CHAPTER 3 ANALYSIS TECHNIQUES (PART 2)
CIRCUITS by Ulaby & MaharbizAll rights reserved. Do not reproduce or distribute.
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07/07/2016 ECE225 CIRCUIT ANALYSIS
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Node-Voltage Method
Node 1
Node 2Node 3
Node 2
Node 3
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Mesh-Current Method
Two equations in 2 unknowns:Solve using Cramer’s rule, matrixinversion, or MATLAB
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Supernode
Current through voltage source is unknown Less nodes to worry about, less work! Write KVL equation for supernode Write KCL equation for closed surface around supernode
A supernode is formed when a voltage source connects twoextraordinary nodes
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KCL at Supernode
Note that “internal” current in supernode cancels, simplifying KCL expressions
Takes care of unknown current in a voltage source
=
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Example 3-3: Supernode
Determine: V1 and V2
Solution:
Supernode
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Press
Supermesh
A supermesh results when two meshes have a current source( with or w/o a series resistor) in common
Voltage across current source is unknown Write KVL equation for closed loop that ignores branch with current source Write KCL equation for branch with current source (auxiliary equation)
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Example 3-6: Supermesh
Mesh 2
SuperMesh 3/4
Mesh 1
Supermesh Auxiliary Equation
Solution gives:
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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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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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Linearity
A circuit is linear if output is proportional to input
A function f(x) is linear if f(ax) = af(x) All circuit elements will be assumed to be linear
or can be modeled by linear equivalent circuits Resistors V = IR Linearly Dependent Sources Capacitors Inductors
We will examine theorems and principles that apply to linear circuits to simplify analysis
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Superposition
Superposition trades off the examination of several simpler
circuits in place of one complex circuit
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and Science Press
Example 3-9: Superposition
Contribution from I0Contribution from V0
I1 = 2 A I = I1 + I2 = 2 ‒ 3 = ‒1 A
alone alone
I2 = ‒3 A
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Tech Brief 4: The LED
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Tech Brief 4: The LEDAll rights reserved. Do not reproduce
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Tech Brief 4: The LED
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Summary
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