Where does the -174 dBm/Hz number come from?

Thermal noise power is N = kTB, where k is Boltzmann's constant (1.38 times 10^-23 J/K), T is temperature in Kelvin, and B is bandwidth in Hz. At room temperature (290K, about 17 degrees C), kT = 4.00 times 10^-21 watts per Hz = -174 dBm/Hz. This is the fundamental floor of thermal noise: no receiver at room temperature can have a noise floor below -174 dBm in a 1 Hz bandwidth unless it is cooled below 290K. A cryogenic receiver at 20K has a thermal noise floor of -185.6 dBm/Hz, which is why radio telescopes and deep-space receivers use cryogenic cooling.

How does bandwidth affect the noise floor?

The noise floor rises by 10 log10(B) relative to the 1 Hz reference. In a 1 Hz BW: -174 dBm. In a 1 kHz BW: -174 + 30 = -144 dBm. In a 1 MHz BW: -174 + 60 = -114 dBm. In a 200 MHz BW (5G NR channel): -174 + 83 = -91 dBm. This is why narrowing the measurement or channel bandwidth improves sensitivity: halving the bandwidth lowers the noise floor by 3 dB. It is also why wideband systems inherently have worse sensitivity than narrowband systems, requiring higher transmit power or antenna gain to compensate.

What is the difference between noise floor and sensitivity?

The noise floor is the total noise power at the receiver input (or at any point in the signal chain). Sensitivity (minimum detectable signal, MDS) is the noise floor plus the minimum required SNR for the application. For a voice receiver needing 10 dB SNR with a noise floor of -120 dBm: sensitivity = -120 + 10 = -110 dBm. For a 64QAM data link needing 25 dB SNR with a noise floor of -100 dBm: sensitivity = -100 + 25 = -75 dBm. The noise floor sets the absolute limit; the modulation scheme's SNR requirement determines how far above that limit the signal must be to achieve acceptable BER.

System Design

Noise Floor

Every resistor at room temperature generates noise. At 290 Kelvin, the noise power spectral density is −174 dBm per hertz. This number, arising from the random thermal motion of electrons described by Boltzmann's constant, is the absolute floor below which no room-temperature receiver can detect signals. Everything built on top of this floor makes it worse: amplifier noise figure, cable loss, phase noise from the LO, and the bandwidth of the measurement all raise the effective noise floor. A spectrum analyzer with a 6 dB noise figure and a 10 kHz resolution bandwidth has a displayed noise floor of −174 + 6 + 40 = −128 dBm. Any signal below that level is invisible.

Category: System Design

Thermal Floor: −174 dBm/Hz at 290K

Formula: N = kTB

Building Up from Boltzmann

Thermal noise power:
N = kTB
k = 1.38 × 10⁻²³ J/K, T = 290K, B = bandwidth (Hz)
N(dBm) = −174 + 10·log₁₀(B)

System noise floor:
N_sys = −174 + NF + 10·log(B) dBm

Sensitivity (MDS):
MDS = N_sys + SNR_min dBm

Noise Floor by Bandwidth

Bandwidth	10·log(B)	Thermal Floor	With NF = 3 dB	With NF = 8 dB	Use Case
1 Hz	0 dB	−174 dBm	−171 dBm	−166 dBm	Phase noise spec reference
1 kHz	30 dB	−144 dBm	−141 dBm	−136 dBm	CW radar, narrow FSK
200 kHz	53 dB	−121 dBm	−118 dBm	−113 dBm	GSM, LoRa SF7
10 MHz	70 dB	−104 dBm	−101 dBm	−96 dBm	LTE 10 MHz channel
100 MHz	80 dB	−94 dBm	−91 dBm	−86 dBm	5G NR 100 MHz
400 MHz	86 dB	−88 dBm	−85 dBm	−80 dBm	5G NR FR2, wideband radar

Common Questions

Frequently Asked Questions

Where does −174 dBm/Hz come from?

kT at 290K = 4.0×10⁻²¹ W/Hz = −174 dBm/Hz. This is the fundamental thermal noise floor. Cooling below 290K lowers it (cryogenic at 20K: −185.6 dBm/Hz). Nothing at room temperature can beat it.

How does bandwidth affect the floor?

Noise floor rises 10·log(B). Halving bandwidth = 3 dB improvement. A 1 Hz BW: −174 dBm. A 200 MHz BW: −91 dBm. Wideband systems need more TX power or antenna gain to compensate.

Noise floor vs. sensitivity?

Noise floor = total noise power. Sensitivity = noise floor + required SNR. Voice (10 dB SNR) at −120 dBm floor: MDS = −110 dBm. 64QAM (25 dB SNR) at −100 dBm floor: MDS = −75 dBm.

Related Terms

← Noise Figure Noise Temperature →

Receiver Design

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