# 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

- Choose a reference node and label (N-1) node-voltages
- Assign currents to voltages (optional)
- 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
- 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.
- Solve the resulting (N-1) linear independent equations for the (N-1) unknown node-voltages.

### Example

To calculate $v_{x}$, always do positive side of voltage minus negative side. Example:

### Three-Points Rule

### Supernode Analysis

You can simply ignore the voltage source between two nodes.