1. Lecture 6 Nodal/Mesh Analysi 4.2,4.3, 4.5 &4.6

2. Definitions

3. Nodes Node: a point where two or more circuit elements join

4. Essential Node Essential Node: a node where three or more circuit elements join

5. Step 1: Number of Nodal Voltage Equations n e is essential nodes Number of nodal voltage Equations is n e -1 n e = 3 n e -1 =2 nodal voltage equations are required.

6. Step 2: Designate a node as the reference node. Suggestion: Select the node with the most branches. (3 branches) (4 branches)

7. Step 3: Define the Node Voltage on the Diagram

8. Step 4: Apply KCL Apply KCL to essential nodes. R1 R2 R10 R5 VS IS

9. Simulation Results

10. Solve i a, i b and i c

11. Hints n e =2 Need n e -1=1 equation

12. Mesh Analysis

13. Definitions

14. Branch Branch: a path that connects two nodes.

15. Essential Branch Essential branch: a path which connects two essential nodes without passing through an essential node.

16. Mesh Mesh: a loop that does not enclose any other loops

17. Step 1: Determine the number of essential nodes n e =3

18. Step 2: Determine the number of essential branches b e =5 # of equations: b e -(n e -1)=5-(3-1)=3

19. Step 3: Apply KVL Around Loop b a.Focus initially on i a. 40-i a R 2 -(i a )8=0 b.Account for i b. 40-i a R 2 -(i a -i b )8=0 + - + -

20. Step 4: Apply KVL Around Loop b a.Focus initially on i b. -(i b )8-i b 6-(i b )6=0 b. Account for i a. -(i b -i a )8-i b 6-(i b )6=0 c. Account for i c. -(i b -i a )8-i b 6-(i b - i c )6=0 + - + - + -

21. Step 5: Apply KVL Around Loop c a.Focus initially on i c. -(i c )6-i c 4-20=0 b. Account for i b -(i c - i b )6-i c 4-20=0 + - + -

22. Solve 3 EQ and 3 Unknowns Using Mathematica 3 Unknown equations3 unknowns

23. Get Mathematica Through SSU

24. Step 1 # of essential branch: 6 # of essential nodes: 4 # of equations: 6-(4-1)=3

25. Step 2 See in the handout.

26. Use Mathematica to Solve Equations Format: Solve[{equations separated by a comma},{list of unknowns}] To solve an equation: Evaluation→Evaluate Cells

27. Degenerated Common Emitter Amplifier (Small signal model)

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

29. Mesh Analysis n e =2 essential nodes b e =3 essential branches 3-(2-1)=2 equations

30. Mesh Analysis 12 Clockwise around loop 1: +V in -i 1 r π -(i 1 +i 2 )R E =0 i2=g m i 1 r π Vout=-i 2 R C Loop 1: clockwise Loop 2: counter-clockwise