Johnson Noise (Thermal Noise) Calculator
Estimate resistor thermal noise using the Nyquist relation:
Uses Boltzmann constant k = 1.380649×10-23 J/K. Assumes white thermal noise over the selected bandwidth.
What Is Johnson Noise?
Johnson noise (also called thermal noise or Johnson–Nyquist noise) is the random electrical noise generated by the thermal motion of charge carriers in a resistor. It exists in every real resistor and passive conductor above absolute zero. Because it is fundamental physics, it cannot be eliminated entirely—only managed.
For analog circuits, sensor front ends, RF links, and data converters, Johnson noise sets a lower bound on detectable signal levels. If your signal is close to this floor, design choices like bandwidth and source resistance become critical.
Core Formula and Meaning
Voltage Noise (RMS)
Vn,rms = √(4kTRB)
- k: Boltzmann constant (1.380649×10-23 J/K)
- T: absolute temperature in kelvin
- R: resistance in ohms
- B: bandwidth in hertz
Current Noise (RMS)
In,rms = √(4kTB/R)
This form is useful when modeling a resistor as an equivalent current noise source.
Available Noise Power
Pn = kTB
When impedance is matched, noise power depends on temperature and bandwidth—not on resistance value. At ~290 K, thermal noise density is approximately -174 dBm/Hz.
How to Use This Johnson Noise Calculator
- Enter temperature (Kelvin or Celsius).
- Enter resistance and choose Ω, kΩ, or MΩ.
- Enter noise bandwidth and choose Hz, kHz, MHz, or GHz.
- Click Calculate to get:
- RMS voltage noise
- Voltage noise density (V/√Hz)
- RMS current noise
- Current noise density (A/√Hz)
- Noise power in watts and dBm
Quick Examples
Example 1: Audio Band Resistor
For a 1 kΩ resistor at 300 K over 20 kHz bandwidth, noise is about 0.576 µV RMS. This is small, but in low-level microphone or sensor circuits it can be very relevant.
Example 2: RF Front-End Estimate
For 50 Ω at 300 K and 1 MHz bandwidth, thermal noise voltage is about 0.91 µV RMS. The available noise power is roughly -114 dBm over that bandwidth.
Design Tips to Reduce Thermal Noise Impact
- Limit bandwidth: filtering can significantly cut integrated noise.
- Avoid unnecessarily large resistors in low-noise nodes.
- Lower temperature when feasible (precision and scientific systems).
- Impedance match thoughtfully in RF chains.
- Budget noise early with amplifier voltage/current noise and resistor contributions together.
FAQ
Is Johnson noise the same as shot noise?
No. Johnson noise comes from thermal agitation in resistive elements; shot noise is tied to discrete charge transport across junctions (for example in diodes and transistors).
Why does noise increase with bandwidth?
Thermal noise is approximately white across many practical ranges, so each extra hertz contributes a little power. Integrating over a wider bandwidth increases total RMS noise as √B.
Can I remove Johnson noise completely?
No. You can only reduce its impact through bandwidth control, impedance choices, cooling, and signal processing.