Nodal Analysis in Electric Circuits

The key difference between nodal analysis and mesh analysis lies in the approach to applying Kirchhoff's laws. Nodal analysis uses Kirchhoff's current law (KCL) and writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. Mesh analysis, on the other hand, uses Kirchhoff's voltage law (KVL) and applies it to the loops in the circuit.

Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. This means that the branch currents must be written in terms of the circuit node voltages, and each branch constitutive relation must give current as a function of voltage, represented by an admittance (conductance) term.

Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs, such as SPICE, use nodal analysis as a basis for efficient and accurate simulations.

Modified nodal analysis can be used when circuit elements do not have admittance representations. It is a more general extension of nodal analysis, allowing for the analysis of circuits where the branch constitutive relations do not have a simple admittance form.

For a resistor in nodal analysis, the branch current (I_{\text{branch}}) is represented as the product of the branch voltage (V_{\text{branch}}) and the admittance (conductance) of the resistor, given by the equation I_{\text{branch}} = V_{\text{branch}} \cdot G, where G (=1/R) is the admittance of the resistor.