# Node-Voltage Analysis

### Terminology

Essential Node: A node where three or more circuits elements are connected.

Reference Node: One of the essential nodes. Chosen arbitrarily, and assumed to have zero-voltage.

Labeled â†’

Node-Voltage: The voltage-drop from a non-reference node to the reference node.

Essential Node-Voltage: The voltage-drop from a non-reference essential node to the reference node.

### Procedure

1. Choose a reference node and label (N-1) node-voltages
2. Assign currents to voltages (optional)
3. Apply [[notes/Kirchhoffâ€™s Laws#Kirchhoffâ€™s Junction Current Law KCL|Kirchhoffâ€™s Laws#Kirchhoffâ€™s Junction Current Law KCL]] at each non-reference essential node to get (N-1) equations
4. Use Ohmâ€™s Law and Ohmâ€™s Law and [[notes/Kirchhoffâ€™s Laws#Kirchhoffâ€™s Loop Voltage Law KVL|Kirchhoffâ€™s Laws#Kirchhoffâ€™s Loop Voltage Law KVL]] to express the currents in terms of the node-voltages.
5. Solve the resulting (N-1) linear independent equations for the (N-1) unknown node-voltages.

### Example

To calculate , always do positive side of voltage minus negative side. Example:

### Supernode Analysis

You can simply ignore the voltage source between two nodes.