Lecture 5

1. Lecture 5 Source Transformation Thevenin Equivalent Circuit Norton Equivalent Circuit

2. Circuit Techinques • Ohm’s Law • P=VI • KCL, KVL • Voltage/current divider • Series/parallel resistance • Mesh/Nodal Analysis • Source Transformation • Thevenin/Norton Equivalent Circuit • Superposition Principle • Maximum Power Transfer

3. Source Transformation Show that iS=vS/R for any RL

4. Thevenin Equivalent Circuit

5. Determine the Thevenin Voltage (VTh) • If RL=∞ (load across a-b is removed), then Vab=VTH • RTH does not play a role!

6. 3 Bit Digital to Analog Converter 741 Op-Amp Chapter 5

7. Sample DAC Waveform DAC Output Digital Input

8. Applications • Most modern audio signals are stored in digital form (e.g. MP3 and CDs) and in order to be heard through speakers they must be converted into an analog signal

9. Thevenin Equivalent Circuit

10. Determine VTH

11. Methods of Finding RTH • RTH=VTH/iSC • If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH. • So RTH=VTh/isc • If the network contains only independent sources: • Deactivate a voltage source by replacing it with a short • Deactivate a current source by replacing it with an open • If the network contains dependent sources • Apply a test source

12. Calculate the Thevenin Resistance RTH

13. If the network contains only independent sources RTH?

14. RTH

15. Methods of Finding RTH • RTH=VTH/iSC • If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH. • So RTH=VTh/isc • If the network contains only independent sources: • Deactivate a voltage source by replacing it with a short • Deactivate a current source by replacing it with an open • If the network contains dependent sources • Apply a test source

16. Degenerated Common Emitter Amplifier (from last lecture)

17. What if we drive the base with a small signal? Vin, m=1 mV Vout, m=46 mV

18. Mesh Analysis (Last Lecture) ne=2 essential nodes be=3 essential branches 3-(2-1)=2 equations

19. Mesh Analysis (Last Lecture) 1 2 Loop 1: clockwise Loop 2: counter-clockwise Clockwise around loop 1: +Vin-i1rπ-(i1+i2)RE=0 Counter-clockwise around loop 2: i2=gmi1rπ Vout=-i2RC

20. Mesh Analysis (Details)

21. Determine RTH when a Dependent Source is Present IT

22. Methods of Finding RTH • RTH=VTH/iSC • If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH. • So RTH=VTh/isc • If the network contains only independent sources: • Deactivate a voltage source by replacing it with a short • Deactivate a current source by replacing it with an open • If the network contains dependent sources • Apply a test source

23. Another Way to Find RTH isc

24. RTH Calculation • iSC=10V/100 KOhms=0.1 mA • VTH=10V/2=5V • RTH=VTH/iSC=5V/0.1 mA=50 KOhms

25. Norton Equivalent Circuit • A Norton Equivalent circuit consists of • Short-Circuit Current • Norton Equivalent Resistance, which is equal to Thevenin Equivalent Resistance

26. Getting A Norton Equivalent Circuit from Thevenin Equivalent Circuit RTH Thevenin Equivalent Circuit VTH Norton Equivalent Circuit IN=VTH/RTH RTH

27. Derivation of Norton Equivalent Circuit RTH VTH IN=VTH/RTH RTH

28. Extra Credit Assignment Derive 4.1-4.3

29. More about the Extra Credit Assignment

30. Extra Slides on Thevenin

31. Determine vab Show that VTH=vab

32. Determine iSCand RTH

33. Example 4.10 Determine the Thevenin Equivalent Voltage

34. Example 4.10 Determine the short circuit current Determine RTH

35. Slides on Source Transformation

36. RTH

37. Application Determine whether the 6V source is absorbing or delivering the power.

38. Step-by-step simplification

39. Redundant Resistor (1) Prove that the left circuit and the right circuit are equivalent for any load resistor.

40. Redundant Resistor (2) Prove that the left circuit and the right circuit are equivalent for any load resistor.

41. Example 4.9

42. Simplified Circuit