Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
3. 1 Introduction
- Nodal analysis : based on a systematic application of KCL
- Mesh analysis : based on a systematic application of KVL
3.2 Nodal Analysis
- Nodal analysis : a general procedure for analyzing circuits using node
voltages as the circuit variables.
Steps to Determine Node Voltages
1. 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.
2. Apply KCL to each of the n-1 nonreference nodes. Use Ohm’s law
to express the branch currents in terms of node voltages.
3. Solve the resulting simultaneous equations to obtain the unknown
node voltages.
<Fig. 3.1> Common symbols for indicating a reference node,
(a) common ground, (b) ground, (c) chassis ground.
Current flows from a higher potential to a lower potential in a resistor.
i=
vhigher − vlower
R
Example 3.2 Calculate the node voltages
Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
3.3 Nodes Analysis with Voltage Sources
<Fig. 3.7> A circuit with a supernode
Example 3.4 Find the node voltages
Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
3.4. Mesh Analysis
- General procedure for analyzing circuits using mesh currents as the
circuit variables
- Only applicable to a circuit that is planar(No branch crossing)
<Fig.3.15> Planar circuit
<Fig.3.16> A nonplanar circuit
Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
Steps to Determine Mesh Currents:
1. Assign mesh currents i1 , i2 ,..., in to the n meshes.
2. Apply KVL to each of the n meshes. Use Ohm’s law to express the
voltages in terms of the mesh currents
3. Solve the resulting n simultaneous equations to get the mesh
currents
<Fig.3.17> A circuit with two meshes.
Example 3.6 Find I o by using mesh analysis
Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
3.5 Mesh Analysis with Current Sources
<Fig.3.23> Two meshes having a current source in common, (b) a
supermesh, created by exclusing the current source.
Example 3.7 Find i1 and i4
Chungbuk National University Electric Engineering – Circuit Theory I
The first semester, 2010
Chapter 3- Methods of Analysis
Written by Ohmin Kwon
3.6 Nodal and Mesh Analyses by Inspection
⎡G1 + G2
⎢ −G
2
⎣
⎡ R1 + R3
⎢ −R
3
⎣
−G2 ⎤ ⎡ v1 ⎤ ⎡ I1 − I 2 ⎤
=
G2 + G3 ⎥⎦ ⎢⎣v2 ⎥⎦ ⎢⎣ I 2 ⎥⎦
− R3 ⎤ ⎡ i1 ⎤ ⎡ v1 ⎤
=
R2 + R3 ⎥⎦ ⎢⎣i2 ⎥⎦ ⎢⎣ −v2 ⎥⎦
See Example 3.8 and 3.9
3.7 Nodal Versus Mesh Analysis
- Mesh analysis : series-connected elements, voltage sources, or
supermehes(Only method in analyzing transistor circuits)
- Nodal analysis : parallel-connected elements, current sources, or
supernodes(Only method in analyzing OP amp)