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3. ANALYSIS TECHNIQUESCircuit Analysis & Design by Ulaby, Maharbiz & Furse
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Chapter 3
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Node-Voltage Method
Node 1
Node 2Node 3
Node 2
Node 3
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Node-Voltage Method
Three equations in 3 unknowns:Solve using Cramer’s rule, matrixinversion, or MATLAB
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Mesh-Current Method
Two equations in 2 unknowns:Solve using Cramer’s rule, matrixinversion, or MATLAB
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Example 3-5: Mesh Analysis
Mesh 1
Mesh 2
Mesh 3
But
Hence
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Nodal versus Mesh
When do you use one vs. the other? What are the strengths of nodal versus mesh?
Nodal Analysis Node Voltages (voltage difference between each node
and ground reference) are UNKNOWNS KCL Equations at Each UNKNOWN Node Constrain
Solutions (N KCL equations for N Node Voltages) Mesh Analysis
“Mesh Currents” Flowing in Each Mesh Loop are UNKNOWNS
KVL Equations for Each Mesh Loop Constrain Solutions (M KVL equations for M Mesh Loops)
Count nodes, meshes, look for supernode/supermesh
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Nodal Analysis by Inspection
Requirement: All sources are independent current sources
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G=1/R
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Example 3-7: Nodal by Inspection
@ node 1
@ node 2
@ node 3
@ node 4
Off-diagonal elements Currents into nodes
G13G13G11G11
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Mesh by InspectionRequirement: All sources are independent voltage sources
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Thévenin’s Theorem
Linear two-terminal circuit can be replaced by an
equivalent circuitcomposed of a voltage
source and a series resistor
inTh RR
voltage across output with no load (open circuit)
Resistance at terminals with allindependent circuit sources set to zero
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Norton’s TheoremLinear two-terminal circuit can be replaced by an equivalent circuit composed of a current source and parallel resistor
Current through output with short circuit
Resistance at terminals with all circuit sources set to zero
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How Do We Find Thévenin/Norton Equivalent Circuits ?
Method 1: Open circuit/Short circuit
1. Analyze circuit to find
2. Analyze circuit to find
Note: This method is applicable to any circuit, whether or not it contains dependent sources.
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Example 3-11: Thévenin Equivalent
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How Do We Find Thévenin/Norton Equivalent Circuits?Method 2: Equivalent Resistance
1. Analyze circuit to find either
or
Note: This method does not apply to circuits that contain dependent sources.
2. Deactivate all independent sources by replacing voltage sources with short circuits and current sources with open circuits.3. Simplify circuit to find equivalent resistance
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Example 3-12: RTh
Replace with SC
Replace with OC
(Circuit has no dependent sources)
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How Do We Find Thévenin/Norton Equivalent Circuits?
Method 3:
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Power Transfer
In many situations, we want to maximize power transfer to the load
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Example 3-15
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Example 3-15
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Summary