3. Look at a distance z = - L toward the generator -z ZLZL ZcZc z = 0

4. -z ZLZL ZcZc z = 0

5. -z ZLZL ZcZc z = 0

6. -z ZLZL Z c1 z = 0 Z c2

7. -z ZLZL ZcZc z = 0

8. X = Z c tan kL L

9. Should I add something in series or in parallel?

11. Eureka! Use a stub. -z ZLZL ZcZc z = 0 -z ZLZL ZcZc z = 0 -z ZLZL ZcZc z = 0

12. -z ZLZL ZcZc z = 0

13. -z ZLZL ZcZc z = 0  2 1.5 1

15. -z ZLZL ZcZc z = 0 Not matched! -z ZLZL ZcZc z = 0 Needs some -jB somewhere, but where? -z ZLZL ZcZc z = 0 Eureka! Use a stub, somewhere. How long should it be?

16. An article appeared in the January, 1939 issue of Electronics that changed forever the way radio engineers think about transmission lines. Phil Smith [1907-1985] devised an extraordinarily clever circular chart that revealed graphically the complex impedance anywhere along a line. No math and minimum fuss. There's a marvelous symmetry in its design - everything fits together neatly. So ingenious was his invention that it has been the standard of the industry - for over sixty years.

17. -z ZLZL ZcZc z = 0

18. -z ZLZL ZcZc z = 0

19. -z ZLZL ZcZc z = 0

20. -z ZLZL ZcZc z = 0

21. -z ZLZL ZcZc z = 0

22. a x b y r Equation of circle (x - a) 2 + (y - b) 2 = r 2

23. clf; clear; plot([-1 1], [0 0], ’y’) axis equal axis off hold on

24. for r = [0.2.5 1 2 5] rr = 1 / (r + 1); cr = 1 - rr; tr = 2 * pi * (0 :.01: 1); plot(cr + rr * cos (tr), rr * sin (tr), ‘y’); end

25. RrRr RiRi R r = 1

26. for x = [.2.5 1 2 5] rx = 1 / x; cx = rx; tx = 2 * pi * (0 :.01: 1); plot(1 - rx * sin (tx), cx - rx * cos (tx), ‘y’); plot(1 - rx * sin (tx),- cx + rx * cos (tx), ‘y’); end

27. RrRr RiRi R r = 1

28. for x = [.2.5 1 2 5] rx = 1 / x; cx = rx; tx = 2 * atan(x) * (0 :.01: 1); plot(1 - rx * sin (tx), cx - rx * cos (tx), ‘y’); plot(1 - rx * sin (tx),- cx + rx * cos (tx), ‘y’); end

29. RrRr RiRi R r = 1

30. RrRr RiRi

31. To load To generator

32. |R| 1 0

36. Movie to illustrate the frequency dependence of the impedance of a series resonant circuit

37. Movie to illustrate the frequency dependence of the impedance of a parallel resonant circuit

38. Movie to illustrate the transformation of a load impedance at various locations on the transmission line  

39. Movie to illustrate the transformation of an impedance to an admittance

40. y =  z = 0

41. Z c = 50  Z in = ? 

42. z = j1 z = 0

43. Z c = 50  Z in = ? 

44. 0.434 Z c = 100  Z in = ?

45. z L = 2.6 + j1.8 z = 0.7 + j1.2

46. 0.434 Z c = 100  Z in = ?

47. Single stub matching

48. y L = 2 + j1 y = 1 - j1 y = 1 + j1

49. y L =  y = - j1 y = + j1