## Noise factor versus Noise Figure

This page on noise factor versus noise figure describes
**difference between noise factor and noise figure**.

The terms noise factor and noise figure are interchangeably used in RF and microwave field. It defines how much noise is added by any amplifier while amplifying the signal. Most commonly used as specification for a LNA (Low Noise Amplifier) device.

Noise factor and Noise figure are related by following equation.

**Noise Figure** = 10 Log_{10}(Noise Factor)

**Noise Factor** = F= (Si/Ni)/ (So/No)

Where Si/Ni and So/No are the Signal to noise ratio at the input and output of the amplifier device respectively.

### Noise factor of a lossy network

At room temperature the noise factor of a lossy network is equal to its power loss.

Noise Factor, F = Attenuation L (Linear scale),
For 30dB attenuator pad, F=1000.

L= 1/G, Loss is reciprocal of gain.

Remember that Insertion loss=Input/Output for lossy passive network

and Gain= Output/Input for active network.

Noise temperature, Te= (F-1) To, To is the ambient room temperature. F is the noise factor.

The above information is very
useful in calculation of cascaded noise figure with devices pad,LNA and downconverter in receiver chain.

### Aggregate Noise Factor of a cascaded Amplifier chain

Overall Noise Factor, F_{total} = F1 + ((F2-1)/G1) + ((F3-1)/G1G2)

This Equation is referred as Friis formula or Friis equation

Aggregate Noise Figure (dB) = 10 Log_{10} (F_{total})

Gain (Total) (dB) = G1 + G2 + G3

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### Aggregate Noise Figure Calculator

Aggregate Noise Figure calculator