1 / 46

ELECTRIC CIRCUITS ECSE-2010 Spring 2003 Class 15

ELECTRIC CIRCUITS ECSE-2010 Spring 2003 Class 15. ASSIGNMENTS DUE. Today (Tuesday): Homework #5 Due Computer Project #1 Report Due Activities 15-1, 15-2 (In Class) No Regular Class on Wednesday: Section 2 will meet to review Exam I Strictly Optional Thursday: Experiment #5 Report Due

hanh
Download Presentation

ELECTRIC CIRCUITS ECSE-2010 Spring 2003 Class 15

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. ELECTRIC CIRCUITSECSE-2010Spring 2003Class 15

  2. ASSIGNMENTS DUE • Today (Tuesday): • Homework #5 Due • Computer Project #1 Report Due • Activities 15-1, 15-2 (In Class) • No Regular Class on Wednesday: • Section 2 will meet to review Exam I • Strictly Optional • Thursday: • Experiment #5 Report Due • Activities 16-1, 16-2 (In Class)

  3. EXAM I - STATISTICS • Class Average = 75.1 • Class Median = 77.1 • Section 1 Average = 74.1 • Section 1 Median = 76.5 • Section 2 Average = 75.7 • Section 3 Median = 77.0 • Section 3 Average = 75.3 • Section 3 Median = 78.0

  4. REVIEW Output Input Circuit y(t) = yN + yF x(t) = Switched DC

  5. REVIEW • 1ST Order Switched DC Circuit: • yo = y(t = to+) • yss = y(t ) • to = Switching Time • = Time Constant = Req C for Ckt with 1 C = L / Req for Ckt with 1 L • Req = Equivalent Resistance Of Dead Network Seen at Terminals of C or L

  6. REVIEW • Simply Write Down Output: • y(t) = yss + (yo - yss) e - (t - to)/ • Find yss, yo , directly from circuit • Follow 4 Step Procedure • Draw Ckt at t = t0-: Find vC(t0-) = vC(t0+); iL(t0-) = iL(t0+) • Draw Ckt at t = t0+: Find yo • Draw Ckt at t : Find yss • DC Steady State, C => Open Ckt; L => Short Ckt • Draw Dead Network: Find Req => Calculate • Practiced in Activity 14-1, Observed in Experiment 6; Now do Activity 15-1

  7. ACTIVITY 15-1

  8. ACTIVITY 15-1 • Two Switching Times: • Upper Position for t < 0 • Lower Position at t = 0 • Upper Position again at t = .3 sec • Follow 4 Step Procedure for Each: • For 0 < t < .3s: y(t) = yss1 + (yo1 - yss1) e - t / • => Find yss1, yo1, • For t > .3: y(t) = yss2 + (yo2 - yss2) e - (t - .3) / • => Find yss2, yo2, • Will have 2 different time constants

  9. ACTIVITY 15-1

  10. ACTIVITY 15-1

  11. ACTIVITY 15-1 • Part a); Initial Values: • Step 1: Draw Ckt at t = 0-; Find iL(0-) • L will be a Short Circuit (DC Steady State) • 32 V Input to this Circuit for t < 0 • Source Convert to 8 A in parallel with 4 ohms • 4//12 = 3 ohms ( now in parallel with 3 ohms) • => iL(0-) = 4 A • => v(0-) = 3 x 4 = 12 V

  12. ACTIVITY 15-1

  13. ACTIVITY 15-1 • Part a); Initial Values: • Step 2: Draw Ckt at t = 0+; Find i01; v01 • iL Cannot Change Instantaneously • => i(0+) = i(0-) = 4 A = i01 • 12 // 12 = 6 ohms, i01 flows UP thru 6 ohms • => v(0+) = - i01 x 6 = - 24 V = v01

  14. ACTIVITY 15-1

  15. ACTIVITY 15-1 • Part b); Find i(t) and v(t) for 0 < t < .3 msec: • Step 3: Draw Ckt in DC SS: Find iss1, vss1 • Ckt will head for Steady State with vL = 0 • => iss1 = 0 A • => vss1 = 0 V • No Source!

