1. rectangular waveguide TE & TM modes

2. TE mode

3. y b 0 x a z 0 rectangular waveguides TE or H mode

4. y b 0 x a z 0 rectangular waveguides TE or H mode lowest order mode TE10 (or TE01) mode H10 (or H01) mode

6. y b 0 x a z 0 rectangular waveguides TE or H mode @ x = 0 @ x = a lowest order mode A = 0 m = 1

7. y b 0 x a z 0 rectangular waveguides TE or H mode

8. y b Ey 0 x a z 0 0 z a x rectangular waveguides TE or H mode

9. Movie to illustrate the propagation of the lowest order mode in a waveguide.

10. y b 0 x a b z 0 wc w rectangular waveguides TE or H mode

11. y b 0 x a z 0 y b 0 x a z 0 y b 0 x a z 0 rectangular waveguides TE10 mode a = 2b

12. y b 0 x a z 0 rectangular waveguides TE or H mode a = 3 cm

13. y b 0 x a z 0 rectangular waveguides TE or H mode

14. y b 0 x a z 0 rectangular waveguides TE or H mode

15. v c v y b 1 0 x a z 0 vg wc w rectangular waveguides TE or H mode

16. TM mode

17. y b 0 x a z 0 rectangular waveguides TM or E mode

18. y b 0 x a z 0 rectangular waveguides TM or E mode

19. y b 0 x a z 0 rectangular waveguides TM or E mode m cannot be 0 n cannot be 0

21. y b 0 x a z 0 rectangular waveguides TM or E mode Note ==> m = 1 and n = 1 is the lowest mode

22. y b 0 x a z 0 rectangular waveguides TE10 mode lowest order mode

23. y b 0 x a z 0 1 2 3 rectangular waveguides TE10 mode lowest order mode

25. Transmission line modeling simulation with PSpice ASEE conference 2007

26. Transmission Lines Demonstration High Frequency Electronics Course EE527 Andrew Rusek Oakland University Winter 2007 Demonstration is based on the materials collected from measurement set up to show sinusoidal and step responses of a transmission line with various terminations. Results of selected simulations are included.

27. Fig.1a Test circuits

28. Fig. 1b Low frequency sine-wave (1MHz), TL matched (50 ohms), observe small delays and almost identical amplitudes

29. Fig. 1c Low frequency sine-wave (1MHz), TL matched (50 ohms) Channel 4 (output) shows the voltage for grounded center conductor and a probe input connected to the outer conductor (shield), observe the phase inversion of the last wave (180 degrees)

30. Fig. 2a Sine-wave of 17 MHz, matched load The waves have the same amplitudes, the phases are different.

31. Fig. 2b Sine-wave of 17 MHz, matched load Channel 4 (output) shows the voltage for grounded center conductor and a probe input connected to the outer conductor (shield).

32. Fig. 3 Open ended TL, sine-wave of 1 MHz applied, observe 2X larger amplitude in comparison with previous tests, amplitudes are almost the same for all waves.

33. Fig. 4a Open ended TL, 3.5 MHz, observe minimum (input) One quarter wave pattern is shown

34. Fig. 4b Open ended TL, 3.5 MHz, observe minimum (input) One quarter wave pattern is shown

35. Fig. 4c Open ended TL, 3.5 MHz, observe minimum (input) One quarter wave pattern is shown

36. Fig. 5 Open ended TL, 5.5 MHz, observe shift of the minimum The minimum is located quarter wave from the end.

37. Fig. 6 Open ended TL, 11 MHz, observe two minima

38. Fig. 7 Shorted TL, low frequency,1MHz applied, observe zero output voltage

39. Fig. 8 Shorted TL, 5 MHz applied

40. Fig. 9 Shorted TL, 7 MHz, observe two minima (half wave). If the length of the line is known, the dielectric constant can be calculated (Lambda_cable/2 = 12m, open space Lambda = 42.8m).

41. Fig. 10 Shorted TL, 7 MHz, increased vertical sensitivity; observe two minima as before and effects of stray inductance of the source and probe leads (half wave),

42. Fig.11 Shorted TL, 11 MHz, two minima, first shifted towards the load, ¼ wavelength + ½ wavelength

43. Fig. 12 Pulse response of open ended TL, slow pulse (0.3us rise time), no reflections observed, Channel 2 – Input, Channel 4 – Output, observe the delay.

44. Fig. 13a Open ended TL, Input Pulse rise time = 240 ns, Output = 120 ns, Long pulse applied, measurement circuit

45. Fig. 13b Open ended TL, Input Pulse rise time = 240 ns, Output = 120 ns, Why Output is faster than Input ? End of TL reflection adds to incident (Real rise time of the input wave is120 ns), and this effect doubles Input signal rise time. Long pulse applied, simulations.

46. Fig. 13c Open ended TL, Input Pulse rise time = 240 ns, Output = 120 ns, Why Output is faster than Input ? End of TL reflection adds to incident (Real rise time of the input wave is120 ns), and this effect doubles Input signal rise time. Long pulse applied, measurements.

47. Fig. 14a Open ended TL, long pulse applied, source matched, measurement circuit.

48. Fig. 14b Open ended TL, long pulse applied, source matched, simulations.

49. Fig. 14c Open ended TL, Input – Channel 2 shows incident step and reflected step (doubled TL delay), source matched, Output – Channel 4 shows doubled incident wave level, delayed (about 60 ns), long pulse applied. Distance between steps of Channel 2 – 2X TL delay time, measurements.

50. Fig. 15c Open ended TL, short pulses applied to show “radar effect”, circuit.