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Lecture 6

Lecture 6. Nodal/Mesh Analysi 4.2,4.3, 4.5 &4.6. Definitions. Nodes. Node: a point where two or more circuit elements join. Essential Node. Essential Node: a node where three or more circuit elements join. Step 1: Number of Nodal Voltage Equations. n e is essential nodes

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Lecture 6

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  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 • ne is essential nodes • Number of nodal voltage Equations is ne-1 ne=3 ne-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) (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 IS VS R5 R10

  9. Simulation Results

  10. Solve ia, ib and ic

  11. Hints ne=2 Need ne-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 ne=3

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

  19. Step 3: Apply KVL Around Loop b - + + - Focus initially on ia. 40-iaR2-(ia)8=0 Account for ib. 40-iaR2-(ia-ib)8=0

  20. Step 4: Apply KVL Around Loop b - + + - + - • Focus initially on ib. -(ib )8-ib6-(ib )6=0 • Account for ia.-(ib-ia)8-ib6-(ib)6=0 • Account for ic. -(ib-ia)8-ib6-(ib-ic)6=0

  21. Step 5: Apply KVL Around Loop c + - - + Focus initially on ic. -(ic )6-ic4-20=0 Account for ib-(ic-ib)6-ic4-20=0

  22. Solve 3 EQ and 3 Unknowns Using Mathematica 3 Unknown equations 3 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 ne=2 essential nodes be=3 essential branches 3-(2-1)=2 equations

  30. Mesh Analysis 1 2 Loop 1: clockwise Loop 2: counter-clockwise Clockwise around loop 1: +Vin-i1rπ-(i1+i2)RE=0 i2=gmi1rπ Vout=-i2RC

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