# Noise Figure to Noise Temperature Calculator

This tool converts Noise Figure to Noise Temperature.

Enter

• Noise Figure in dB and
• Reference Temperature in either degrees Celsius or Kelvin. Specify the unit using the drop down menu.

Select the unit for the resulting Noise Temperature.

???? Noise Temperature to Noise Figure

## Formula

TNoise = TRef *(10NF/10 – 1)

In the above equation, both TNoise and TRef are in Kelvin while NF is in dB.

## Background

### What is Noise Temperature?

Noise temperature [1] is a measure of noise power introduced by a component or source.

It is given by the formula

T = PN/kB

where

• PN is the noise power (in W, watts)
• B is the total bandwidth in Hz over which the noise power is measured
• k is the Boltzmann constant = 1.381×10−23 J/K, Joules per Kelvin)
• T is the noise temperature (K)

Noise temperature is directly proportional to the Noise Spectral Density PN/B. Use this PSD calculator and substitute the noise power instead of signal to calculate the NSD.

Every element or component in an RF circuit or system (antenna, transmission line, amplifier, etc.) has an equivalent noise temperature operating over a fixed bandwidth.

If an arbitrary noise source is white (shown in the picture below) such that it is independent of frequency, then it can be modeled as an equivalent thermal noise source and characterized with an equivalent noise temperature [2].

An arbitrary white noise source with an impedance R that delivers a noise power Ps to a load resistor R can be modeled as a noisy resistor of the same value at temperature Te (an equivalent temperature such that the same noise power is delivered to the load).

Te = Ps/(kB)

The thermal noise power calculator uses kTB to compute its numerical value in dBm using the formula Pn = 10 * log10 (kTB/1mW)

In the case of a noisy amplifier with Gain G over a bandwidth B, the equivalent load noise power can be obtained by driving an ideal noiseless amplifier with a resistor at temperature

Te = Po/(GkB)

where Po is the output noise power and G = Po/Pi where Pi is the input power.

### What is Reference Temperature?

TRef is the reference noise temperature. Reference usually refers to room temperature which is 293 K [3] but for simplicity is often taken as 290 K.

### What is the difference between Noise Temperature and Noise Figure?

Noise temperature is a measure of noise power introduced by a component or source.

Noise figure on the other hand is a measure of the degradation in Signal-to-Noise ratio due to the component.

Data sheets for RF components such as Amplifiers and Mixers almost always specify noise figure in dB as a function of frequency and temperature.

This calculator can be used to convert the deciBel value of NF to Noise Temperature. Note that NF varies with both temperature and frequency and therefore Noise temp will also vary accordingly.

## Example Calculation

The default value of TRef is the room temperature or 290 K. For a noise figure of 1 dB, TNoise is calculated to be 75.1 K.

## References

[1] Wikipedia post on Noise Temperature

[2]  Microwave Engineering by David M. Pozar