The Basics of Noise Figure

The noise figure can be defined as the degradation of the signal-to-noise ratio (SNR) as a signal passes through a system network.

A lower figure value means the network adds very little noise (good) and a higher noise figure value means it adds a lot of noise (bad). The concept fits only those networks that process signals and have at least one input and one output port.

In a linear amplifier, the ratio of the signal to the noise (SNR) is expressed by an index called the Noise Figure (NF). It is defined as the ratio of SNR out (output signal noise ratio) to SNR in (input SNR).

Noise Factor

Additionally, noise figure is usually expressed in decibels:

NF (in dB) = 10 log (F) = 10 log (No) – 10 log (Ni) 

For a better understanding of this equation, we need to consider a theoretical amplifier without noise. In this circumstance, since the SNR does not change at the amplifier input and output, it is clear that F = 1, and NF = 0 [dB]. When using a semiconductor device linear amplifier and considering the SNR of the input signal (SNRin), clearly the output of the amplifier after multiplication by the gain (G) is So = G x Si and the output multiplied by the gain (G) is No = G x Ni relative to Ni, but it is output with some fixed noise power added (Nadd).

So=G * Si 
No = Nadd + G * Ni 

So,

Noise Factor(F) = (Nadd + G * Ni)/( G * Ni) 

And,

Noise Figure (NF) = 10 Log(F) 

It’s important to remember that a system’s noise figure is separate and distinct from its gain. Once noise is added to the signal, subsequent gain stages amplify signal and noise by the same amount, and this does not change the SNR.

Input and Output SNR of Amplifier

From this figure, the first one shows an input to an amplifier, and the peak is 40 dB above the noise floor, and the second one shows the resulting output signal. Gain has boosted the signal and noise levels by 20 dB and added its noise. As a result, the peak of the output signal is now only 30 dB above the noise floor.

(Si/Ni)dB = 40 dB 
(So/No)dB = 30 dB 
Noise Figure = (Si/Ni)dB - (So/No)dB = 10 dB 

Hence degradation in the SNR is 10 dB, the amplifier has a 10 dB noise figure.

By controlling the noise figure and gain of system components, an RF designer directly controls the noise figure of the overall system and once you’ve characterized what your noise figure value is, system sensitivity can be easily estimated from the system bandwidth.