ParallelPlate.m

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% FILENAME:         ParallelPlate.m
% COURSE:           EE5322--21st Century Electromagnetics
% INSTRUCTOR:       Raymond C. Rumpf
% NAME:             Manuel F. Martinez
% SEMESTER:         Spring 2018
% DUE DATE:         02/06/2018
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% RESTORE MATLAB STATE
clear all;
close all;
clc;

% UNITS
meters      = 1;
seconds     = 1;
degrees     = pi/180;
F           = 1;
H           = 1;

% CONSTANTS
e0 = 8.85418782e-12 * F/meters;
u0 = 1.25663706e-6 * H/meters;
N0 = sqrt(u0/e0);
c0 = 299792458 * meters/seconds;

% OPEN FIGURE WINDOW
figure('Color','w');

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%% DASHBOARD
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% TRANSMISSION LINE PARAMETERS
w   = 3;  % Width of traces
h   = 1;  % Separation between traces
er  = 2.5 * eye(3,3);    % Permittivity of substrate

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%% DEFINE GRID
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% GRID PARAMETERS
BUFF  = 3 * w; % Spacer region
Sx    = BUFF + w + BUFF;
Sy    = BUFF + h;
Nx    = 512;
Ny    = 512;

% INITIAL GUESS AT GRID RESOLUTION
dx = Sx/Nx;
dy = Sy/Ny;

% SNAP GRID TO CRITICAL DIMENSIONS
nx = ceil(w/dx);
dx = w/nx;
ny = ceil(h/dy);
dy = h/ny;

% COMPUTE 2x GRID
Nx2 = 2*Nx;
dx2 = dx/2;
Ny2 = 2*Ny;
dy2 = dy/2;

% GRID AXES
xa = [0:Nx-1]*dx; xa = xa - mean(xa);
ya = [0:Ny-1]*dy; ya = ya - mean(ya);

% 2x GRID AXES
xa2 = [0:Nx2-1]*dx2; xa2 = xa2 - mean(xa2);
ya2 = [0:Ny2-1]*dy2; ya2 = ya2 - mean(ya2);

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%% BUILD DEVICE ON GRID
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% INITIALIZE SIGNAL TRACES
SIG.V = [0 0.5 -0.5];
SIG.GND = zeros(Nx,Ny);
SIG.SIG1 = SIG.GND;
SIG.SIG2 = SIG.GND;

% FORCE CONDUCTORS
SIG.GND(:,1)  = 1;
SIG.GND(:,Ny) = 1;
SIG.GND(1,:)  = 1;
SIG.GND(Nx,:) = 1;
% Calculate indices
nx1 = 1 + floor((Nx-nx)/2);
nx2 = nx1 + nx - 1;
ny1 = 1 + floor((Ny-ny)/2);
ny2 = ny + ny1 - 1;
% Build SIG.SIG1
SIG.SIG1(nx1:nx2,ny1) = 1;
% Build SIG.SIG2
SIG.SIG2(nx1:nx2,ny2) = 1;

% DEFINE DIELECTRICS ON 2X GRID
ER2xx = er(1,1) * ones(Nx2,Ny2);
ER2xy = er(1,2) * ones(Nx2,Ny2);
ER2yx = er(2,1) * ones(Nx2,Ny2);
ER2yy = er(2,2) * ones(Nx2,Ny2);

% PARSE MATERIALS TO 1X GRID
DEV.ERxx = ER2xx(2:2:Nx2,1:2:Ny2);
DEV.ERxy = ER2xy(1:2:Nx2,2:2:Ny2);
DEV.ERyx = ER2yx(2:2:Nx2,1:2:Ny2);
DEV.ERyy = ER2yy(1:2:Nx2,2:2:Ny2); 

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%% PERFORM SIMULATION
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% CALL anisotropicTL.m
RES = [dx dy];
TL = anisotropicTL(RES,DEV,SIG);

% Calculate total field
E = sqrt(abs(TL.Ex).^2 + abs(TL.Ey).^2);

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%% POST-PROCESS DATA
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% SHOW NUMERICAL PARAMETERS ON CONSOLE
disp(['C    = ' num2str(TL.C/1e-12,'%3.5f') ' pF/m']);
disp(['L    = ' num2str(TL.L/1e-09,'%3.5f') ' nH/m']);
disp(['Z0   = ' num2str(TL.Z0) ' Ohms']);
disp(['nEff = ' num2str(TL.nEff)]);

% VISUALIZE POTENTIAL AND FIELDS
imagesc(xa,ya,TL.V');
colormap(hot);
colorbar;
axis equal tight;
set(gca,'FontSize',12,'FontWeight','bold');
title('Electric Potential V','FontSize',14);
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);

figure('Color','w');
imagesc(xa,ya,E');
caxis([0 1]);
colorbar
colormap(hot);
axis equal tight;
set(gca,'FontSize',12,'FontWeight','bold');
title('|E|','FontSize',14);
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
hold on;

% ADD QUIVER
[Y,X] = meshgrid(ya,xa);
quiver(X(1:16:Nx,1:16:Ny),Y(1:16:Nx,1:16:Ny),TL.Ex(1:16:Nx,1:16:Ny),...
      TL.Ey(1:16:Nx,1:16:Ny),'Color','w');
hold off;

% VISUALIZE DIELECTRIC TENSORS
figure('Color','w');
a = subplot(2,2,1);
set(a,'FontSize',12);
imagesc(xa2,ya2,ER2xx');
title('$\varepsilon_{xx}$','FontSize',14,'Interpreter','LaTex');
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
caxis([1.5 +1.5*max(ER2xx(:))]);
colorbar;
colormap(hot);

a = subplot(2,2,2);
set(a,'FontSize',12);
imagesc(xa2,ya2,ER2xy');
title('$\varepsilon_{xy}$','FontSize',14,'Interpreter','LaTex');
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
caxis([-2*max(ER2xy(:)) +2*max(ER2xy(:))]);
colorbar;
colormap(hot);

a = subplot(2,2,3);
set(a,'FontSize',12);
imagesc(xa2,ya2,ER2yx');
title('$\varepsilon_{yx}$','FontSize',14,'Interpreter','LaTex');
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
caxis([-2*max(ER2yx(:)) +2*max(ER2yx(:))]);
colorbar;
colormap(hot);

a = subplot(2,2,4);
set(a,'FontSize',12);
imagesc(xa2,ya2,ER2yy');
title('$\varepsilon_{yy}$','FontSize',14,'Interpreter','LaTex');
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
caxis([1.5 +1.5*max(ER2yy(:))]);
colorbar;
colormap(hot);

% PLOT CONDUCTORS
figure('Color','w');
subplot(1,2,1);
imagesc(xa,ya,SIG.GND');
title('GND','FontSize',14);
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
axis square;
colormap(gray);
colorbar;
caxis([0 1]);

subplot(1,2,2);
imagesc(xa,ya,SIG.SIG1' | SIG.SIG2');
title('SIG1 | SIG2','FontSize',14);
xlabel('x (mm)','FontSize',12);
ylabel('y (mm)','FontSize',12);
axis square;
colormap(gray);
colorbar;
caxis([0 1]);