Receiver Sensitivity Calculator
Calculate minimum detectable signal power of an RF receiver from noise bandwidth, noise figure, and required SNR. Reports thermal noise floor and MDS in dBm.
How to Use
- Enter receiver noise bandwidth (Hz), noise figure (dB), and required SNR (dB).
- Result: thermal noise floor, receiver noise floor, and minimum detectable signal (MDS).
Show Work
Formulas
History of Receiver Sensitivity
John B. Johnson at Bell Labs discovered thermal noise in 1927 — the random agitation of electrons in a conductor creates a voltage noise proportional to temperature. Harry Nyquist derived the theoretical equation N = kTB the same year. The -174 dBm/Hz thermal noise floor at room temperature (290 K) is the hard lower bound on receiver sensitivity, set by physics.
Noise figure as a receiver metric was formalized by Harald Friis at Bell Labs in 1944, following his transmission-formula work. Friis\'s cascade formula (NF_total = NF₁ + (NF₂-1)/G₁ + ...) shows that the first amplifier\'s NF dominates the whole chain — which is why front-end LNAs are the most-engineered part of any receiver.
Modern cryogenic HEMT amplifiers in radio telescopes achieve NF < 0.5 dB (noise temp < 35 K) by cooling the first stage to 20 K. Satellite ground stations and GPS receivers use uncooled GaAs/InP MMICs with NF 0.5-1.5 dB at L-band. Consumer WiFi/cellular receivers settle for 3-6 dB NF as a cost/performance trade-off.
About This Calculator
Enter noise bandwidth (the IF/digital filter bandwidth that limits receiver noise), noise figure of the receiver chain, and the required SNR for your modulation scheme. The tool computes thermal noise (kTB), receiver noise floor (+NF), and minimum detectable signal (MDS = floor + SNR).
Required SNR depends on modulation: BPSK 4-7 dB, QPSK 7-10 dB, 16-QAM 14-17 dB, 64-QAM 20-24 dB. LoRa spread-spectrum can go NEGATIVE SNR (-20 dB for SF12) because of its processing gain. Everything runs client-side.
Frequently Asked Questions
What is MDS?
Minimum Detectable Signal = noise floor + NF + required SNR. The weakest signal the receiver can reliably detect above its own noise.
Why kTB?
Thermal (Johnson) noise power in a matched load = k·T·B where k is Boltzmann\'s constant. At 290K (room temp), -174 dBm/Hz — the universal thermal noise floor.
NF vs Noise Temp?
Equivalent. NF = 10·log(1 + T_e/290). NF = 3 dB corresponds to noise temp ~290K; NF = 0.5 dB → ~35K (cooled LNA).
Common Use Cases
GPS Receiver
2 MHz BW, 2 dB NF, 10 dB SNR: MDS ≈ -129 dBm.
WiFi 802.11n
20 MHz BW, 5 dB NF, 4 dB SNR (BPSK): MDS ≈ -92 dBm.
LoRa SF12
125 kHz BW, 5 dB NF, SF12 gives -20 dB SNR: MDS ≈ -137 dBm.
Last updated: