CIRCUIT ANALYSIS GUIDE

Two-node nodal analysis

Nodal analysis writes Kirchhoff current equations at each node. A resistor network becomes a conductance matrix multiplied by node voltages.

FORMULA

G · V = I

WORKED EXAMPLE

With R1 from node 1 to ground, R2 from node 2 to ground, R12 between nodes, and current injections I1 and I2, solve a 2×2 conductance matrix for V1 and V2.

STEP BY STEP

Choose a reference node

Ground is the voltage reference. Every node voltage is measured relative to it.

Convert resistors to conductances

Use G = 1/R. Diagonal matrix terms collect conductances connected to each node; the shared branch contributes negative off-diagonal terms.

Solve for node voltages

Solve G·V=I, then calculate branch currents from the voltage difference divided by resistance.