Taller de Antenas: Ejercicios de Campo Eléctrico en Matlab, Ejercicios de Antenas y Propagación de Radios

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Presentado por:

Taller de antenas

Facultad de ingeniería

Bogotá D.C.

Punto 1

Código :

%%%%%%%DOS CARGAS%%%%%%%%%%%%%%%%

% This simple program computes the Electric Fields due to dipole % in a 2-D plane using the Coulomb's Law %-------------------------------------------------------------------------% clc close all; clear all; %-------------------------------------------------------------------------% % SYMBOLS USED IN THIS CODE %-------------------------------------------------------------------------% % E = Total electric field % Ex = X-Component of Electric-Field % Ey = Y-Component of Electric-Field % n = Number of charges % Q = All the 'n' charges are stored here % Nx = Number of grid points in X- direction % Ny = Number of grid points in Y-Direction % eps_r = Relative permittivity % r = distance between a selected point and the location of charge % ex = unit vector for x-component electric field % ey = unit vector for y-component electric field %-------------------------------------------------------------------------% %-------------------------------------------------------------------------% % INITIALIZATION % Here, all the grid, size, charges, etc. are defined %-------------------------------------------------------------------------% % Constant 1/(4piepsilon_0) = 910^ k = 910^9; % Enter the Relative permittivity eps_r = 1; charge_order = 10^-9; % milli, micro, nano etc.. const = k*charge_order/eps_r; % Enter the dimensions Nx = 101; % For 1 meter Ny = 101; % For 1 meter % Enter the number of charges. n = 2;

xlabel('x ','fontsize',14); ylabel('y ','fontsize',14); title('Electric field distribution, E (x,y) in V/m','fontsize',14); %-------------------------------------------------------------------------% % REFERENCE % SADIKU, ELEMENTS OF ELECTROMAGNETICS, 4TH EDITION, OXFORD %-------------------------------------------------------------------------% Grafica: Explicación:

En este código tenemos 2 cargas una positiva y una negativa en un plano 2d|

PUNTO 2

CODIGO:

%%%%%%%TRES CARGAS%%%%%%%%%%%%%%%%

% This simple program computes the Electric Fields due to dipole % in a 2-D plane using the Coulomb's Law %-------------------------------------------------------------------------% clc close all; clear all; %-------------------------------------------------------------------------% % SYMBOLS USED IN THIS CODE %-------------------------------------------------------------------------% % E = Total electric field % Ex = X-Component of Electric-Field % Ey = Y-Component of Electric-Field % n = Number of charges % Q = All the 'n' charges are stored here % Nx = Number of grid points in X- direction % Ny = Number of grid points in Y-Direction % eps_r = Relative permittivity % r = distance between a selected point and the location of charge % ex = unit vector for x-component electric field % ey = unit vector for y-component electric field %-------------------------------------------------------------------------% %-------------------------------------------------------------------------% % INITIALIZATION % Here, all the grid, size, charges, etc. are defined %-------------------------------------------------------------------------% % Constant 1/(4piepsilon_0) = 910^ k = 910^9; % Enter the Relative permittivity eps_r = 1; charge_order = 10^-9; % milli, micro, nano etc.. const = k*charge_order/eps_r; % Enter the dimensions Nx = 101; % For 1 meter Ny = 101; % For 1 meter % Enter the number of charges. n = 3;

xlabel('x ','fontsize',14); ylabel('y ','fontsize',14); title('Electric field distribution, E (x,y) in V/m','fontsize',14); %-------------------------------------------------------------------------% % REFERENCE % SADIKU, ELEMENTS OF ELECTROMAGNETICS, 4TH EDITION, OXFORD %-------------------------------------------------------------------------% GRAFICA : EXPLICACION: En ese código tenemos 3 cargas positivas en un plano 2d

PUNTO 3

CODIGO: % Constant 1/(4piepsilon_0) = 9*10^

k = 910^9; % Enter the Relative permittivity eps_r = 1; charge_order = 10^-9; % milli, micro, nano etc.. const = kcharge_order/eps_r; % Enter the dimensions Nx = 101; % For 1 meter Ny = 101; % For 1 meter % Enter the number of charges. n = 3; % Electric fields Initialization E_f = zeros(Nx,Ny); Ex = E_f; Ey = E_f; % Vectors initialization ex = E_f; ey = E_f; r = E_f; r_square = E_f; % Array of charges Q = [-1,1,-1,1]; % Array of locations X = [5,-5,0]; Y = [0,0,-5]; %------------------------------------------------------------------------ -% % COMPUTATION OF ELECTRIC FIELDS %------------------------------------------------------------------------ -% % Repeat for all the 'n' charges for k = 1:n q = Q(k); % Compute the unit vectors for i=1:Nx for j=1:Ny r_square(i,j) = (i-51-X(k))^2+(j-51-Y(k))^2; r(i,j) = sqrt(r_square(i,j)); ex(i,j) = ex(i,j)+(i-51-X(k))./r(i,j);

