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Thermal noise (Johnson-Nyquist noise, Nyquist noise, white noise) refers to the electronic signal in an audio system which is generated by thermal agitation of free electrons in a conductor. A resistor generates noise even without applied voltage. The random motion of electrons constitutes a random current in the conductor, leading to the appearance of random noise voltage across its terminals.
History
This form of noise was identified and initially quantified by John B. Johnson at Bell Labs in 1926.[Johnson] Johnson shared his observations with Harry Nyquist, also affiliated with Bell Labs, who successfully provided an explanation for the results.[Nyquist]
Noise Voltage and Power
Formula for the RMS noise voltage:
V_{n} = \sqrt{4k_BT \Delta fR}
with: Boltzmann constant: kB = 1.3806504*10-23 Absolute temperature in kelvin: T=273.15 + ϑ in °C Bandwidth being considered: Δ f = f2 − f1 = fmax − fmin in Hz; 20 kHz − 20 Hz = 19980 Hz Resistance of the circuit element R (R does not mean the universal gas constant!)
NoiseVoltage-Thermalnoise The noise level Lu has the reference voltage V0 = 0.7746 V = 774 596.67 µV ≡ 0 dBu. The noise level LV has the reference voltage V0 = 1 V = 1 000 000 µV ≡ 0 dBV.
NoiseVoltage-Thermalnoise2 Please don't forget the minus sign, when you enter the noise voltage level.
Acousticians and sound protectors ("noise fighters") need the sound intensity ("acoustic intensity") – but sound engineers and sound designers ("ear people") don't need that sound energy quantity.
Who is involved in audio engineering, should rather take care of the sound field quantity, that is the sound pressure or the sound pressure level (SPL) as an effect at the eardrums of our hearing and on the diaphragms of the microphones, and the corresponding audio voltage and its voltage level.
Note: The radiated sound power (sound intensity) serves as the cause, while sound pressure is the resultant effect. The particular interest of a sound engineer is the effect.
White Noise
Thermal noise is often charactarized as Gaussian white noise, because it is a combination of a very large number of random events (random motion of electrons). The term white refers to the even distribution of power across the frequency spectrum, which is assumed to be uniform from 0 Hz to about 1013 Hz.[Crecraft] The energy of thermal noise increases with temperature and the noise voltage varies in time with a gaussian probability distribution function and mean value of zero.
