Electromagnetic Theory 55:170

1. Electromagnetic Theory55:170 Professor Karl E. Lonngren [lonngren@engineering.uiowa.edu] 4312 SC office hours: 12:15-1:00 T & Th Kent Hutchinson – teaching assistant

2. Books • References: • Fields and Waves in Communication Systems • Fundamentals of Electromagnetics with MATLAB 2007

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

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

5. MATLAB

6. 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

7. 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 • >>

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

9. 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 - addition

10. 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 - dot product

11. 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

12. 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

13. z B - A A B y x |B - A| = norm(B -A)

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

15. simple graph >> x = [1 2 3 4 5] x= 1 2 3 4 5 >> plot(x) >> xlabel(‘#’) >> ylabel(‘value’)

16. semicolon >>x=[1 2 3 4 5]; >>y=[5 4 3 2 1]; >>plot(x,y,’*’) >>xlabel(‘x’) >>ylabel(‘y’) two values

17. Add to graph • clear;clf • x=0:.1:4*pi; • plot(sin(x),'linewidth',3) • hold on • plot(cos(x),'linewidth',3,'linestyle','--') • xlabel('x','fontsize',18) • ylabel('V','fontsize',18) • set(gca,'fontsize',18) • whitebg('black')

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

19. >>[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)

20. >>[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)

21. >>[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)

22. >>[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)

23. >>[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)

24. >>[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);

25. >>mesh(x,y,V) >>view(-37.5-90,10) >>colormap(hot)

26. >>mesh(x,y,V) >>view(-37.5-90,10) >>colormap(hot)

27. >>[ex,ey]=gradient(V,.2,.2); >>quiver(x,y,ex,ey) >>grid

28. >>[ex,ey]=gradient(V,.2,.2); >>quiver(x,y,ex,ey) >>grid

29. divergence

30. curl

31. Iterate labels Change styles customize graphs -subplots

32. Integration technique func = inline (‘x.*y.*z’) quad (func, xmin, xmax) dblquad (func, xmin, xmax, ymin, ymax) triplequad (func, xmin, xmax, ymin, ymax, zmin, zmax) func = inline (‘x’) quad (func, 0, 1) 0.5000

33. movies

34. 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.

36. .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