![Polar form for a Loop Antenna with Uniform Current Theory and Matlab code](https://connectkreations.com/wp-content/uploads/2023/02/Polar-form-for-a-Loop-Antenna-with-Uniform-Current-Theory-and-Matlab-code.jpg)
- 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 loop antenna with uniform current.
Introduction
The polar form for a loop antenna with uniform current can be determined using the far-field approximation and the formula for the electric field radiated by a circular loop antenna.
In the far-field approximation, the radiated electric field is proportional to the derivative of the current with respect to time, and is given by:
E_theta = k * I * R * sin(theta) / (4 * pi * R)
where I is the current flowing in the loop, R is the radius of the loop, theta is the angle between the direction of observation and the plane of the loop, and k is the wave number.
For a loop antenna with uniform current, the radiated electric field in polar coordinates can be written as:
E_theta = k * I * R^2 / (2 * R) * sin(theta)
This expression represents the polar form for the electric field radiated by a loop antenna with uniform current, and can be used to compute the radiation characteristics of the antenna, such as the directivity, gain, and beamwidth.
Software Required
Matlab Software or online matlab
Algorithm
➢ START
➢ Initialize eta and theta
➢ Eta=(180*pi)
➢ Theta=(1:180)*(pi/180)
➢ Declare step-size
➢ Read radius of loop
➢ Calculate F and U
o F=besselj(1,(2*pi*A*sin(theta)))
o U=A^2*(2*pi)^2*F.^2*eta/8
➢ Calculate radiated power
o Prad=sum(u.*sin(theta)*dth*2*pi)
➢ Calculate directivity
o D=(A*pi*max(u))/prad
➢ Converting in dB
o D_db=10*log10(D)
➢ Calculating radiating resistance
o Rr=2*prad
➢ Initialize IO and r and lambda values
o IO=1, r=10, lambda=1
➢ Calculate k value
o K=(2*pi)/lambda
➢ Calculate H-theta,HdB and theta
➢ Polar plot normalized for field elevation pattern for loop with set up
rlim(f) constant & current
➢ sto
Matlab Code
clear all;close all; clc;
format long;
%-Definition of constants and initialization---%
%Free space impedance:
eta = 120*pi;
% Angle vector:
theta=(1:180)*(pi/180);
%Integration step size
dth = theta(2) - theta(1);
%Reading the radius of the loop
A = input ('\nSpecify radius of loop in wavelengths:');
%-------------------------------------------------------
%diation intensity calculation:
%A^2*omega*2 X mu^2 |I0|^2*J1^2(k*A*sin(theta))
%U
%8*eta
%Using omega = 2*pi*f and f = C/lambda,
%C 1/sqrt(mu * epsilon) and eta = sqrt{mu/epsilon) = 120*pi
%Simplified radiation intensity is given by:
% A2*(2*pi*2*eta |I0|^2*J1^2*(k*A*sin(theta))
%----------------------------------------------------------
F = besselj(1,(2.0*pi*A*sin(theta)));
U = A^2*(2*pi)^2*F.^2*eta/8;
%Radiated power:
Prad = sum(2*pi*U.*sin (theta) *dth);
%Directivity:
D = (4.0*pi*max(U))/Prad;
D_dB = 10*log10(D);
%Padiation resistance:
Rr = 2.0*Prad;
%Calculation of eievation pattern:
% -A*k*I0*exp(-jkr)
% H_theta = ----------------------*J1*(k*A*sin(theta))
% 2*r
% Normalized Peak Current
I0 = 1;
%Distance r in neters:
r=10;
% Wavellength in meters:
lambda=1;
%Wave nunber:
k=(2*pi)/lambda;
H_theta=-A*k*I0*exp(-1j*k*r)*besselj(1,k*A*sin(theta))/(2*r);
HdB= 20*log10(abs(H_theta)/max(abs(H_theta)));
HdB = [HdB fliplr(HdB)];
theta = [theta, theta+pi];
figure(1),polarplot(theta,HdB);
title ('Normalized far field elevation pattern for loop with constant current');
rlim([-40 01]);
%Printing the values:
fprintf('\nMaximum radiated power: %f watts\n',Prad);
fprintf(' \nMaximum directivity: %f (dimensionless) \n',D);
fprintf (' \nMaximum directivity: %f (dBi) \n' ,D_dB);
fprintf('\nRadiation resistance: %f ohms\n',Rr);
Code Output
![](https://connectkreations.com/wp-content/uploads/2023/02/Uniform.jpg)
![](https://connectkreations.com/wp-content/uploads/2023/02/Screenshot-195.png)
Conclusion
In conclusion, the polar form for a loop antenna with uniform current is a useful representation of the radiated electric field from the antenna. It provides information about the distribution of radiated power in different directions and can be used to evaluate the directivity, gain, and beamwidth of the antenna.
The polar form can be derived using the far-field approximation and the formula for the electric field radiated by a circular loop antenna. It takes into account the current flowing in the loop, the radius of the loop, and the angle between the direction of observation and the plane of the loop.
The polar form is an important tool for the analysis and design of loop antennas, and is widely used in various applications, such as radio communication, navigation, and sensing systems. Understanding the polar form and its application is essential for the optimization and performance improvement of loop antennas.
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 Finite… 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 systems… 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 digital… 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 two… 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 form… 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 refers… 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 the… 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 of… 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..🤓
- Our Websites: Connect Kreations
- Our Websites: StudentsDev Connect Kreations