1. What is Nodal Voltage Analysis?

Nodal Voltage Analysis is a systematic method to determine the voltage at each node (connection point) in an electrical circuit. The equation V = G⁻¹ × I represents the solution to the system of equations derived from applying Kirchhoff's Current Law at each node.

2. How Does the Calculator Work?

The calculator uses the nodal voltage equation:

Where:

• \( G \) — Conductance matrix (n×n) representing the circuit
• \( G^{-1} \) — Inverse of the conductance matrix
• \( I \) — Current vector (n×1) representing injected currents
• \( V \) — Resulting voltage vector (n×1) at each node

Explanation: The calculator first inverts the conductance matrix G, then multiplies it by the current vector I to obtain the nodal voltages.

3. Importance of Nodal Analysis

Details: Nodal voltage analysis is fundamental in circuit theory for solving complex electrical networks. It's used in power system analysis, electronic circuit design, and network simulations.

4. Using the Calculator

Tips:

• Enter the conductance matrix G with one row per line
• Separate matrix elements with spaces or commas
• Enter the current vector I with all values on one line
• Matrix must be square and non-singular (invertible)
• Vector length must match matrix dimensions

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between nodal and mesh analysis?
A: Nodal analysis uses node voltages as variables and KCL, while mesh analysis uses mesh currents and KVL. Nodal is generally preferred for computer solutions.

Q2: How do I construct the G matrix for my circuit?
A: Diagonal elements are sum of conductances connected to the node. Off-diagonal elements are negative conductances between nodes.

Q3: What if my matrix is singular?
A: A singular matrix usually indicates a problem in circuit formulation, like a floating node or incorrect reference node selection.

Q4: Can this handle dependent sources?
A: The basic calculator doesn't handle dependent sources directly. They require modified matrix formulation.

Q5: What units should I use?
A: Use consistent units - typically siemens for conductance, amperes for current, and volts for the resulting voltages.