MATLAB: Hi I want to plot the transcendental equation for dielectric waveguide the equation for that is

transcendental equation for wave guide

tan(x)=sqrt(v^2-x^2)/x where v is 8.219. the hand made plot is in the figure I know the basics but still couldn't figure out. any help would be appreciated.

Best Answer

This should get you started:
v = 8.219;
wvgd = @(x) sqrt(v^2-x.^2)./x;
intx = @(x) tan(x) - wvgd(x);
x = linspace(0,2.5*pi,500);
xi = 1:max(x);
for k1 = 1:length(xi)
    itx(k1) = fzero(intx, xi(k1));      % Find Intersections Of tan(x) & wvgd(x)
end
itx = unique(itx);
figure(1)
plot(x, wvgd(x))
hold on
plot(x, tan(x))
plot(itx, tan(itx), 'pr', 'MarkerSize',7)
hold off
grid
axis([0  max(x)    -50  50])
lblx = strsplit(sprintf('(%.2f,%.2f) ', [itx; tan(itx)]));
text(itx, tan(itx), lblx(1:length(itx)), 'VerticalAlignment','bottom', 'HorizontalAlignment','center')
This gives you the upper curve and the values of its intersection with your waveguide equation. I know nothing about waveguide engineering, so I don’t know how to calculate the lower curve you drew. I have to leave that for you.
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