Ch. 3 – Methods of Analysis

Nodal analysis:Based on KCLExpress unknown currents in terms of node voltages.

Node Voltage vs. Element Voltage• voltage across an element• potential energy change/work done in moving unit charge across element.

• voltage with respect to a reference node.

Example:

Nodal analysis: Steps

1. Select a reference node. Assign node voltages to the remaining nodes.

2. Apply KCL to each non-reference node. Express unknown currents in terms of node voltages using Ohm’s Law.

3. Solve for variables of interest.

For step 2:between

lowerhigher

Rvv

i

Short Cut

• Direction of assumed current does not matter• Always “assume” all unknown currents are into the node.

Ans: 40/3 V, 20 V

Example. Find node voltages V1 and V2.

Ans.: 4.8 V, 2.4 V, -2.4 V

Example: Find node voltages v1, v2 and v3.

Nodal Analysis with Voltage Sources

Case 1: Vs between reference node and a non-reference node.- Node voltage of non-reference node same as Vs.

Ex. Find current in 2- resistor.

Ans: vA=24V, 4A

Case 2: Vs between 2 non-reference nodes.-Relate the two node voltages.-Apply KCL to supernode.

Ex. Find vo.

Ans: 1.1111 V

Ex. Find all node voltages.

Ans. 26.667, 6.667, 173.333,-46.667

Mesh Analysis

- Based on KVLMesh – a loop that does not contain any other loops in it.Steps:1. Assign mesh currents.2. For each mesh, apply KVL. For Ohm’s Law, use mesh currents.

- Net current in element is the a3. Solve equations. Solve for variables of interest.

Ex. Find current in 8- resistor using mesh analysis. Ans: 3 A

Find the current Io.

Ans: i1=2.25, i2=.75, i3=1.5, Io=1.5

Mesh Analysis with Current Sources

Case 1. Current source only in one mesh mesh current must equal source.

Example

Case 2. Current source between two meshes

• Express the two mesh current in terms of each other net current to the current source is equal to the source.– By “inspection” or– By applying KCL

• Apply KVL for the supermesh to “avoid” the current source.

Find the current in each resistor.

Nodal Analysis by Inspection

Mesh Analysis by Inspection

Set up all nodal equations by inspection.

Set up all mesh equations by inspection.