Noise Factor vs. Noise Figure: Understanding the Difference

This page explains the difference between noise factor and noise figure. The terms “noise factor” and “noise figure” are used interchangeably in the RF and microwave fields. Both define how much noise is added by an amplifier while amplifying a signal. They are most commonly used as specifications for an LNA (Low Noise Amplifier) device. Noise factor and noise figure are related by the following equation:

Noise Figure = 10 Log₁₀ (Noise Factor)

Noise Factor = F = (S_i/N_i) / (S_o/N_o)

Where S_i/N_i and S_o/N_o are the Signal-to-Noise ratios 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 a 30dB attenuator pad, F = 1000. L = 1/G, where Loss is the reciprocal of gain.

Remember that Insertion loss = Input/Output for a lossy passive network and Gain = Output/Input for an active network.

Noise temperature, T_e = (F - 1)T_o, where T_o is the ambient room temperature and F is the noise factor.

The above information is very useful in calculating the cascaded noise figure with devices like pads, LNAs, and downconverters in a 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 to as Friis’ formula or Friis’ equation.

Aggregate Noise Figure (dB) = 10 Log₁₀ (F_total)

Gain (Total) (dB) = G₁ + G₂ + G₃