1. Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

2. Announcements Assignment 0 due Thursday Lab reports due today and tomorrow Physics Colloquium 4pm tommorrow

3. Method 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) Léon Charles Thévenin 1857-1926

4. Method 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

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. Calculation of R T and R N R T =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)

7. Calculation of R T and R N continued Calculate equivalent resistance seen by the load

8. Calculation of V T Remove the load and calculate the open circuit voltage (Voltage Divider)

9. Example Use Thevenin’s theorem to calculate the current through Resistor R6. –(solution R TH =6.67Ω, V TH =12V, I=0.95A)

10. 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. To find V TH Remove the load and calculate the open circuit voltage

11. Exercise: Draw the Thevenin Equivalent To find R TH 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 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 V AB = 20 - (20Ω x 0.33amps) = 13.33V

13. Exercise: Draw the Thevenin Equivalent To find R TH 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 V AB = 20 - (20Ω x 0.33amps) = 13.33V

14. Exercise: Draw the Thevenin Equivalent To find R TH 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

15. Calculation of I N Short the load and calculate the short circuit current (R 1 +R 2 )i 1 - R 2 i SC = v s -R 2 i 1 + (R 2 +R 3 )i SC = 0 (KCL at v) (mesh analysis) R N =R TH

16. Source Transformation Summary: Thevenin’s Theorem Any two-terminal linear circuit can be replaced with a voltage source and a series resistor which will produce the same effects at the terminals V TH is the open-circuit voltage V OC between the two terminals of the circuit that the Thevenin generator is replacing R TH is the ratio of V OC to the short-circuit current I SC ; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them.

17. Summary: Norton’s Theorem Any two-terminal linear circuit can be replaced with a current source and a parallel resistor which will produce the same effects at the terminals I N is the short-circuit current I SC of the circuit that the Norton generator is replacing Again, R N is the ratio of V OC to the short-circuit current I SC ; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them. For a given circuit, R N =R TH

18. Maximum Power Transfer Why use Thevenin and Norton equivalents? –Very easy to calculate load related quantities –E.g. Maximum power transfer to the load It is often important to design circuits that transfer power from a source to a load. There are two basic types of power transfer –Efficient power transfer: least power loss. Power is usually large (e.g. power utility) –Maximum power transfer (e.g. communications circuits) Want to transfer an electrical signal (data, information etc.) from the source to a destination with the most power reaching the destination. Power is usually small so efficiency is not a concern.

19. Maximum Power Transfer: Impedance matching so maximum power transfer occurs whenand Differentiate w.r.t. R L using quotient rule: Set to zero to find maximum: http://circuitscan.homestead.com/files/ancircp/maxpower1.htm

20. Maximum Power Transfer: Impedance matching so maximum power transfer occurs whenand Differentiate w.r.t. R L using quotient rule: Set to zero to find maximum: http://circuitscan.homestead.com/files/ancircp/maxpower1.htm