Node Voltage Analysis

Node Voltage Analysis finds unknown voltage drops around a circuit between different nodes that provide a common connection for two or more circuit components.

Node Voltage Analysis complements previous network analysis in terms of being equally powerful and based on the same matrix analysis concepts.As its name suggests, Knotted Voltage Analysis uses the "Node" equations of Kirchhoff's first law to find the potential for tension around the circuit.

Thus, by collecting all these node voltages, the net result will be equal to zero.Next, if there are nodes "n" in the circuit, there will be independent node equations "n-1", which alone are enough to identify and therefore solve the circuit.

At each node point, type Kirchhoff's first-law equation, that is, " the value of currents entering a node is exactly equal to the currents that come out of the node ", and then express each current in voltage on the branch.For nodes "n", a node will be used as a reference node, and all other voltages will be referenced or measured according to this common node.

For example, consider the circuit in the previous section:

Node Voltage Analysis Circuit

Node Voltage Analysis
Node Voltage Analysis Circuit

In the above circuit, node D is selected as the reference node and the other three nodes are assumed to have Va, Vb, and Vc voltages relative to node D.For example, if you want to use

Node Voltage Analysis

Va = 10v and Vc = 20v , Etc. can be easily found:

Node Voltage Analysis

The same value is 0.286 amps , we found in the previous lesson using Kirchhoff's Circuit Law.

From both mesh and node analysis methods that we have examined so far, this is the simplest method of solving this particular circuit.In general, node voltage analysis is more convenient when there are more current sources around.The network is then defined as follows: [ I ] = [ Y ] [ V ] where [ I ] drive current sources, [ V ] are node voltages to be found, and [ Y ] is the acceptance matrix of the running network.

Node Voltage Analysis Summary

Node The basic procedure for solving analysis equations is as follows:

  • 1.Type current vectors assuming that the currents coming into a node are positive. that is, the "N" is the a ( N x 1 ) matrices for independent nodes.
  • 2.Type the network's acceptance matrix [ Y ] here:
    • Y 11 = total acceptance of the first node.
    • Y 22 = the total input of the second node.
    • The total input that connects the R JK = J node to node K.
  • 3.For a network with independent nodes, "N" will be positive for [ E], one (will be N x N) matrix and Ynn will be positive, and Yjk will have a negative or zero value.
  • 4.The voltage vector ( N x L ) will be and will list the "N" voltages to be found.

Now, we have seen that a number of theorems are present that simplify the analysis of linear circuits.In the next lesson, we will look at Thevenin Theorem, which allows a network of linear resistors and sources to be represented by a single voltage source and a circuit equivalent to a series of resistances.