Ch 3 Methods of Analysis Nodal analysis Based

Ch. 3 – Methods of Analysis Nodal analysis: Based on KCL Express unknown currents in terms of node voltages. Node Voltage vs. Element Voltage • voltage across an element • voltage with respect to a • potential energy change/work done reference node. Example: in moving unit charge across element.

Nodal analysis: Steps 1. 2. 3. Select a reference node. Assign node voltages to the remaining nodes. Apply KCL to each non-reference node. Express unknown currents in terms of node voltages using Ohm’s Law. Solve for variables of interest. For step 2:

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

Example. Find node voltages V 1 and V 2. Ans: 40/3 V, 20 V

Example: Find node voltages v 1, v 2 and v 3. Ans. : 4. 8 V, 2. 4 V, -2. 4 V

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: v. A=24 V, 4 A

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, 173. 333, -46. 667

Mesh Analysis Based on KVL Mesh – 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 a 3. Solve equations. Solve for variables of interest.

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

Find the current Io. Ans: i 1=2. 25, i 2=. 75, i 3=1. 5, Io=1. 5

Mesh Analysis with Current Sources Case 1. Current source only in one 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.