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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 Nodal/Mesh Analysi 4.2,4.3, 4.5 &4.6
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 • ne is essential nodes • Number of nodal voltage Equations is ne-1 ne=3 ne-1 =2 nodal voltage equations are required.
Step 2: Designate a node as the reference node. • Suggestion: Select the node with the most branches. (3 branches) (3 branches) (4 branches)
Step 4: Apply KCL • Apply KCL to essential nodes. R1 R2 IS VS R5 R10
Hints ne=2 Need ne-1=1 equation
Branch Branch: a path that connects two nodes.
Essential Branch Essential branch: a path which connects two essential nodes without passing through an essential node.
Mesh Mesh: a loop that does not enclose any other loops
Step 2: Determine the number of essential branches be=5 # of equations: be-(ne-1)=5-(3-1)=3
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
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
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
Solve 3 EQ and 3 Unknowns Using Mathematica 3 Unknown equations 3 unknowns
Step 1 # of essential branch: 6 # of essential nodes: 4 # of equations: 6-(4-1)=3
Step 2 See in the handout.
Use Mathematica to Solve Equations Format: Solve[{equations separated by a comma},{list of unknowns}] To solve an equation: Evaluation→Evaluate Cells
Degenerated Common Emitter Amplifier (Small signal model)
What if we drive the base with a small signal? Vin, m=1 mV Vout, m=46 mV
Mesh Analysis ne=2 essential nodes be=3 essential branches 3-(2-1)=2 equations
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