1. ECEN3714 Network Analysis Lecture #1 12 January 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen3714

2. Goal of this class: n Builds on Material from ECEN2613 n Add to your Circuit Design & Analysis Tool Set n Examine Transform Theory u Laplace Transforms u Fourier Series (subset of Fourier Transforms) n Provide a hands-on experience with experiments related to the lectures.

3. Why bother learning math functions when machines can do it?

4. Because you can't always trust those fancy machines.

5. Class Home Page www.okstate.edu/elec- engr/scheets/ecen3714/ www.okstate.edu/elec- engr/scheets/ecen3714/ Class Home Page www.okstate.edu/elec- engr/scheets/ecen3714/ www.okstate.edu/elec- engr/scheets/ecen3714/ ECEN Home Page People Scheets Personal Home Page

6. Contact Information n EMail: george.scheets@okstate.edu n Phone (405)744-6553 n Tentative Office Hours u Monday & Wednesday: 1:00 – 2:00 pm u Tuesday & Thursday: 1:00 – 2:30 pm n Lab Teaching Assistant u Tristan Underwood u tristan.underwood@okstate.edu

7. Grading n Class Work u 10 x 10 point Quizzes u 2 x 100 point Exams u 1 x 150 point Comprehensive Final u 450 points Total n Lab Work u 10 x 10 point Lab Experiments u 1 x 30 point Practical u 1 x 30 point Design Project u 160 points Total n Overall u Class work weighted 1.0, Lab work weighted 1.375 u 670 points total; 450 + 160*1.375 = 450 + 220 n 90%, 80%, 70% etc. A/B/C break points will be curved... unless you miss any lab work, then no curve.

8. Extra Credit n Errors in text, HW solutions, instructor notes, test or quiz solutions, lab manual (20 points max) n Attend IEEE functions (15 points) u 3 presentations (3 points apiece + dinner) u ECE spring banquet (6 points)

9. Lectures n Quiz or Exam Every Friday u Except: 16 January, 13 March, & 1 May n Quizzes u Open book, notes, instructor n Tests u Open book & notes n Monday & Wednesday u Lectures u Feel free to interrupt with pertinent questions or comment at any time

10. Grading n In Class: Quizzes, Tests, Final Exam Open Book & Open Notes WARNING! Study for them like they’re closed book! n Ungraded Homework: Assigned most every class Not collected Solutions Provided Payoff: Tests & Quizzes

11. ECEN3714 Network Analysis Lecture #1 12 January 2014 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen3714 n Review Appendix (Complex Numbers) & Chapter 12.1 n Ungraded Homework Problems: None

12. Why work the ungraded Homework problems? n An Analogy: Linear Systems vs. Soccer n Reading text = Reading a book about Soccer n Looking at the problem solutions = watching a scrimmage n Working the problems = practicing or playing in a scrimmage n Quiz = Exhibition Game or Scrimmage n Test = Big Game

13. To succeed in this class... n Show some self-discipline!! Important!! For every hour of class...... put in 1-2 hours of your own effort. n PROFESSOR'S LAMENT If you put in the time You should do fine. If you don't, You likely won't.

14. What to study? S

15. S Readings

16. What to study? S ReadingsHomework

17. What to study? S ReadingsHomework Class Notes

18. Cheating n Don’t do it! If caught, expect to get an ‘F’ for the course. n My idol: Judge Isaac Parker U.S. Court: Western District of Arkansas 1875-1896 a.k.a. “Hanging Judge Parker” a.k.a. “Hanging Judge Parker”

19. Calvin’s Thoughts on Cheating…

23. Labs n Start at Scheduled Time on Week #2 n But NOT in scheduled place n First 2 Wednesday Labs in EN 510 n First 2 Friday Labs in EN 019

25. 5 Hertz Square Wave... 1 volt peak, 2 volts peak-to-peak, 0 mean 0 1.5 -1.5 0 1.0

26. Generating a Square Wave... 0 1.5 -1.5 0 1.0 0 1.5 -1.5 0 1.0 1 vp 5 Hz 1/3 vp 15 Hz

27. Generating a Square Wave... 0 1.5 -1.5 0 1.0 5 Hz + 15 Hz

28. Generating a Square Wave... 0 1.5 -1.5 0 1.0 1/5 vp 25 Hz 0 1.5 -1.5 0 1.0 5 Hz + 15 Hz

29. Generating a Square Wave... 0 1.5 -1.5 0 1.0 5 Hz + 15 Hz + 25 Hz

30. Generating a Square Wave... 0 1.5 -1.5 0 1.0 1/7 vp 35 Hz 0 1.5 -1.5 0 1.0 5 Hz + 15 Hz + 25 Hz

31. Generating a Square Wave... 0 1.5 -1.5 0 1.0 5 Hz + 15 Hz + 25 Hz + 35 Hz cos2*pi*5t - (1/3)cos2*pi*15t + (1/5)cos2*pi*25t - (1/7)cos2*pi*35t)

