by Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus

1. Fundamentals of Electromagneticsfor Teaching and Learning:A Two-Week Intensive Course for Faculty inElectrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India by Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, India

2. Program for Hyderabad Area and Andhra Pradesh FacultySponsored by IEEE Hyderabad Section, IETE Hyderabad Center, and Vasavi College of EngineeringIETE Conference Hall, Osmania University CampusHyderabad, Andhra PradeshJune 3 – June 11, 2009Workshop for Master Trainer Faculty Sponsored byIUCEE (Indo-US Coalition for Engineering Education)Infosys Campus, Mysore, KarnatakaJune 22 – July 3, 2009

3. Module 7 • Transmission Line Analysis in Time Domain • 7.1 Line terminated by a resistive load • 7.2 Transmission-line discontinuity • 7.3 Lines with reactive terminations and discontinuities • 7.4 Lines with initial conditions • 7.5 Lines with nonlinear elements

4. Instructional Objectives • 49. Find the voltage and current variations at a location on a • lossless transmission line a functions of time and at an • instant of time as functions of distance, and the steady • state values of the line voltage and current, for a line • terminated by a resistive load and excited by turning on a • constant voltage source, by using the bounce-diagram • technique • 50. Design a lossless transmission line system by determining • its parameters from information specified concerning the • voltage and/or current variations on the line • 51. Design a system of three lines in cascade for achieving a • specified unit impulse response

5. Instructional Objectives (Continued) • 52. Compute the reflected power for a wave incident on a • junction of multiple lossless transmission lines from one • of the lines and the values of power transmitted into each • of the other lines, where the junction may consist of lines • connected in series, parallel, or series-parallel, and • include resistive elements • 53. Find the solutions for voltage and current along a • transmission-line system excited by a constant voltage • source and having reactive elements as • terminations/discontinuities • 54. Find the voltage and current variations at a location on a • lossless transmission-line system as functions of time and • at an instant of time as functions of distance, for specified • nonzero initial voltage and/or current distributions along • the system

6. Instructional Objectives (Continued) • 55. Analyze a transmission line terminated by a nonlinear • element by using the load line technique • 56. Understand the effect of time delay in interconnections • between logic gates

7. 7.1 Line Terminated • by Resistive Load • (EEE, Sec. 6.2; FEME, Sec. 7.4)

8. Notation

10. Assuming Z0 = 50 Ω,

11. Assuming Z0 = 50 Ω,

12. Excitation by Constant Voltage Source • Semi-infinite Line, No Source Resistance

15. E7.1 t, ms t, ms

16. t = 1 ms

17. Effect of Source Resistance B.C. (+) Wave

19. Line Terminated by Resistance

20. B.C: 7-19

21. Define Voltage Reflection Coefficient, • Then, Current Reflection Coefficient

24. 7-23

25. 7-24

27. For constant voltage source, • Actual Situation in the Steady State • One (+) Wave and One (–) Wave

28. Four equations for the four unknowns

29. E7.2

30. Solving, we obtain

31. Bounce Diagram Technique: Constant Voltage Source E7.3 7-30 7-30

32. Voltage 7-31

33. Current 7-32

34. VoltageCurrent 7-33

35. t, ms t, ms

36. t, ms t, ms

37. t, ms t, ms

39. Rectangular Pulse Source Use superposition. E7.4 7-38 t, ms

40. t, ms 7-39 t, ms

41. Review Questions • 7.1. Discuss the general solutions for the line voltage and • line current and the notation associated with their • interpretation in concise form. • 7.2. What is the fundamental distinction between the • occurrence of the response in one branch of a lumped • circuit to the application of an excitation in a different • branch of the circuit and the occurrence of the response • at one location on a transmission line to the application of • an excitation at a different location on the line? • 7.3. Describe the phenomenon of the bouncing back and forth • of transient waves on a transmission line excited by a • constant voltage source in series with internal resistance • and terminated by a resistance.

42. Review Questions (Continued) • 7.4. What is the nature of the formula for the voltage • reflection coefficient? Discuss its values for some • special cases. • 7.5. What is the steady state equivalent of a line excited by a • constant voltage source? What is the actual situation in • the steady state? • 7.6. Discuss the bounce diagram technique of keeping track • of the bouncing back and forth of transient waves on a • transmission line for a constant voltage source. • 7.7. Discuss the bounce diagram technique of keeping track • of the bouncing back and forth of transient waves on a • transmission line for a pulse voltage source.

43. Problem S7.1. Plotting line voltage and line current on a transmission-line system involving two lines

44. Problem S7.2. Finding several quantities associated with a transmission-line system from given observations

45. Problem S7.3. Time-domain analysis of a transmission-line system using the bounce diagram technique

46. Problem S7.4. Time-domain analysis of a transmission-line system for a sinusoidal excitation

47. 7.2 Transmission-Line • Discontinuity • (EEE, Sec. 6.3)

48. Transmission-Line Discontinuity