48-nodal-analysis

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Nodal analysis (also called node voltage analysis or branch current method) is practical method for electric circuit analysis with small number of nodes and possibly large number of mesh. All equations are written according KCL, so it is important to have small number of nodes i.e. small number of equations to solve.

Steps of the analysis:

  1. Find one node (possibly with a lot of branches) and make it reference node (node with potential of zero volts).
  2. Assign a variable for each node whose voltage is unknown. If the voltage is already known, it is not necessary to assign a variable.
  3. If there is a branch with only ideal voltage source in it, set of equations has to be modified, since it is not possible to calculate current to/from ideal voltage source, apart from other currents in node given.
  4. Write set of equations based on KCL, where each of individual currents is calculated simply by applying Ohm’s law – as difference of voltage potential between two nodes over resistance.
  5. Solve formed system of equations.

In the following example, given scheme is analyzed with node voltage analysis.

nodal_a

In given scheme, node V0, is chosen to be reference voltage (not necessarily on ground potential). Remaining nod is marked as VA, and only one equating should be written:

nodal_eq_05

By separating values:

nodal_eq_06

Final solution is:

nodal_eq_07

Now, currents I3 and I2 are easy to calculate as:

nodal_eq_08

System of equations is significantly reduced comparing to direct application of Kirchhoff circuit laws, where should be one equation written according to Kirchhoff’s current law and two according to Kirchhoff’s voltage law. For comparison, the same circuit is analyzed with mesh analysis.

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