Thermal Noise Power

Formula

Description

Johnson-Nyquist thermal noise is the fundamental noise floor generated by the random thermal motion of charge carriers in any resistive element. It is white noise (flat spectral density) and is unavoidable in any circuit at temperatures above absolute zero. Boltzmann's constant k = 1.380649 × 10⁻²³ J/K connects thermal energy to temperature. At room temperature (290K), the noise power spectral density is -174 dBm/Hz, which is the ultimate sensitivity limit for any receiver. Reducing noise below this floor requires cooling the receiver, as done in radio astronomy.

Variables

• Pn — Available noise power (W)
• k — Boltzmann constant (1.38 × 10⁻²³ J/K)
• T — Temperature in Kelvin (K)
• BW — Measurement bandwidth (Hz)

Practical Notes

At 290K: noise floor = -174 dBm/Hz. In 1 Hz BW: -174 dBm. In 1 kHz: -144 dBm. In 1 MHz: -114 dBm. In 20 MHz (WiFi): -101 dBm. Noise voltage across a resistor: Vn = √(4kTRBW). A 10kΩ resistor at room temperature generates about 13 µV RMS noise in a 1 MHz bandwidth.