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Lecture 5

Lecture 5. Source Transformation Thevenin Equivalent Circuit Norton Equivalent Circuit. Circuit Techinques. Ohm’s Law P=VI KCL, KVL Voltage/current divider Series/parallel resistance Mesh/Nodal Analysis Source Transformation Thevenin /Norton Equivalent Circuit

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Lecture 5

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  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

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