# Node-Voltage Analysis

```
Always assume that the current is leaving the node unless otherwise indicated.
Leaving currents will be taken as **positive (+)** while entering currents are taken to be **negative (-)** in KCL equations.
```

### 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 ->

**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/Kirchhoff’s Laws#Kirchhoff’s Junction Current Law KCL|Kirchhoff’s Laws#Kirchhoff’s Junction Current Law KCL]] at each non-reference essential node to get (N-1) equations
- Use Ohm’s Law and Ohm’s Law and [[notes/Kirchhoff’s Laws#Kirchhoff’s Loop Voltage Law KVL|Kirchhoff’s Laws#Kirchhoff’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.