Receiver Sensitivity & Noise Floor Calculator (kTB)

How it works

thermal noise N = k × T × B · kT at 290 K = −173.98 dBm/Hz · noise floor (dBm) = 10 log₁₀(kT × 1000) + 10 log₁₀ B + NF · sensitivity = noise floor + required SNR · V_rms = √(P × Z) · k = 1.380649 × 10⁻²³ J/K

Every resistor generates Johnson–Nyquist thermal noise of power kTB, which at room temperature (290 K) is −174 dBm in each hertz of bandwidth. A receiver adds its own noise on top (its noise figure), and the demodulator needs the signal to be some SNR above that noise. So sensitivity improves by 3 dB every time you halve the bandwidth or lower the noise figure by 3 dB — which is how narrow-band and spread-spectrum links reach −130 dBm and below.

Worked example

A receiver with 200 kHz bandwidth, a 6 dB noise figure and a 10 dB SNR requirement at 290 K: kTB = −173.98 + 10 log₁₀(200,000) = −120.96 dBm, the receiver noise floor is −114.96 dBm and the sensitivity is −104.96 dBm — about 31.88 fW, or 1.263 µV across 50 Ω (2.02 dBµV).

Sources: Wikipedia — Johnson–Nyquist noise (noise power, −174 dBm/Hz) · NIST CODATA — Boltzmann constant

Frequently asked questions