The noise level in an electronic system is typically measured as an electrical power P in Watts or dBm, a root mean square (RMS) voltage (identical to the noise standard deviation) in volts, dBµV or a mean squared error (MSE) in volts squared. Noise may also be characterized by its probability distribution and noise spectral density N0(f) in watts per hertz.


Noise Power  ` P = k*T*B `  where  ` k = 1.3806504 * 10^-23 J/K `  (Boltzmann Constant). T is the temperature in [K] (Kelvin) and B is the Bandwidth in [Hz].


` P = 10*log_10 (P/P_0) `  in [dBm] and P₀= 1 mW


Noise Voltage  ` U = sqrt(P*R) `  or  ` U=sqrt(k*T*B*R) `  where R = 50 Ω. (usually)


Reference Temperature  ` T = 273.15 K + theta_(a m b) `  usually T = 300 K.


Noise Figure   may be given as a linear factor or in dB. It is a measure of degradation of the signal-to-noise ratio (SNR), caused by one or more components in a signal chain.

F = SNR_input / SNR_output   whereas SNR_input` = S_(i n)/N_(i n) `   and SNR_output` = S_(o u t)/N_(o u t) `

F_dB `= 10*log_10 (F) `


SNR_input > SNR_output as the 'device' adds noise, decribed by the Noise Figure :-(

⇒ You can compare receivers with the noise-figure. When using the 'sensitivity' a comparison is only possible if this is done at the same bandwidth.


Multi-Stage-Systems

When using multi-stage-systems the noie figures add up using the 'de Friis-Formula'. calculator

F_total = F₁ + ` (F2 -1 )/ G1 + (F3 -1 )/ (G1 G2) + ...`

This formula lets you know, that :

• The Noise Figure of the first device is decisive for the overall Noise Figure

• The Noise Figures of the following stages loose influence with the Gain of the first stage.


Example : FM-Receiver

We have a Receiver with F = 2 dB operated at an Antenna. Between Receiver and Antenna we have an Coaxial cable of 25 m with an Attenuation of 7 dB/100 m at 100 MHz. This means we have an attenuation of 1.75 dB which is equal to F = 1.75 dB. F = 1.49 ( F = 10^(F_dB/10)). This gives an overall Noise Figure of :

F_total = F₁ `+ (F2 -1 )/ G1 = 1.49 + (1.58 - 1)/(1/1.49) = 2.37 ` ≡ 3.75 dB

The Attenuation of the Coaxial cable worsens the overall Noise Figure.

From a friend, we hear that adding an amplifier will improve the situation. Unfortunately we forgot to ask, where to put it. Amplifier : Gain 20dB, F = 3 dB.

If we put it between Antenna and Coaxial cable, this results in F = 3.03 dB
If we put it between Coaxial cable and Receiver, this results in F = 4.76 dB

Aha !

With the above formula (Noise Power), we may also calculate the Noisefloor of a Receiver. It depends only on the Noise Figure and the Bandwidth :

Noise floor = -174 + NF + 10 log (Bandwidth)


Noisy Resistors

Resistors are noisy. This noise depends on temperature. Therefore it is called 'thermal noise'. It further depends on bandwidth. (See formula above). Using T = 300 K and B = 1 Hz we get :

P_therm = - 174 (dBm/Hz)