Week 5: Nodal Analysis

Nodal Analysis

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.

In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, Ibranch = Vbranch * G, where G (=1/R) is the admittance (conductance) of the resistor.

Nodal Analysis without Voltage Sources

Steps to determine nodal voltages:

To apply the node voltage method to a circuit with n nodes (with m voltage sources), perform the following steps:

Select a reference node (usually ground) and name the remaining n-1 nodes.  Also label currents through each current source. 

-Assign a name to the current through each voltage source.  We will use the convention that the current flows from the positive node to the negative node of the source.

-Apply Kirchoff's current law (KCL) to each node.  We will take currents out of the node to be positive.

-Write an equation for the voltage each voltage source.

-Solve the system of n-1 unknowns.

Example:

Sample Problem

Nodal Analysis with Voltage Sources

In order to solve problems involving Nodal Analysis with Voltage Sources, We need to consider the following cases:

Case 1: If the voltage source (dependent or independent) is connected between two non-reference nodes, the two non-reference nodes form a generalized node or supernode, we apply both KCL and KVL to determine the node voltages.

Case 2: if a voltage source is connected between the reference node and a non-reference node, we simply set the voltage at the non-reference node equal to the voltage of the voltage source in figure 2 for example,

As you can see in Case 1, It said something about a "Supernode". You might be wondering "What is a supernode?", A supernode is:

-formed by enclosing a (dependent or independent) voltage source connected between two non-reference nodes and any elements connected in parallel with it.

Reflection:

In our Cpe Class this week, We reached a new chapter and as a first topic of this chapter, We discussed Nodal Analysis. In my own words, Nodal Analysis is basically a method of determining the voltages between nodes or more commonly known as "Nodal Voltages".  Nodal Analysis most of the time uses Kirchoff's Current Law (KCL) and as long as you follow the steps in solving it properly, then you will be able to solve the problem. For me, I think that Nodal Analysis is one of the most difficult topics I have encountered in this class because it requires extensive knowledge of our previous topics but I believe that if you study hard, Then nothing is hard to learn and you will be able to understand the lesson properly.

Video:

Nodal Analysis:

Nodal Analysis practice problems:

Supernode Problem:

Thank you for visiting my Blog!! The sixth post will be arriving next week. See ya!! 

“There must be a positive and negative in everything in the universe in order to complete a circuit or circle, without which there would be no activity, no motion”

-John McDonald