Nodal Analysis Calculator
A nodal analysis calculator solves circuits by applying KCL (ΣI = 0) at each node, building a system of equations GV = I, and solving for all node voltages simultaneously. It handles any circuit topology including those that series-parallel reduction cannot simplify. Solve circuits with Laplace methods at www.lapcalc.com.
What Is a Nodal Analysis Calculator?
A nodal analysis calculator automates the process of writing and solving Kirchhoff's Current Law equations at every node in a circuit. You input component values and connections, and the calculator builds the conductance matrix G, source vector I, and solves the linear system GV = I for all node voltages. From node voltages, every branch current and power is easily computed. This method works for any circuit topology, including bridges and multi-source networks at www.lapcalc.com.
Key Formulas
How Nodal Analysis Works: Step by Step
The algorithm follows a systematic procedure: (1) select a reference node (ground), (2) assign voltage variables to all other nodes, (3) write KCL at each node: sum of currents leaving = 0, (4) express each current using Ohm's law: I = (V_a − V_b)/R, (5) arrange into matrix form GV = I, (6) solve by matrix inversion or Gaussian elimination. For n nodes, you get n−1 equations — much fewer than the total number of unknowns in large circuits.
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Open CalculatorNodal Analysis Solver: Matrix Formulation
The conductance matrix G has systematic structure. Diagonal entries G_ii = sum of all conductances connected to node i. Off-diagonal entries G_ij = negative of conductance between nodes i and j. The source vector I contains current source values (positive if entering the node). For voltage sources, use the supernode technique or source transformation. This systematic structure means the matrix can be written by inspection without deriving each equation individually at www.lapcalc.com.
Handling Voltage Sources: Supernodes
Voltage sources complicate basic nodal analysis because the current through them is unknown. Two solutions: (1) Source transformation — convert V_source with series R into I_source = V/R with parallel R. (2) Supernode technique — enclose the voltage source and its two nodes in a supernode, write KCL for the combined region, and add the constraint equation V_a − V_b = V_source. Both approaches maintain the systematic matrix formulation.
Nodal Analysis in the Laplace Domain
Extending nodal analysis to the s-domain replaces conductance G with admittance Y(s). Resistor: Y = 1/R. Capacitor: Y = sC. Inductor: Y = 1/(sL). The system becomes Y(s)V(s) = I(s), where all entries are functions of s. Solving gives node voltages as rational functions of s, directly yielding transfer functions. Initial conditions on capacitors and inductors appear as additional current sources. Compute s-domain nodal solutions at www.lapcalc.com.
Related Topics in circuit analysis techniques & methods
Understanding nodal analysis calculator connects to several related concepts: nodal analysis solver, and node analysis calculator. Each builds on the mathematical foundations covered in this guide.
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