ Read more: Pulse Width Modulation(PWM) working Principal using Matlab
- Quadrature Amplitude Modulation(QAM): Theory and MatlabIntroduction Quadrature Amplitude Modulation(QAM): Theory and Matlab QAM stands for Quadrature Amplitude Modulation. It is a method of combining twoâ€¦ Read more: Quadrature Amplitude Modulation(QAM): Theory and Matlab
- Polar form for a Symmetrical Dipole of Finite Length: Matlab ScriptPolar form for a Symmetrical Dipole of Finite Length: Matlab Script. This Experiment include finding of: Introduction The polar formâ€¦ Read more: Polar form for a Symmetrical Dipole of Finite Length: Matlab Script
- Radiated Power and Maximum Directivity of any Antenna: Theory and Matlab codeRadiated Power and Maximum Directivity of any Antenna: Theory and Matlab code. Introduction The radiated power of an antenna refersâ€¦ Read more: Radiated Power and Maximum Directivity of any Antenna: Theory and Matlab code
- Polar form for a Loop Antenna with Uniform Current: Theory and Matlab codeIntroduction The polar form for a loop antenna with uniform current can be determined using the far-field approximation and theâ€¦ Read more: Polar form for a Loop Antenna with Uniform Current: Theory and Matlab code
- Two Dimensional(2-D) Polar and Semi-Polar Patters using Matlab codeIntroduction Two Dimensional(2-D) Polar and Semi-Polar Patters using Matlab code. Two-dimensional (2-D) polar and semi-polar patterns are graphical representations ofâ€¦ Read more: Two Dimensional(2-D) Polar and Semi-Polar Patters using Matlab code

## Join us for Regular Updates

Telegram | Join Now |

Join Now | |

Join Now | |

Join Now | |

Join Now | |

Join our Telegram | connectkreations |

**About Connect Kreations**

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..đź¤“

**Our Websites: Connect Kreations****Our Websites: StudentsDev Connect Kreations**