Noise Figure Calculator (NF from input & output SNR, noise temperature)

Understanding the noise figure calculator — concept and principle

This calculator finds the noise figure of an amplifier or receiver from its input and output signal-to-noise ratios, and gives the noise factor, equivalent noise temperature, thermal noise power kTB and the input-referred noise floor for a chosen bandwidth. RF engineers and radio amateurs use it to compare low-noise amplifiers and receiver front ends.

How it is calculated

Noise factor F = (S_i/N_i) ÷ (S_o/N_o); noise figure NF = 10 log₁₀ F

With SNRs in dB: NF = SNR_in − SNR_out

Equivalent noise temperature T_e = 290 K × (F − 1)

Thermal noise kTB at 290 K = −174 dBm/Hz + 10 log₁₀(B in Hz)

Noise floor referred to input = kTB + NF

• k = 1.380649 × 10⁻²³ J/K; bandwidth in MHz.

The principle

Every amplifier adds some noise of its own, so the signal-to-noise ratio at its output is always a little worse than at its input. The noise factor measures how much worse, with the input noise defined at the standard temperature of 290 K. Thermal noise from a matched resistor is kTB, independent of resistance; at 290 K it is −174 dBm in each hertz of bandwidth. Adding the noise figure gives the effective noise floor of the device.

Worked example

Default inputs: SNR in 40 dB, SNR out 37 dB, bandwidth 1 MHz.

1. NF = 40 − 37 = 3 dB.
2. F = 10^0.3 = 1.9953.
3. T_e = 290 × (1.9953 − 1) = 288.6 K.
4. kTB in 1 MHz = −174 + 60 = −114 dBm.
5. Input-referred noise floor = −114 + 3 = −111 dBm.

How to read the result

A 3 dB noise figure means the device roughly doubles the noise power relative to an ideal noiseless amplifier at 290 K. Good low-noise amplifiers achieve well under 1 dB. In a chain of stages, the first stage's noise figure matters most, which is why low-noise amplifiers are placed right after the antenna.

Common mistakes

• Subtracting SNRs in linear ratios instead of dB.
• Forgetting that noise figure is defined at 290 K.
• Using the wrong bandwidth for the noise floor.
• Ignoring the gain of the first stage when combining stages.

Frequently asked questions

What is a good noise figure?

Lower is better; low-noise amplifiers are often below 1 dB.

How are noise figure and noise temperature related?

T_e = 290 K × (F − 1), with F the linear noise factor.

Why −174 dBm/Hz?

It is kT at 290 K expressed in dBm per hertz.

Which stage dominates a receiver's noise figure?

The first one, if its gain is reasonably high (Friis formula).

Sources: Agilent (Keysight) Application Note 57-1, "Fundamentals of RF and Microwave Noise Figure Measurements"