LECTURE_4_EE-211 PATHOLOGY ORAL MEDIC.pptx

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1. EE-211 Electrical Network Analysis (LEC-4) Instructor: Dr taosif iqbal Dept. of Electrical Engineering College of Electrical and Mechanical Engineering NUST 1 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

2. Network functions Complex exponential signal is of the type S is the complex frequency, its units are complex nepers /second 2 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

3. COMPLEX FREQUENCY . 3 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

4. example Assuming 4 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

5. practice 5 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

6. 6

7. Generalized impedance and admittance Generalized impedance is defined as Generalized admittance is defined as 7 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

8. S-domain circuit analysis Replace input and output by their phasors Replace R, L and C by their generalized impedances Carry out the phasor analysis techniques 8 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

9. 9

10. Network functions The input x(t) and the output y(t) of a linear network are related by a differential equation We get 10 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

11. Network functions Network function is defined as 11 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

12. Network functions 12 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

13. Poles and zeros Poles and zeros can be real, imaginary or complex, in case of imaginary or complex they always appear in conjugate pairs 13 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

14. practice 14 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

15. Procedure to find and check network function 15 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

16. practiCe a 16 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

17. practiCe a 17 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

18. practiCe a 18 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

19. Natural response using h(s) If 19 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

20. Important cases 20 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

21. Important cases 21 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

22. Important cases 22 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

23. Important observations 23 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

24. Important observations a 24 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

25. practice a 25 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

26. practice a 26 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

27. Complete response using H(s) DC steady state response 27 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

28. Complete response using H(s) The AC steady state response 28 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

29. praCtice 29 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

30. Complete response 30 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

31. Frequency response The manner in which the AC response varies with frequency is known as the frequency response Frequency response can be predicted mathematically using the network function and calculating it on axis. This plotting is best done on semi logarithmic scales due to numerous reasons   31 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

32. Semilogarithmic scales a 32 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

33. Semilogarithmic scales 33 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

34. decibels a 34 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

35. Some properties 35 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

36. Semilog graph paper 36 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

37. Bode plots The transfer function can be written as Taking the natural logarithm of both sides, The real part of lnH is a function of the magnitude while the imaginary part is the phase. 37 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

38. The magnitude plot In a Bode magnitude plot, the gain is plotted in decibels (dB) versus frequency A transfer function may be written in terms of factors that have real and imaginary parts. One such representation might be The above representation of H(ω) is called the standard form. 38 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

39. Network function building blocks In constructing a Bode plot, we plot each factor separately and then combine them graphically. The factors can be considered one at a time and then combined additively because of the logarithms involved. 39 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

40. Straight line graphs-Constant term K. If K is positive, the magnitude remains 20 |K| and the phase is 0◦. If K is negative, the magnitude remains 20 |K| but the phase is ±180◦.   40 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

41. Straight line graphs-pole/zero at the origin. F or the zero (jω) at the origin, the magnitude is 20 ω and the phase is 90◦. The Bode plots for the pole are similar except that the slope of the magnitude plot is −20 dB/decade while the phase is −90◦.   41 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

42. Straight line graphs- simple pole/zero showing that we can approximate the magnitude as zero (a straight linewith zero slope) for small values of ω and by a straight line with slope 20 dB/decade for large values of ω. The frequency ω = z1 where the two asymptotic lines meet is called the corner frequency or break frequency. Approximate plot is close to the actual plot except at the break frequency, where ω = z1 and the deviation is 20 log10|(1 + j1)| = 20 log10 √2 = 3dB. 42 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

43. Straight line graphs- simple pole/zero 43 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

44. Straight line graphs- Quadratic pole/zero 44 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

45. Straight line graphs- Quadratic pole Note that the actual plot depends on the damping factor ζ 2 as well as the corner frequency ω n . The significant peaking in the neighborhood of the corner frequency should be added to the straight-line approximation if a high level of accuracy is desired. However, we will use the straight-line approximation for the sake of simplicity. 45 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

46. Straight line graphs- Quadratic pole The phase can be expressed as 46 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

47. Summary of Bode straight-line magnitude and phase plots. 47 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

48. Summary of Bode straight-line magnitude and phase plots. 48 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

49. Summary of Bode straight-line magnitude and phase plots. 49 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

50. practice 50 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

51. practice 51 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023

52. Credits and references The images and information used in the preparation of these slides are taken from Electric Circuits Fundamentals, 1st Edition, by Sergio Franco, Oxford English Press 1995. Fundamentals of Electric Circuits, 3rd Edition, by Charles K. Alexander & Matthew N. O. Sadiku, McGraw Hill 2003. 52 EE-211 ELECTRICAL NETWORK ANALYSIS SPRING2023