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

At room temperature (T = 290 K), the thermal noise power spectral density is N0 = kT = 1.38 times 10 to the minus 23 times 290 = 4.00 times 10 to the minus 21 watts per hertz. Converting to dBm: 10 times log10(4.00 times 10 to the minus 21 / 0.001) = minus 174 dBm/Hz. This is the noise floor of any system at 290 K in a 1 Hz bandwidth. To find the noise floor in a wider bandwidth, add 10 times log10(B). In 1 MHz bandwidth: minus 174 + 60 = minus 114 dBm. In 100 MHz: minus 174 + 80 = minus 94 dBm. This number is physics: it cannot be reduced by any circuit design. The only way to lower the noise floor below minus 174 dBm/Hz is to cool the system below 290 K, which is why radio telescopes use cryogenic receivers at 15 to 20 K.

How does thermal noise affect receiver sensitivity?

The minimum detectable signal (MDS) of a receiver is: MDS = kTB times F times SNR_required, where F is the receiver noise factor and SNR_required is the minimum signal-to-noise ratio for acceptable performance. In dBm: MDS = minus 174 + 10 log10(B) + NF + SNR_req. For a cellular receiver with 10 MHz bandwidth, 3 dB noise figure, and 0 dB required SNR: MDS = minus 174 + 70 + 3 + 0 = minus 101 dBm. Every 1 dB of noise figure degradation costs 1 dB of sensitivity. Every doubling of bandwidth costs 3 dB. Every Kelvin of temperature change shifts the noise floor by 0.015 dB near 290 K. Thermal noise is the inescapable floor that all other noise sources (shot noise, flicker noise, quantization noise) add to.

Is thermal noise the same as white noise?

Thermal noise is white in the classical sense: its power spectral density is constant across frequency from DC to approximately kT/h (where h is Planck's constant), which at room temperature is about 6 THz. Below 6 THz, thermal noise is perfectly flat, making it indistinguishable from ideal white noise for all practical RF and microwave applications. Above 6 THz (in the infrared and optical regions), quantum effects cause the noise power to roll off, and the classical kTB formula underestimates the actual noise. For RF engineering (up to 300 GHz), thermal noise is effectively white, Gaussian (by the central limit theorem applied to billions of random electron motions), and stationary (its statistical properties do not change with time). These properties make it the reference noise source for defining noise figure, noise temperature, and receiver sensitivity.

Fundamentals

Thermal Noise

Johnson-Nyquist Noise

Every resistor in the universe generates noise. A 50 Ω termination sitting on a lab bench at 290 K (17 °C) produces −174 dBm of noise power in every hertz of bandwidth. In a 1 MHz measurement bandwidth, that is −114 dBm. In a 100 MHz 5G channel, −94 dBm. This thermal noise floor is not a design flaw; it is a thermodynamic certainty. The random motion of electrons in any conducting material generates a voltage across the material's resistance, first measured by John B. Johnson in 1928 and explained theoretically by Harry Nyquist the same year. No amplifier, no filter, no circuit technique can reduce this noise below kTB. It is the ultimate sensitivity limit of every receiver ever built.

Category: Fundamentals

Floor: −174 dBm/Hz at 290 K

Formula: P = kTB

Thermal Noise Floor by Bandwidth

Bandwidth	kTB at 290 K	Application
1 Hz	−174 dBm	Phase noise reference
1 kHz	−144 dBm	CW radar, narrowband comms
200 kHz	−121 dBm	GSM channel
1 MHz	−114 dBm	LTE 1.4 MHz, WCDMA
20 MHz	−101 dBm	LTE 20 MHz, WiFi
100 MHz	−94 dBm	5G NR 100 MHz
400 MHz	−88 dBm	5G NR mmWave

Thermal noise power:
P = kTB (watts)
k = 1.38 × 10⁻²³ J/K (Boltzmann constant)
T = temperature (K), B = bandwidth (Hz)

In dBm:
P (dBm) = −174 + 10·log₁₀(B)
Add NF to get receiver noise floor: N = −174 + 10·log(B) + NF

Minimum detectable signal:
MDS = −174 + 10·log(B) + NF + SNR_req
10 MHz BW, 3 dB NF, 10 dB SNR: MDS = −174 + 70 + 3 + 10 = −91 dBm

Common Questions

Frequently Asked Questions

Where does −174 dBm/Hz come from?

kT at 290 K = 4.00 × 10⁻²¹ W/Hz. In dBm: 10·log(4e−21/0.001) = −174.0 dBm/Hz. Physics, not design. Only cryogenic cooling (radio telescopes at 15 to 20 K) can lower this floor.

Impact on receiver sensitivity?

MDS = −174 + 10·log(B) + NF + SNR_req. Every 1 dB NF = 1 dB sensitivity loss. Every 2× BW = 3 dB loss. Thermal noise is the inescapable floor all other noise sources add to.

Is thermal noise white?

Flat from DC to ~6 THz (kT/h at 290 K). Above: quantum roll-off. For RF/microwave (<300 GHz): perfectly flat, Gaussian (central limit theorem), stationary. The reference noise source for NF, Te, and sensitivity specs.

Related Terms

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