1. Copyright © 2009 Pearson Education, Inc. Admin for next week: Mid-term date Friday March 20 th. Review lecture Monday (16 th ). Any requests? Labs as usual NO DISCUSSION SECTIONS NEXT WEEK Extra Office hours 2-4pm Monday: Dr Holder Sharp Lab 222 2-4pm Tuesday: Dr Holder Sharp Lab 222 2-4pm Wednesday: Seth Sharp Lab 308 2-4pm Thursday: Zach Sharp Lab 320 Email is also OK – or stop by my office any time Monday or Tuesday I will be away Wednesday – Friday. Dr Ji will give Wednesday’s class and the exam.

2. Copyright © 2009 Pearson Education, Inc. Admin: Assignments : Fourth assignment due Monday (16 th ) Any questions? Fifth Assignment is posted. Not due until Monday (23 rd ), but good exam practice Three questions on Thevenin circuits

3. Thevenin and Norton Equivalent Circuits v TH = open circuit voltage at terminal (a.k.a. port) R TH = Resistance of the network as seen from port (V m ’s, I n ’s set to zero) Any network of sources and resistors will appear to the circuit connected to it as a voltage source and a series resistance

4. Thevenin and Norton Equivalent Circuits v TH = open circuit voltage at terminal (a.k.a. port) R TH = Resistance of the network as seen from port (V m ’s, I n ’s set to zero) Léon Charles Thévenin 1857-1926

5. Norton Equivalent Circuit Any network of sources and resistors will appear to the circuit connected to it as a current source and a parallel resistance Ed Norton – Bell Labs, 1898-1983

6. The Thevenin and Norton equivalent cicuits are just different representations of the same thing. They are used to simplify circuit analysis V TH =I N R TH : so you only usually need I N or V TH R TH =R N

7. Calculation of Thevenin and Norton Resistance (R TH = R N ) R TH =R N ; same calculation (voltage and current sources set to zero) Remove the load. Set all sources to zero (‘kill’ the sources) –Short voltage sources (replace with a wire) –Open current sources (replace with a break) Calculate the equivalent resistance

8. Remove the load. Kill the sources Calculate the equivalent resistance R TH =R 3 + R 1 || R 2

9. Calculation of the Thevenin Voltage (V TH ) Put the sources back. Remove the load and calculate the open circuit voltage Note: How much current flows through R 3 ? What is the Voltage across R 3 ? The Thevenin equivalent is then just V TH in series with R TH

10. Calculation of the Thevenin Voltage (V TH ) Put the sources back. Remove the load and calculate the open circuit voltage Note: How much current flows through R 3 ? What is the Voltage across R 3 ? Voltage divider! The Thevenin equivalent is then just V TH in series with R TH

11. Exercise: Draw the Thevenin Equivalent as seen by the 40Ω load resistor To find R TH, remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance. To find V TH Remove the load and calculate the open circuit voltage

12. Exercise: Draw the Thevenin Equivalent To find R TH remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

13. Exercise: Draw the Thevenin Equivalent Replace the sources To find V TH remove the load resistor and calculate the open circuit voltage V AB = 20 - (20Ω x 0.33amps) = 13.33V

14. Exercise: Draw the Thevenin Equivalent Draw the Thevenin equivalent

16. What about the Norton equivalent?

18. But what if we don’t know V TH ? Remember – if you suppress the “kilo” in the resistance, the current calculated is in milliAmps

20. STOP HERE for mid-term 1 Anything you’d like me to cover in detail on Monday? Requests so far: mesh analysis 2 voltage divider & current divider light bulbs Thevenin