Calculation of thermal noise - sengpielaudio
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• Calculation: Thermal noise •

Johnson noise, Nyquist noise, and white noise
Noise voltage in microvolts, noise level in dBu, and dBV
Hi-Fi bandwidth from 20 Hz to 20,000 Hz = 19,980 Hz

Temperature theta   °Celsius
Needed bandwidth Δ f    Hz
Resistance R   ohms
                      
RMS Noise voltage Vn  μV (microvolts)
Noise level Lu  dBu 
Noise level LV  dBV 
Formula for the rms noise voltage:

Rauschspannungs-Formel - sengpielaudio		 White noise

Boltzmann constant  kB = 1.3806505×10-23 J/K (joule/kelvin); J = W · s
Absolute temperature in kelvin  T = 273.15 + theta 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!

To each noise potential the temperature and the bandwidth must be indicated,
with which it was measured.

Enter a value in the left or right box, then press the TAB bar or make
a mouse click at an empty space at the side, to get the solution.
The calculator works in both directions of the ↔ sign.
Noise voltage level LV:
dBu		  ↔  Noise voltage V:
µV (microvolt)
L_V = 20\, \log_{10}\left(\frac{V}{V_0}\right) \ \mbox{dBu}   V = V_0 \cdot 10^\frac{L_V}{20} \ \mbox{volts}
Reference voltage V0 = 0.7746 Volt = 774596,67 µV (0 dBu)

Don't forget the minus sign, when you enter the noise voltage level.

White Noise Generator

Thermal noise: Also called Johnson noise, is the random white noise generated by thermal agitation of electrons in a conductor or electronic device. It is produced by the thermal agitation of the charges in an electric conductor and is proportional to the absolute temperature of the conductor. It manifests itself in the input circuits of audio equipment such as microphone pre amps, where the signal levels are low. The thermal noise level is the limiting minimum noise any circuit can attain at a given temperature. Modern high-quality microphone pre amps, under proper conditions, have noise specifications that come very close to this theoretical limit.

Noise figure NF or noise factor F:
The Noise factor of a transducer at a specified input frequency is the ratio of (a/b) where "a and b" are:
a) the available Signal to Noise Ratio (SNR) at the signal generator terminals per unit bandwidth when the temperature of the input termination (generator or source) is (usually 20°C = 293.15 K) and the bandwidth is limited by the transducer, to
b) the available SNR per unit bandwidth at the output terminals of the transducer.

Noise figure NF = 10 log (noise factor F) in dB

Noise temperature Te = T0 (F − 1)
T0 is standard temperature, usually 20°C = 293.15 K

It is determined by
a) measuring (determining) the ratio, usually expressed in dB, of the thermal noise voltage at the output, to that at the input, and
b) subtracting from that result, the gain, in dB, of the system. Typical noise figures range from 0.5 dB for very low noise devices, to 4 to 8 dB.

EIN means Equivalent Input Noise. It is a specification that helps measure the "quietness" of a gain stage by deriving the equivalent input noise voltage necessary to obtain a given pre amps output noise. Numerically, it’s the output noise at a given gain setting minus the gain. EIN is usually measured at maximum gain and typically ranges from −125 to −130 dBu.

Signal-to-noise ratio, often abbreviated SNR or S/N, is an electrical engineering concept defined as the ratio of a signal power to the noise power corrupting the signal. In less technical terms, signal-to-noise ratio compares the level of a desired signal (such as music) to the level of background noise. The higher the ratio, the less obtrusive the background noise is.

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