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. It's based on Kirchhoff's Current Law (KCL) and solves the equation G V = I, where G is the conductance matrix, V is the voltage vector, and I is the current vector.

2. How Does the Calculator Work?

The calculator solves the nodal voltage equation:

Where:

• \( G \) — Conductance matrix (n×n)
• \( V \) — Unknown voltage vector (n×1)
• \( I \) — Known current vector (n×1)

Explanation: The calculator uses matrix operations to solve the linear system of equations, providing the voltage at each node in the circuit.

3. Importance of Nodal Analysis

Details: Nodal analysis is fundamental for circuit design and analysis, helping engineers determine voltages throughout a circuit, which are essential for understanding circuit behavior and performance.

4. Using the Calculator

Tips: Enter the conductance matrix and current vector in proper format. The conductance matrix must be square, and the current vector must match its dimensions.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between nodal and mesh analysis?
A: Nodal analysis uses KCL and solves for node voltages, while mesh analysis uses KVL and solves for loop currents.

Q2: How do I construct the conductance matrix?
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 means the system has no unique solution, possibly due to floating nodes or incorrect circuit modeling.

Q4: Can I analyze non-linear circuits?
A: This calculator is for linear circuits. Non-linear circuits require iterative methods or small-signal analysis.

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