Electromagnetic Theory55:170

Professor Karl E. Lonngren[lonngren@engineering.uiowa.edu

]4312 SC

office hours: 12:15-1:00 T & ThKent Hutchinson – teaching

assistant

Books

• References:• Fields and Waves in

Communication Systems• Fundamentals of

Electromagnetics with MATLAB 2007

Topics• MATLAB in EM • Electrostatics • Magnetostatics • Maxwell’s equations; boundary conditions• Transmission lines • Plane waves • Waveguides • Cavities • Radiation

Grading• Mid-term exam ¼ • Final exam ¼ • Term paper/lecture/movie ¼• Homework ¼

MATLAB• in the college computers•easy to use & learn•easy to produce 2-d & 3-d plots•ODE & PDE• integrate & differentiate•get pictures -- .m files in 070

web page

math• >> MATLAB icon• >> x = 1• x = • 1• >>• complex numbers• >> y = 1+1j (or 1+ 1i)• y =• 1.0000 + 1.0000i• >> z = x - y• z =• 0 - 1.0000i• >>

• >> x = 1; SAVE SPACE TRICK “ ; “• >> y = 2;• >> z = x * y; % multiply• >> z• z =• 2• >> w = x / y; % divide• >> w• w =• 0.5000

vectors - addition•a = 1ux + 2uy + 3uz

•b = 3ux + 2uy + 1uz•c = a + b •c = 4ux + 4uy + 4uz•a = [1 2 3];•b = [3 2 1];•c = a + b;•c • 4 4 4

vectors - dot product•a = 1ux + 2uy + 3uz

•b = 3ux + 2uy + 1uz•a • b = b • a •= 3 + 4 + 3 = 10•a = [1 2 3];•b = [3 2 1];•c = dot(a, b);•c• = 10

vectors - cross product

•a = 1ux + 0uy + 0uz ==> a = [1 0 0]

•b = 0ux + 1uy + 0uz ==> b = [0 1 0]

•d = cross (a,b)•d = • 0 0 1

vectors - cross product

•a = 1ux + 0uy + 0uz ==> a = [1 0 0]

•b = 0ux + 1uy + 0uz ==> b = [0 1 0]

•e = cross (b, a)•e =• 0 0 -1

x

y

z

A BB - A

|B - A| = norm(B -A)

• In MATLAB• >>colormap(hot) or cool or • >>whitebg(‘black’) or ‘green’ or • “print screen”• “paint”

simple graph

0 2 4 60

2

4

6

#x

>> x = [1 2 3 4 5]

x=

1 2 3 4 5

>> plot(x)

>> xlabel(‘#’)

>> ylabel(‘value’)

two valuessemicolon

1 2 3 4 51

2

3

4

5

y

x

>>x=[1 2 3 4 5];

>>y=[5 4 3 2 1];

>>plot(x,y,’*’)

>>xlabel(‘x’)

>>ylabel(‘y’)

clear;clfx=0:.1:4*pi;plot(sin(x),'linewidth',3)hold onplot(cos(x),'linewidth',3,'linestyle','--')xlabel('x','fontsize',18)ylabel('V','fontsize',18)set(gca,'fontsize',18)whitebg('black')

0 50 100 150-1

0

1

x

V

Add to graph

>>[x,y]=meshgrid(-xa:x:xb,-ya:y:yb)

>>[x,y]=meshgrid(-1:.1:1,-2:.4:4);

>>R=(x.^2+(y+1).^2).^.5;

>>Z=(1./R);

>>surf(x,y,Z)

>>view(-37.5-90,30)

>>[x,y]=meshgrid(-1:.1:1,-2:.4:4);

>>R=(x.^2+(y+1).^2).^.5;

>>Z=(1./R);

>>surf(x,y,Z)

>>view(-37.5-90,30)

>>[x,y]=meshgrid(-1:.1:1,-2:.4:4);

>>R=(x.^2+(y+1).^2).^.5;

>>Z=(1./R);

>>surf(x,y,Z)

>>view(-37.5-90,30)

>>[x,y]=meshgrid(-1:.1:1,-2:.4:4);

>>R=(x.^2+(y+1).^2).^.5;

>>Z=(1./R);

>>surf(x,y,Z)

>>view(-37.5-90,30)

>>[x,y]=meshgrid(-1:.1:1,-2:.4:4);

>>R=(x.^2+(y+1).^2).^.5;

>>Z=(1./R);

>>surf(x,y,Z)

>>view(-37.5-90,30)

>>[x,y]=meshgrid(-2:.2:2,-2:.2:2);>>r1=(x.^2+(y-.5).^2).^.5;>>r2=(x.^2+(y+.5).^2).^.5;>>V=(1./r1)-(1./r2);

>>mesh(x,y,V)

>>view(-37.5-90,10)

>>colormap(hot)

>>mesh(x,y,V)

>>view(-37.5-90,10)

>>colormap(hot)

>>[ex,ey]=gradient(V,.2,.2);

>>quiver(x,y,ex,ey)

>>grid

>>[ex,ey]=gradient(V,.2,.2);

>>quiver(x,y,ex,ey)

>>grid

divergence

curl

customize graphs -subplotsIterate labels

Change styles

Integration technique

quad (func, xmin, xmax)dblquad (func, xmin, xmax, ymin, ymax)triplequad (func, xmin, xmax, ymin, ymax, zmin, zmax)

func = inline (‘x.*y.*z’)

func = inline (‘x’) quad (func, 0, 1)0.5000

movies

There are “.m” programs for all of the figures and examples that are included in the book “Fundamentals of Electromagnetics with MATLAB” on the class web page for 55: 070.

.m files • text editor or unix editor• !vi name.m• [esc] i ---- start typing• [esc] x ---- remove one letter• [esc] dd --- remove one line• [esc] r ---- change one letter• [esc] h ---- return to start• a - [esc] - [shift] zz ---- leave unix