  16. ACTIVITY 15-1

  17. ACTIVITY 15-1 • Part b); i(t) and v(t) for 0 < t < .3 msec: • Step 4: Draw Dead Network: Find Req1 • Req1 = 6 + 3 = 9 ohms

  18. ACTIVITY 15-1 • Part b); i(t) and v(t) for 0 < t < .3 msec: • For 0 < t < .3 sec: • => i(t) = 0 + (4 - 0) e – t /.2 = 4e – t /.2; t in sec • => v(t) = 0 + (-24 - 0) e – t/.2 = -24e – t /.2 ; t in sec • At t = .3 sec: • => i(.3-) = 4 e –1.5 = .893 A = i(.3+) = i02 • => v(.3-) = - 24 e –1.5 = - 5.36 V

  19. ACTIVITY 15-1

  20. ACTIVITY 15-1 • Part c); t > .3 sec: • Step 1: Draw Ckt at t = .3- sec: • => i(.3-) = 4 e –1.5 = .893 A • => v(.3-) = - 24 e –.1.5 = - 5.36 V

  21. ACTIVITY 15-1

  22. ACTIVITY 15-1 • Part c); t > .3 sec: • Step 2: Draw Ckt at t = .3+ sec: • i02 = i(.3+) = i(.3-) = .893 A • v02 = v(.3+) = 4//12 (8 - i02) = 21.3 V

  23. ACTIVITY 15-1

  24. ACTIVITY 15-1 • Part c); t > .3 sec: • Step 3: Draw Ckt as t : • Circuit again heads for DC Steady State • L is a Short Circuit • => iss2 = 4 A • => vss2 = 12 V (as in Part a)

  25. ACTIVITY 15-1

  26. ACTIVITY 15-1 • Part c); t > .3 sec: • Step 4: Draw Dead Network: • Req2 = 3 + 3 = 6 ohms • For t > .3 sec: • i(t) = 4 + (.893– 4) e – (t-.3)/.3 = 4 – 3.11e -(t-.3)/.3 • v(t) = 12 + (21.3 - 12) e – (t-.3)/3 =12 + 9.3 e -(t-.3)/.3

  27. COMPLETE TIME RESPONSE

  28. COMPLETE TIME RESPONSE • Can Always Relate y(t) to x(t) by a Differential Equation: • Obtain Differential Equation from Circuit using Techniques we have developed • Order of Differential Equation determined by the number of Energy Storage elements • For 1st Order Circuits, We Solved the Differential Equation:

  29. COMPLETE TIME RESPONSE • For Higher Order Circuits => Want to Find a Better Way! • Solving Second Order or Higher Differential Equations can be a Real Pain • Would Prefer Algebraic Equations, not Differential Equations

  30. COMPLETE TIME RESPONSE • Use Method of Laplace Transforms: • Powerful Mathematical Tool • Will transform Differential Equations into Algebraic Equations • Can then use all the Circuit Analysis Techniques we developed for Resistive Circuits!!

  31. LAPLACE TRANSFORMS • Very Important Topic in Course: • Will Allow Us to Find the Complete Time Response, y(t) = yN(t) + yF(t) for Any Circuit with Any Input: • Very Powerful Technique: • Will Use in Other Courses • Will Introduce Laplace Transforms before looking at 2nd Order Circuits

  32. LAPLACE TRANSFORMS

  33. LAPLACE TRANSFORMS

  34. LAPLACE TRANSFORMS • Concept :

  35. LAPLACE TRANSFORMS • Definitions:

  36. LAPLACE TRANSFORMS • Definitions:

  37. LAPLACE TRANSFORM PAIRS

  38. LAPLACE TRANSFORM PROPERTIES

  39. UNIT STEP FUNCTION

  40. TIME DELAY

  41. TIME DELAY

  42. IMPULSE FUNCTION

  43. IMPULSE FUNCTION

  44. ACTIVITY 15-2

  45. ACTIVITY 15-2

  46. ACTIVITY 15-2

More Related