GRAFICA : EXPLICACION: Se modifica el código del punto 2 para que genere carga positivas y negativas

PUNTO 4

CODIGO:

%%%%%%%POLARIZATION FIRST%%%%%%%%%%%%%%%%

fontSize = 20; A = 10; % Amplitude. t = linspace(0, 2 * pi, 40); signal = A .* cos(t) + A .* sin(t); stem(t, signal, 'bo-', 'LineWidth', 2); xlabel('t', 'FontSize', fontSize); ylabel('signal', 'FontSize', fontSize); title('RHCP', 'FontSize', fontSize); grid on; % Enlarge figure to full screen. set(gcf, 'units','normalized','outerposition',[0 0 1 1]); % Give a name to the title bar. set(gcf,'name','Demo by ImageAnalyst','numbertitle','off')

GRAFICA:

plot( x2, 0x2,'k','LineWidth',3); plot( x2, 0.3x2,'k','LineWidth',3); plot(0*x2, x2,'k','LineWidth',3); hold off axis([-4 20 -2 3]) title('Linear polarized wave','fontsize',18) % title('Right-handed circularly polarized wave','fontsize',18) % title('Left-handed circularly polarized wave','fontsize',18) M(:,n) = getframe(gcf); end clf reset set(gcf,'Position',[100 100 800 600]) axis off movie(M,1,6) close all Grafica:

EXPLICACION:

Vemos en la primera grafica una reñal RHCP con

deltas y en la 2 grafica el movimiento 3d del

campo polarizada

PUNTO 5

CODIGO:

clear all % Parameters for different media % free space: kr=1, ki=1, phi= % plasma medium: kr=0, ki=1, phi=pi/ % very lossy medium: kr=1, ki=1, phi=pi/ kr = 11; ki = 01; phi = pi/2; xmax = 30; xmin = -4; delx = 0.1; x = [ 0:delx:xmax]; x2 = [xmin:delx:xmax]; framemax = 48; M = moviein(framemax); set(gcf,'Position',[100 100 640 480]) for n=1:framemax % % ==== Right-handed circularly polarized wave % E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); % E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax+phi); % ==== Left-handed circularly polarized wave E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax-phi); E=E1+E2; figure(1)

GRAFICA: EXPLICACION: Notamos que con una polarización diferente la onda se graficada en 3d tiene un movimiento diferente en el espacio

PUNTO 6

CODIGO

%%%%POLARIZACION OBLICUA

clear all % Parameters for different media % free space: kr=1, ki=1, phi= % plasma medium: kr=0, ki=1, phi=pi/ % very lossy medium: kr=1, ki=1, phi=pi/ kr = 11; ki = 01; phi = 0; xmax = 30; xmin = -4; delx = 0.1; x = [ 0:delx:xmax]; x2 = [xmin:delx:xmax]; framemax = 48; M = moviein(framemax); set(gcf,'Position',[100 100 640 480]) for n=1:framemax % % ==== Right-handed circularly polarized wave % E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); % E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax+phi); % ==== Left-handed circularly polarized wave E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax-phi); E=E1+E2; figure(1) whitebg([1 1 1]); %plot(x, E ,'r' ,'LineWidth',3); plot(x+round(100E2)/30,E,'b' ,'LineWidth',3); hold on plot(x(1)+round(100E2(1))/30,E(1),'ro' ,'LineWidth',3); % plot(x, S ,'g' ,'LineWidth',3);

EXPLICACION: Notamos que con una polarización diferente la onda se graficada en 3d tiene un movimiento diferente en el espacio

PUNTO 7

CODIGO:

%%%%%%%%%%%%POLARIZACION CIRCULAR

clear all % Parameters for different media % free space: kr=1, ki=1, phi= % plasma medium: kr=0, ki=1, phi=pi/ % very lossy medium: kr=1, ki=1, phi=pi/ kr = 11; ki = 01; phi = pi/2; xmax = 30; xmin = -4; delx = 0.1; x = [ 0:delx:xmax]; x2 = [xmin:delx:xmax]; framemax = 48; M = moviein(framemax); set(gcf,'Position',[100 100 640 480]) for n=1:framemax % % ==== Right-handed circularly polarized wave % E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); % E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax+phi); % ==== Left-handed circularly polarized wave E1 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax ); E2 = exp(-0.3.x.ki).cos(kr.x-2pin/framemax-phi); E=E1+E2; figure(1) whitebg([1 1 1]); %plot(x, E ,'r' ,'LineWidth',3); plot(x+round(100*E2)/30,E,'b' ,'LineWidth',3);