Download Lecture 4: Methods of Analysis

Methods of Analysis
Circuits 1
Fall 2005
Harding University
Jonathan White
Outline
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Nodal Analysis
• Define a symbol for all unknown node voltages.
• Write KCL at each node where variables occur
• Using Ohm’s Law, solve resulting equations.
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Mesh Currents
• Set up the currents
• Use KVL
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Methods to solve linear equations
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Substitution
Determinants
Calculator
Method from Numerical Methods
Nodal Analysis
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Steps:
• Define a voltage at every node in the circuit
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Note: Some may be known, such as the source and
ground
• Write KCL at the nodes where the unknown voltages
exist
• Now, plug into these KCL equations with the unknown
voltages, remembering how Ohm’s Law works. In this
case, I = (VH – VL)/R, because we are writing voltages
for nodes, not just resistors. Since current flows from a
higher potential to a lower potential, the voltage over a
resistor that is connected to 2 nodes is just VH – VL
• Other current and voltage sources must be factored in to
either the KCL equations or the unknown voltages. They
sometimes actually make the equations easier.
• Solve for the unknown voltages.
Nodal Analysis Example 1
Find all voltages and currents.
Nodal Analysis Example 2
Find Vo
+ Vo -
Mesh Currents
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Steps:
• Label each unknown current in each mesh, going
clockwise.
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A mesh is a loop which does not contain any other loops
within it.
Also, write down the polarities of the currents as they go
through each resistor.
• Write KVL equations for each mesh. In this case, use
V=I*R. When resistors are in both meshes, I=(I1-I2).
• Use Ohm’s Law to express the voltages in terms of the
mesh currents.
• Again, you may need extra equations if there are other
current/voltage sources.
• Solve for the unknown currents.
Mesh Current Example - 1
Calculate the mesh currents.
Mesh Current Example - 2
Find the current through the 1 ohm R
Methods of Solving Sets of
Equations
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Calculator
• rref function
• solve function
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Linear Algebra
Substitution
Graphing
Euclid’s Method