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Node-Voltage Analysis and
Mesh-Current Analysis
ELEC 308
Elements of Electrical Engineering
Dr. Ron Hayne
Images Courtesy of Allan Hambley and Prentice-Hall
Node-Voltage Analysis
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Selecting the Reference Node
 Remember:

A NODE is point at which two or more circuit
elements are joined together
 Must FIRST select one of the nodes in the
circuit to be a REFERENCE node

Which one???
Theoretically, ANY will work
 Usually one end of a voltage source
 Mark reference node with GROUND SYMBOL

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Finding Element Voltages
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Exercise 2.5
 Find expressions for vy, and vz, in term of the node
voltages v1, v2, and v3.
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Writing KCL Equations
 To find the current flowing out of node n through a
resistance toward node k, subtract the voltage at
node k from the voltage at node n and divide the
difference by the resistance
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Example 2.6
 Write KCL equations
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Standard Form Equations
g11v1  g12v2  i1
g 21v1  g 22v2  i2
g11v1  g12v2  g13v3  i1
g 21v1  g 22v2  g 23v3  i2
g 31v1  g 32v2  g 33v3  i3
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Example 2.9
 Write KCL equations


Put equations in standard form
Solve
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Example 2.8
 Find ix
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Exercise 2.14
 Find ia
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Mesh-Current Analysis
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Mesh Currents
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Example
 Find the mesh currents i1 and i2
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Exercise
 Find the current through the 2Ω resistor
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Circuits With Current Sources
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Exercise 2.23
 Find the mesh currents i1 and i2
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Summary
 Node-Voltage Analysis
 Mesh-Current Analysis
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