1. Circuits Lecture 7: Equivalence 李宏毅 Hung-yi Lee

2. Textbook Chapter 2.1, 2.3

3. Outline Concept of Equivalent networks Equivalent networks only with resistors Equivalent networks with independent sources Equivalent networks with controlled sources

4. Outline Concept of Equivalent networks Equivalent networks only with resistors Equivalent networks with independent sources Equivalent networks with controlled sources

5. Network Two-terminal network  Network: Part of a complete circuit

6. Equivalent Network Network A and B are equivalent. Network A v i Network B v i i v i-v characteristics Equivalent networks in circuits are just like functions in programming!

7. Circuit Design is like Programming int main () { // create array of grades double quiz1_grade[50] = …… double total = 0; for (int i=0; i<50; i++){ total += quiz1_grade[i]; } double avg = total / 50; print avg; return 0; } (the program for computing the average score of the first quiz) The complete circuit is the “main”. Put everything in “main” is not a good idea.

8. Circuit Design is like Programming Use function int main () { // create array of grades double quiz1_grade[50] = …… print avg_score(quiz1_grade); } function avg_score(double* score){ double total = 0; for (int i=0; i<50; i++){ total += score[i]; } return total/50; } Define IO of a function: input: double array (scores) output: double (average score) Easy to read! Can be re-used! Understandable name We do not care what happens in the function.

9. Circuit Design is like Programming Complete Circuit (Main) i v (IO of function) Name??? Network (function) Simpler equivalent network (function name) Function i-v characteristics

10. Benefit of Equivalent Network 1. Simplify the complete circuit Easier to analyze 2. Useful network can be reused just like elements Voltage amplifier (refer to lecture 5) Current source (later) Negative Resistor (later)

11. Outline Concept of Equivalent networks Equivalent networks only with resistors Equivalent networks with sources Equivalent networks with controlled sources

12. Series i-v curse

13. Parallel i-v curse

14. Example 2.4 Find i

15. Beyond Series and Parallel = What is R eq ? R eq Find i-v characteristics Way1: Add voltage source find current Way2: Add current source find voltage

16. Cubic Puzzle All resistors have resistance R. A and B are the two terminals of the network. = What is R eq ? R eq Hint: consider i-v characteristics

17. Cubic Puzzle 2 (solution is at the end of the slides)

18. Infinity Puzzle = What is R eq ? R eq Infinite resistors (solution is at the end of the slides)

19. Outline Concept of Equivalent networks Equivalent networks only with resistors Equivalent networks with sources Equivalent networks with controlled sources

20. Sources i-v curse Voltage Sources Current Sources i-v curse

21. Source Transformation

22. The two circuits are equivalent. and

23. Source Transformation

25. Why Source Transformation? Parallel

26. Why Source Transformation? Series Be careful about the directions of voltage and current sources

27. Example Find v o Simply the networks by their equivalent networks

28. Example Find v o Network A Network B

29. Example Find v o Bad idea…… Do not put the target in the network to be simplified. How about ….

30. Example Find v o Two-terminal Network

31. Example Find equivalent network Typical Network

32. Example Find equivalent network

33. Example

34. Outline Concept of Equivalent networks Equivalent networks only with resistors Equivalent networks with sources Equivalent networks with controlled sources

35. Equivalent Network with Controlled Source – Example 2.8 What is the equivalent network? Find the i-v characteristics Resistor Negative Resistor!

36. Source Transformation for Controlled Sources vcvc icic

37. Equivalent Network with Controlled Source – Example 2.8

38. Remind 1 When computing i-v characteristics, we need reference direction of v and i Without reference direction, we cannot really answer the i-v characteristics Load Network Source Network The current goes into the terminal with high potential. The current goes out the terminal with high potential. Network without sources Network with sources

39. Remind 2 Select good networks Put a controlled source and its control variable in the same network

40. Three-terminal Network Chapter 4.6 (out of the scope) Three-terminal network

41. Four-terminal Network Chapter 14

42. Problem 2.32, 2.36

43. Thank you!

44. Beyond Series and Parallel = What is R eq ? R eq Find i-v characteristics: Way1: Add voltage source find current Way2: Add current source find voltage Ans:1.1K

45. Cubic Puzzle All resistors have resistance R. A and B are the two terminals of the network. = What is R eq ? R eq

46. Cubic Puzzle 2 http://e2e.ti.com/blogs_/archives/b/thesignal/archive/2013/03/18/resistor- puzzle-solution-and-a-rant-on-schematics.aspx?DCMP=scblog&HQS=hpa-pa- opamp-thehub-20140129-thesignal-20130318-en

47. Infinity Puzzle = What is R eq ? R eq Infinite resistors https://www.youtube.com/watch?v=MgN7h1z5bMQ (the answer in the video is not correct)

48. Problem - Answer

49. Brain Teaser http://rochester.ieee.org/files/2014/03/Newsletter_4-2014.pdf

50. Acknowledgement 感謝 范廷瀚 (b02) 糾正 Infinity Puzzle 的錯誤答案