Node Voltage Analysis Calculator

Solve node voltages for resistor networks and sources. Review matrix terms, branch currents, and power. Download practical reports for clear circuit checks every time.

Calculator Inputs

Positive current injection enters a node. Negative current injection leaves a node. Blank resistor fields are ignored.

Node Data

Resistors Between Nodes

Example Data Table

Item Example value Meaning
Unknown nodes 2 Two node voltages are solved against ground.
N1 resistor to ground 2000 Ω Conductance from node one to reference.
N2 resistor to ground 3000 Ω Conductance from node two to reference.
Resistor N1 to N2 1000 Ω Shared branch between both unknown nodes.
N1 current injection 5 mA Current source entering node one.

Formula Used

The calculator uses nodal analysis in matrix form:

[G][V] = [I]

G is the admittance matrix in siemens. V is the node voltage vector. I is the current injection vector.

For a resistor from node i to ground:

Gii = Gii + 1 / R

For a resistor between node i and node j:

Gii = Gii + 1 / R, Gjj = Gjj + 1 / R, Gij = Gij - 1 / R, Gji = Gji - 1 / R

After solving node voltages, branch current is found by:

Iij = (Vi - Vj) / Rij

Resistor power is found by:

P = V² / R

How to Use This Calculator

  1. Choose the number of unknown nodes.
  2. Enter each node resistor to ground when present.
  3. Enter current injection for each node.
  4. Enter resistors connected between node pairs.
  5. Leave unused branches blank.
  6. Press the calculate button.
  7. Review node voltages, currents, matrix terms, and power.
  8. Download the CSV or PDF report when needed.

Why Node Voltage Analysis Matters

Node voltage analysis is a direct method for solving linear circuits. It focuses on unknown node potentials measured from a chosen reference node. This view is useful when many branches share common points. It also reduces repeated loop equations. Students use it for homework. Technicians use it for checks. Designers use it before simulation.

What This Calculator Does

This calculator builds a conductance matrix from the values you enter. Each resistor to ground adds conductance to one node. Each resistor between two nodes adds conductance to both connected nodes. It also adds negative mutual conductance between those two nodes. Current sources are entered as injected current into a node. A negative value means the source leaves that node.

Advanced Circuit Review

The tool solves up to four unknown node voltages. It accepts ohm, kiloohm, and megaohm resistor units. It accepts ampere, milliampere, and microampere current units. The result includes the admittance matrix, voltage list, ground currents, branch currents, and estimated power. These details help you confirm signs and directions.

Practical Use Cases

Use this page for resistive networks, current-source models, bias circuits, sensor dividers, load sharing, and training examples. It is best for linear DC circuits where every unknown node connects through resistors or current sources. Voltage sources between unknown nodes need supernode handling. For those cases, convert sources when possible or check with a circuit simulator.

Accuracy Notes

Input values should be positive for resistors. Leave unused branches blank. Use a very large resistance for an almost open branch. Use consistent signs for current sources. The matrix must be solvable. If a node floats with no path to reference, the calculator will warn you.

Report Options

After solving, export the results as a CSV file. You can also create a PDF report from the displayed result. The example table shows common circuit data. Compare it with your own entries to learn the expected format. This workflow gives a clear audit trail for class notes, maintenance records, and design reviews. It also helps teams share circuit assumptions quickly. Saved reports make troubleshooting easier when values change, because each exported line shows inputs, solved voltages, and currents for later comparison during reviews and lab work too.

FAQs

What is node voltage analysis?

It is a circuit method that solves node voltages against a reference node. It uses Kirchhoff current law and conductance values. The unknowns are node voltages, not loop currents.

What does positive current injection mean?

Positive current injection means the current source enters the node. A negative value means current leaves the node. This sign choice affects the solved voltage direction.

Can I leave a resistor field blank?

Yes. Blank resistor fields are ignored. Use blanks for missing branches. Do not enter zero ohms, because a zero-ohm branch creates an invalid conductance.

Why does the calculator show a singular matrix?

A singular matrix usually means one or more nodes are floating. Add a ground path, add a valid connecting resistor, or reduce the node count.

Does this handle voltage sources?

This version is built for resistors and current sources. Voltage sources between unknown nodes require supernode equations. Convert simple source-resistor networks when practical.

What is the admittance matrix?

It is a table of conductance terms. Diagonal entries contain connected conductance sums. Off-diagonal entries show negative shared conductance between connected nodes.

How are branch currents calculated?

Branch current uses Ohm's law. The calculator subtracts the second node voltage from the first node voltage, then divides by branch resistance.

What can I export?

You can download a CSV report with voltages, matrix terms, branch currents, and power. You can also download a PDF report from the displayed result.

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