32. Generating a Square Wave... 5 cycle per second square wave generated using first 50 cosines, Absolute Bandwidth = 495 Hertz. 0 1.5 -1.5 0 1.0

33. Generating a Square Wave... 5 cycle per second square wave generated using first 100 cosines, Absolute Bandwidth = 995 Hertz. 0 1.5 -1.5 0 1.0

34. Sines & Cosines n Can be used to construct any time domain waveform n x(t) = ∑ [ a i cos(2πf i t) + b i sin(2πf i t) ] n cosines & sines are 90 degrees apart cos(2πft) + j sin(2πft) n Phasor e jπft = cos(2πft) + j sin(2πft) n cos(2πft) = Real {e jπft } n sin(2πft) = Imaginary {e jπft } n Wikipedia Example Wikipedia Example Wikipedia Example

35. Phasor Projection n Projection on Real Axis = Cosine n Projection on Imaginary Axis = Sine Snapshot after 1 phasor revolution

37. ECEN3714 Network Analysis Lecture #2 14 January 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen3714 n Read 13.1 – 13.4 n Ungraded Homework Problems 12.1, 2, & 3

38. OSI IEEE n January General Meeting n 5:50-6:30 pm, Wednesday, 21 January n ES201b n Reps from Grand River Dam will present u Operate 3 dams, 2 lakes, Salina Pump Storage n Dinner will be served n All are invited

39. Complex Numbers Rectangular & Polar Coordinates Easiest to use... Addition (x+y)Rectangular Subtraction (x-y)Rectangular Multiplication (x*y)Rectangular or Polar Division (x/y)Polar 3 ways to represent a complex number Ex) 9 + j9 = 81 / 45o = 81ejπ/4

40. Last Time… n Two complex numbers x = 7 + j4 = 8.062 / 29.74 o = 8.062e j0.1652π y = 2 – j4 = 4.472/ - 63.43 o = 4.472e -j0.3524π y = 2 – j4 = 4.472/ - 63.43 o = 4.472e -j0.3524π

42. Pierre-Simon Marquis de Laplace n Born 1749 n Died 1827 n French Mathematician & Astronomer n Previously, you've had y(t) = function{ x(t) } u Solved in time domain (derivatives?, integrals?) n In 1785, Laplace noticed it's frequently easier to solve these via x(t) → X(s) →Y(s) → y(t) transform massage transform

44. ECEN3714 Network Analysis Lecture #3 16 January 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen3714 n Problems: 13.2, 4, & 6

45. OSI IEEE n January General Meeting n 5:50-6:30 pm, Wednesday, 21 January n ES201b n Reps from Grand River Dam will present u Operate 3 dams, 2 lakes, Salina Pump Storage n Dinner will be served + 3 pts extra credit n All are invited

46. Time Bounds n None Specified? Assume 0 - < t < ∞ = 0 < t < ∞ u (Default bounds for this class) n Assume time function = 0 where not specified u Example: x(t) = 7t; t > 3 Assume x(t) = 0 when t 3 Assume x(t) = 0 when t < 3

47. Laplace Transform F(s) = f(t) e -st dt 0-0- ∞ "s" is a complex number = σ + jω Fourier Transform is similar σ = 0 Lower Bound = -∞

48. Correlation n Provides a measure of how "alike" x(t) and y(t) are n If integral evaluates positive u x(t1) and y(t1) tend to be doing same thing t1 an arbitrary time u if x(t1) is positive, y(t1) tends to be positive u if x(t1) is negative, y(t1) tends to be negative x(t) y(t) dt

49. Correlation n If integral evaluates negative u x(t1) and y(t1) tend to be doing the opposite n If evaluates = 0 u x(t) & y(t) are not related (uncorrelated) no predictability x(t) y(t) dt

50. Laplace Transform F(s) = f(t) e -st dt 0-0- ∞

51. Laplace Transform of f(t) = e -2t F(s) = e -2t e -st dt 0-0- ∞

52. Laplace Transform of e -2t F(0) = e -2t e -0t dt 0-0- ∞

53. Laplace Transform of e -2t t e -0t = u(t) t e -2t n This evaluates to F(0) = 1/2

54. Laplace Transform of e -2t F(2) = e -2t e -2t dt 0-0- ∞ F(s) = e -2t e -2t dt 0-0- ∞

55. Laplace Transform of e -2t t e -2t n Product is e -4t, which has area F(2) = 1/4. t e -st evaluated at s = 2 Ideally, these two waveforms would have the highest + correlation. Laplace Transform is an imperfect correlator.

56. Normalized Energy e -2t e -st dt ∞ 0-0- e -st dt ∞ 0-0- NE(s) =

57. Normalized Energy Plot s NE(s) = s 0.5 /(s+2).354 02 Peak is at s = 2.

58. Correlation & Laplace Transform n Somewhat similar x(t) y(t) dt