Measurement and Noise
Model class: Exact thermal-noise relationship
Johnson noise calculator
Calculate ideal resistor thermal-noise voltage density, integrated RMS noise, and available kTB noise power.
Interactive engine
Start with the stated conditions.
Values stay in this browser. Choose a representative scenario, then calculate deliberately.
Example ready
Calculate to inspect the result.
The result will identify the direct answer, assumptions, and any warning that changes the next decision.
How much does each input matter?
Each row holds every other input fixed at its current value and moves one input by ±10%, using the same model as the main result. It identifies which input is the binding lever, not a full tolerance stack.
Assumptions to check
- The entered Johnson-noise values represent the stated operating condition.
- This exact thermal-noise relationship is evaluated in the declared lumped or first-pass model.
- A Johnson-noise calculation is not a component qualification or safety approval.
What this Johnson-noise calculation establishes
Calculate ideal resistor thermal-noise voltage density, integrated RMS noise, and available kTB noise power. The useful result is the stated electrical quantity and the decision it supports, not an unstated claim about a finished product. This engine keeps the governing relationship visible so an input, unit, condition, or model boundary can be reviewed before a value becomes a component or layout choice.
Integrated resistor noise is the square root of four times Boltzmann’s constant, temperature, resistance, and equivalent noise bandwidth. Treat the number as a first-pass result for the declared operating point. When a source, load, temperature, frequency, waveform, component tolerance, or measurement condition changes, repeat the calculation at the relevant corner rather than assuming the nominal answer persists.
Worked decision context
At 300 K, 1 kΩ over 20 kHz has 0.5756 µV RMS Johnson voltage noise; available kTB power is independent of resistance. That example verifies the equation and illustrates the scale of the result, but it does not select a part by itself. Compare the result with available values, ratings, tolerance bands, and the receiving circuit or physical environment before implementation.
Use the primary output to identify the binding constraint. If it leaves little margin, document which input dominates and use selected-part data, a higher-fidelity model, simulation, or measurement. This is especially important when a small numerical difference changes a thermal, timing, noise, or reliability decision.
Limits and validation handoff
It omits amplifier noise, filter shape beyond the entered equivalent bandwidth, aliasing, impedance interaction, and measurement uncertainty. The calculation does not silently include omitted parasitics, installation conditions, manufacturing variation, or product policy. Those conditions can be decisive even when the arithmetic is exact for the selected model.
Record inputs, units, model assumptions, and the intended decision with the result. Verify the leading risk against the selected component data sheet and a representative measurement when the circuit has consequential energy, high voltage, safety, compliance, or reliability requirements.
Common mistakes
- Treating the Johnson-noise result as a guaranteed operating limit rather than a first-pass exact thermal-noise relationship estimate.
- Mixing a data-sheet value measured under one condition with this Johnson-noise calculation performed at another.
- Selecting a component before checking the boundary this calculation names: it omits amplifier noise, filter shape beyond the entered equivalent bandwidth, aliasing, impedance interaction, and measurement uncertainty.
Model limit and handoff
Keep the entered Johnson-noise conditions with the calculation, then validate the binding limit using the selected component, physical implementation, and representative operating corner.
FAQs
Is this Johnson-noise result sufficient to approve a design?
No. It applies exact thermal-noise relationship reasoning to the entered Johnson-noise values and names the checks that still need selected-part data, a higher-fidelity model, or measurement. It omits amplifier noise, filter shape beyond the entered equivalent bandwidth, aliasing, impedance interaction, and measurement uncertainty.
What does this Johnson-noise calculator assume that could make the result wrong?
Integrated resistor noise is the square root of four times Boltzmann’s constant, temperature, resistance, and equivalent noise bandwidth. If the entered values do not match the real operating condition, the result no longer describes the actual circuit.
Where should this Johnson-noise result go next?
Compare this Johnson-noise result with Electronics noise fundamentals, then use the stated next decision below the calculator to move from this first-pass number toward an implementation.