Why is -174 dBm/Hz important?

The value -174 dBm/Hz is the available noise power density from any matched source at 290 K (standard temperature). It is the starting point for every receiver sensitivity calculation. Sensitivity = -174 + NF + 10*log10(BW) + SNR_min. Example for LTE with 10 MHz BW, NF=5 dB, SNR=0 dB: Sensitivity = -174 + 5 + 70 + 0 = -99 dBm. For 5G NR with 100 MHz BW, NF=7 dB: Sensitivity = -174 + 7 + 80 + 0 = -87 dBm. This formula shows that every dB of NF directly costs 1 dB of sensitivity. The noise floor cannot be reduced below kTB without cooling the system below 290 K.

How is Johnson noise different from other noise types?

Johnson noise (thermal): white spectrum (constant power density vs. frequency up to ~6 THz at 290K), Gaussian amplitude distribution. Present in all conductors at T > 0K. Shot noise: caused by discrete charge carriers crossing a junction (diode, transistor). Power proportional to DC current: P_shot = 2*q*I*B. Also white spectrum, Gaussian distribution. Dominant in low-bias devices. Flicker noise (1/f): power spectral density proportional to 1/f. Dominant at low frequencies (below 1 kHz to 1 MHz depending on technology). Caused by trapping/detrapping in semiconductors. Phase noise: random phase fluctuations on an oscillator. Related to 1/f noise upconverted around the carrier. Quantization noise: from ADC digitization. Uniform distribution, white spectrum.

Can you reduce Johnson noise?

Since P_n = kTB, there are three ways: (1) Reduce temperature: cooling to 20 K reduces noise by 10*log10(290/20) = 11.6 dB. Used in radio astronomy and deep space. Cryogenic LNA systems achieve noise temperatures of 5-10 K. (2) Reduce bandwidth: halving the bandwidth reduces noise by 3 dB but also halves the data rate. This is the fundamental trade-off between sensitivity and throughput. Narrowband systems (morse code, IoT) achieve extreme sensitivity. (3) Signal processing: averaging N samples improves SNR by 10*log10(N) dB. Pulsar astronomers average for hours to pull signals out of the noise. Spread spectrum: spreading the signal over a wide bandwidth allows processing gain upon despreading. GPS: -130 dBm signal recovered from noise floor using 43 dB processing gain.

Noise Fundamentals

Johnson Noise (Thermal Noise)

/jon-son noyz/

Johnson noise is thermal agitation of charge carriers: P_n = kTB = -174 dBm/Hz at 290 K. V_n = √(4kTRB). White spectrum, Gaussian amplitude. Sets the fundamental receiver sensitivity floor. Sensitivity = -174 + NF + 10log(BW) + SNR_min. Every dB of NF costs 1 dB of sensitivity. Only way below kTB: cryogenic cooling.

Floor: -174 dBm/Hz

k: 1.38×10^-23 J/K

Spectrum: White

Understanding Johnson Noise

Johnson noise represents the ultimate physical limit on receiver sensitivity. Discovered by John B. Johnson in 1928 at Bell Labs and theoretically explained by Harry Nyquist in the same year, it arises from the random thermal motion of electrons in any conductor at any temperature above absolute zero. The noise power is independent of resistance, depends only on temperature and bandwidth, and sets the floor that no amount of amplification or signal processing can overcome without cooling.

Johnson Noise Formulas

Thermal (Johnson-Nyquist) noise:
V_n = √(4kTRB) V (rms voltage)
P_n = kTB W (available power)
k = 1.381×10⁻²³ J/K

Noise floor:
P_n = −174 dBm/Hz @290 K
N₀ = kT = −174 dBm/Hz

In bandwidth B:
P_n = −174+10log(B) dBm

Noise Type Comparison

Noise Type	Source	Spectrum	Distribution	Reduction Method
Johnson (thermal)	Carrier agitation	White	Gaussian	Cooling
Shot	Discrete carriers	White	Gaussian	Reduce DC bias
Flicker (1/f)	Trapping/detrapping	1/f	Non-Gaussian	Chopper, better process
Phase noise	Oscillator instability	1/fⁿ	Gaussian	Better reference
Quantization	ADC digitization	White	Uniform	More bits / dither

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

BW	P_n @290K	V_n @50Ω	Application	Notes
1 Hz	−174 dBm	0.9 nV	Reference	Fundamental
1 kHz	−144 dBm	28 nV	Audio	Low noise
1 MHz	−114 dBm	0.9 μV	Narrowband Rx	NF matters
10 MHz	−104 dBm	2.8 μV	Wideband Rx	LNA needed
1 GHz	−84 dBm	28 μV	Radar Rx	Challenging

Common Questions

Frequently Asked Questions

Why -174?

P = kTB at 290K, 1 Hz: 4e-21 W = -174 dBm. Starting point for all receiver sensitivity calculations. Add NF, BW, and required SNR. Every dB of NF costs 1 dB of sensitivity directly.

Other noise types?

Shot noise: discrete charge carriers, white, proportional to current. 1/f: dominant at low frequencies. Phase noise: oscillator instability. Quantization: ADC digitization. Only Johnson and shot are fundamental physics limits.

Reduce it?

Cool system: 20K = 11.6 dB improvement (radio astronomy). Reduce BW: halves noise but halves throughput. Processing gain: GPS recovers -130 dBm from noise with 43 dB spreading gain. Averaging: N samples = 10log(N) dB improvement.

Related Terms

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