1. 305221, 226231 Computer Electrical Circuit Analysis การวิเคราะห์วงจรไฟฟ้าทาง คอมพิวเตอร์ 3(2-3-6) ณรงค์ชัย มุ่งแฝงกลาง คมกริช มาเที่ยง สัปดาห์ที่ 11 Frequency Response ( Second-Order circuits )

2. Outline Objectives 1 The Source-Free Series RLC Circuit 2 The Source-Free Parallel RLC Circuit 3 Step Response of a Series RLC Circuit 4 Step Response of a Parallel RLC Circuit 5

3. Objectives  เพื่อให้นิสิตมีความรู้ความเข้าใจเกี่ยวกับวงจร ( อนุพันธ์ ) อันดับสอง (Second Oder Circuit)  The Source-Free Series RLC Circuit  The Source-Free Parallel RLC Circuit  เพื่อให้นิสิตมีความรู้ความเข้าใจเกี่ยวกับผลการ ตอบสนองแบบทันทีทันใด (Step Response)  Step Response of a Series RLC Circuit  Step Response of a Parallel RLC Circuit

4. What is second order circuit ?  A second-order circuit is characterized by a second-order differential equation. It consists of resistors and the equivalent of two energy storage elements.

5. Finding Initial and Final Values  The major students problem face in handling second-order circuits is finding the initial and final conditions on circuit variables.  Especially, the difficulty finding the initial values of their derivatives: and.  For this reason, this section is explicitly devoted to the subtleties of getting,,,, and.

6.  There are two key points to keep in mind in determining the initial conditions.  First key, we must carefully handle the polarity of voltage across the capacitor and the direction of the current through the inductor. Finding Initial and Final Values (cont.) Figure 6.14 Figure 6.15

7.  Second key, keep in mind that the capacitor voltage is always continuous so that  And the inductor current is always continuous so that  where denotes the time just before a switching event and is the time just after the switching event, assuming that the switching event takes place at. Finding Initial and Final Values (cont.)

8. Example #1

9.  Find the initial values of and. Example #1(cont.)

10.  Find the initial values of and. Example #1(cont.)

12.  Find the initial values of and. Example #1(cont.)

13. Outline Objectives 1 The Source-Free Series RLC Circuit 2 The Source-Free Parallel RLC Circuit 3 Step Response of a Series RLC Circuit 4 Step Response of a Parallel RLC Circuit 5

14. The Source-Free Series RLC Circuit

15. This is a second-order differential equation and is the reason for calling the RLC circuits in this chapter second-order circuits.

16. The Source-Free Series RLC Circuit (cont.)

22. Overdamped Case

23. Critically Dapmed Case

24. Underdamped Case

25. Example #2

26. Example #2 (cont.)

29. Outline Objectives 1 The Source-Free Series RLC Circuit 2 The Source-Free Parallel RLC Circuit 3 Step Response of a Series RLC Circuit 4 Step Response of a Parallel RLC Circuit 5

30. The Source-Free Parallel RLC Circuit

31. The Source-Free Parallel RLC Circuit (cont.)

35. Example #3

36. Example #3 (cont.)

39. Outline Objectives 1 The Source-Free Series RLC Circuit 2 The Source-Free Parallel RLC Circuit 3 Step Response of a Series RLC Circuit 4 Step Response of a Parallel RLC Circuit 5

40. Step Response of a Series RLC Circuit

41. Step Response of a Series RLC Circuit (cont.)

44. Outline Objectives 1 The Source-Free Series RLC Circuit 2 The Source-Free Parallel RLC Circuit 3 Step Response of a Series RLC Circuit 4 Step Response of a Parallel RLC Circuit 5

46. Step Response of a Parallel RLC Circuit (cont.)

48. Assignment #1

49. Assignment #2

50. Assignment #3

51. Assignment #4

52. Assignment #5