1. Lecture 6, Slide 1EECS40, Fall 2004Prof. White Slides from Lecture 6 with clearer markups 16 Sept. 2004

2. Lecture 6, Slide 2EECS40, Fall 2004Prof. White Superposition A linear circuit is one constructed only of linear elements (linear resistors, and linear capacitors and inductors, linear dependent sources) and independent sources. Linear means I-V charcteristic of elements/sources are straight lines when plotted. Principle of Superposition: In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.

3. Lecture 6, Slide 3EECS40, Fall 2004Prof. White Superposition Procedure: 1.Determine contribution due to one independent source Set all other sources to 0: Replace independent voltage source by short circuit, independent current source by open circuit 2.Repeat for each independent source 3.Sum individual contributions to obtain desired voltage or current

4. Lecture 6, Slide 4EECS40, Fall 2004Prof. White Superposition Example Find V o –+–+ 24 V 2  4  4 A 4 V + – +Vo–+Vo–

5. Lecture 6, Slide 5EECS40, Fall 2004Prof. White

6. Lecture 6, Slide 6EECS40, Fall 2004Prof. White Calculating a Thévenin Equivalent 1.Calculate the open-circuit voltage, v oc 2.Calculate the short-circuit current, i sc Note that i sc is in the direction of the open-circuit voltage drop across the terminals a,b ! network of sources and resistors a b + v oc – network of sources and resistors a b i sc

7. Lecture 6, Slide 7EECS40, Fall 2004Prof. White Thévenin Equivalent Example Find the Thevenin equivalent with respect to the terminals a,b:

8. Lecture 6, Slide 8EECS40, Fall 2004Prof. White

9. Lecture 6, Slide 9EECS40, Fall 2004Prof. White

10. Lecture 6, Slide 10EECS40, Fall 2004Prof. White Thévenin Equivalent Example Find the Thevenin equivalent with respect to the terminals a,b:

11. Lecture 6, Slide 11EECS40, Fall 2004Prof. White

12. Lecture 6, Slide 12EECS40, Fall 2004Prof. White Alternative Method of Calculating R Th For a network containing only independent sources and linear resistors: 1.Set all independent sources to zero voltage source  short circuit current source  open circuit 2.Find equivalent resistance R eq between the terminals by inspection Or, set all independent sources to zero 1.Apply a test voltage source V TEST 2.Calculate I TEST network of independent sources and resistors, with each source set to zero R eq network of independent sources and resistors, with each source set to zero I TEST –+–+ V TEST

13. Lecture 6, Slide 13EECS40, Fall 2004Prof. White R Th Calculation Example #1 Set all independent sources to 0: