Nodal Analysis, Supernodes, and Circuit Equations

Vocabulary flashcards covering key nodal analysis concepts, including nodes, ground, KCL, supernodes, and source equations.

Node voltage analysis

A method of circuit analysis that uses Kirchhoff's Current Law at each node to solve for unknown node voltages with respect to a reference ground.

Node

A circuit junction where two or more elements connect; it has a single voltage value.

Ground (reference)

The chosen zero-voltage node used as a reference to measure other node voltages.

Unknown node voltages

Voltages at non-reference nodes (e.g., V1, V2, V3) that must be solved.

KCL (Kirchhoff's Current Law)

The algebraic sum of currents at a node equals zero; used to form nodal equations.

Current through a resistor

I = (Voltage difference across the resistor) / R.

Supernode

A combined node that encloses two non-reference nodes connected by a voltage source, treated as one node for KCL.

Voltage source between non-reference nodes

Creates a supernode and imposes a fixed voltage difference between the two nodes.

Source equation (voltage equation)

The relation Vplus - Vminus = V_source describing the voltage source between two nodes.

Known node voltage from a source to ground

If a node is connected to ground through a voltage source, its voltage is known and does not require a KCL equation.

Unknown currents I1, I2

Currents through specified branches that are computed from node voltages once they are known.

Simultaneous equations

A set of linear equations that must be solved together to determine the unknowns in the circuit.

Grounded node selection

Choosing a convenient ground location to simplify equations and fix the reference voltage to zero.

Equation completeness

In KCL, include all currents connected to a node; omitting any term yields incorrect results.

Nodal analysis procedure

Steps: assign unknown node voltages, identify supernodes, write source equations, write KCL for normal nodes and supernodes, solve simultaneously.

Voltage source to ground example

If a node is fixed at a known voltage by a voltage source (e.g., 10 V), use that value to simplify the equations.