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Nodal_Analysis__Lecture description.pptx
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- 2. Objective of Lecture •Provide step-by-step instructions for nodal analysis, which is a method to calculate node voltages and currents that flow through components in a circuit. • Chapter 3.2 and Chapter 3.3
- 3. Nodal Analysis • Techniqueto find currents at a node using Ohm’s Law, Kirchhoff’s Current Law, and the potential differences between nodes. • • First result: determination of node voltages (referenced to ground) • • Second result: calculation of currents
- 4. Steps in NodalAnalysis • Vin
- 5. Steps in NodalAnalysis • Pick one node as a reference node • Its voltage will be arbitrarily defined to be zero • Vin
- 6. Step 1: Pickone node as a reference node • Its voltage will be arbitrarily defined to be zero • Vin
- 7. Step 2 • Labelthe voltage at the other nodes • Vin
- 8. Step 2 • Labelthe voltage at the other nodes • Vin
- 9. Step 3 • Labelthe currents flowing through each of the components in the circuit
- 10. Step 4 • UseKirchhoff’s Current Law
- 11. Step 5 • UseOhm’s Law to relate the voltages at each node to the currents flowing in and out of them. • • Current flows from a higher to a lower potential • • Voltage difference drives current I
- 12. Step 5 • Wedo not write an equation for I7 as it is equal to I1
- 13. Step 6: Solvefor the node voltages • In this problem we know that V1 = Vin
- 14. Step 6 • Substitutethe equations obtained using Ohm’s Law into the equations obtained using KCL.
- 15. Step 7 • Oncethe node voltages are known, calculate the currents.
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- 18. Substituting Ohm’s Lawinto KCL equations
- 19. Chugging through theMath - Node Voltages (V) • V1: 10 • V2: 5.55 • V3: 4.56 • V4: 3.74 • V5: 3.46 • • Node voltages must be < total voltage sources • • Some may be negative depending on
- 20. Chugging through theMath - Voltage across Resistors (V) • VR1 = V1 – V2 = 4.45 • VR2 = V2 – V3 = 0.990 • VR3 = V3 – V5 = 1.10 • VR4 = V3 – V4 = 0.824 • VR5 = V4 – V5 = 0.274 • VR6 = V5 – 0 = 3.46 • • No voltage drop can exceed total source voltage (10V)
- 21. Chugging through MoreMath - Currents (mA) • I1: 495 • I2: 220 • I3: 220 • I4: 275 • I5, I6, I7: -
- 22. Check • • Nocurrent should exceed the total current from the 10V supply's equivalent series resistor. • • Only valid if there’s one voltage source.
- 23. Summary: Steps inNodal Analysis • 1. Pick one node as reference • 2. Label voltages at other nodes • 3. Label currents • 4. Apply KCL • 5. Apply Ohm’s Law • 6. Solve for node voltages • 7. Calculate currents