电路原理课件讲义英文版 Chapter_3.ppt

Scientists study the world as it is, engineer create the world that never has been.
---Theodore von Karman
Chapter 3 Methods of Analysis
Introduction
Nodal Analysis
Nodal Analysis with Voltage Sources
Mesh Analysis
Mesh Analysis with Current Sources
Nodal and Mesh Analysis by Inspection
Nodal Versus Mesh Analysis
Summary
Introduction
Two powerful techniques for circuit analysis:
Nodal analysis
(based on a systematic application of KCL)
Mesh analysis
(based on a systematic application of KVL)
Nodal Analysis
Methods: Choosing node voltages instead of element voltages
Finding the node voltages
Merits: Convenient
The number of equations is reduced
Steps to Determine Node Voltages:
Select a node as the reference node. Assign voltages v1, v2, …, vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node.
Apply KCL to each of the n-1 nonreference nodes. Use Ohm’s law to express the branch currents in terms of node voltages.
Solve the resulting simultaneous equations to obtain the unknown node voltages.
The First Step :
Selecting a node as the reference or datum node (called the ground with zero potential )
Typical circuit
for nodal analysis:
The Second Step :
Applying KCL to each nonreference node in the circuit
At node 1:
At node 2:
Notice :
Current flows from a higher potential to a lower potential in a resistor.
Then:
In terms of the conductance, there are
So we obtain:
The Third Step :
To solve for the node voltages
Standard Methods:
Substitution method
Elimination method
Cramer’s rule
Matrix inversion
The last two equations can be cast in matrix form as
which can be solved to get v1 and v2.
Example 1
Simplifying the equations, there is
At node 1:
At node 2:
Example 2
Simplifying the equations, there is
At node 1:
At node 2:
At node 3: