Ch. 3 – Methods of Analysistomrebold.com/engr12/CUR/Lecture3-annot.pdfNodal analysis: Steps 1....
Transcript of Ch. 3 – Methods of Analysistomrebold.com/engr12/CUR/Lecture3-annot.pdfNodal analysis: Steps 1....
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Ch. 3 – Methods of Analysis
Nodal analysis:Based on KCLExpress unknown currents in terms of node voltages.
Node Voltage vs. Element Voltage• voltage across an element• potential energy change/work done in moving unit charge across element.
• voltage with respect to a reference node.
Example:
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Nodal analysis: Steps
1. Select a reference node. Assign node voltages to the remaining nodes.
2. Apply KCL to each non-reference node. Express unknown currents in terms of node voltages using Ohm’s Law.
3. Solve for variables of interest.
For step 2:between
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Short Cut
• Direction of assumed current does not matter• Always “assume” all unknown currents are into the node.
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Ans: 40/3 V, 20 V
Example. Find node voltages V1 and V2.
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Ans.: 4.8 V, 2.4 V, -2.4 V
Example: Find node voltages v1, v2 and v3.
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Nodal Analysis with Voltage Sources
Case 1: Vs between reference node and a non-reference node.- Node voltage of non-reference node same as Vs.
Ex. Find current in 2- resistor.
Ans: vA=24V, 4A
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Case 2: Vs between 2 non-reference nodes.-Relate the two node voltages.-Apply KCL to supernode.
Ex. Find vo.
Ans: 1.1111 V
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Ex. Find all node voltages.
Ans. 26.667, 6.667, 173.333,-46.667
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Mesh Analysis
- Based on KVLMesh – a loop that does not contain any other loops in it.Steps:1. Assign mesh currents.2. For each mesh, apply KVL. For Ohm’s Law, use mesh currents.
- Net current in element is the a3. Solve equations. Solve for variables of interest.
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Ex. Find current in 8- resistor using mesh analysis. Ans: 3 A
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Find the current Io.
Ans: i1=2.25, i2=.75, i3=1.5, Io=1.5
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Mesh Analysis with Current Sources
Case 1. Current source only in one mesh mesh current must equal source.
Example
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Case 2. Current source between two meshes
• Express the two mesh current in terms of each other net current to the current source is equal to the source.– By “inspection” or– By applying KCL
• Apply KVL for the supermesh to “avoid” the current source.
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Find the current in each resistor.
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Nodal Analysis by Inspection
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Mesh Analysis by Inspection
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Set up all nodal equations by inspection.
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Set up all mesh equations by inspection.