This tool converts Noise Temperature to Noise Figure.

Enter

- Noise Temperature and
- Reference Temperature

along with appropriate units – Celsius or Kelvin.

???? Noise Figure to Noise Temperature

**Formula**

**Noise Figure (dB) = 10*Log _{10}(T_{Noise}/T_{Ref }+ 1)**

where

**T _{Ref}** is the reference noise temperature (reference usually refers to room temperature which is 293 K [1] but is often taken as 290 K).

**T _{Noise}** is the noise temperature in Kelvin

This formula is derived from the definition of Noise factor **F**

**F = (T_{Noise}+T_{Ref})/T_{Ref}**

and Noise Figure (NF)

**NF (dB) = 10*Log _{10}(F)**

*Use this tool to convert from Noise factor to Noise figure*

**Background**

Noise temperature [2] is a measure of noise power introduced by a component or source. 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* 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 [3].

An arbitrary white noise source with an impedance **R** that delivers a noise power **P _{s}** to a load resistor

**R**can be modeled as a noisy resistor of the same value at temperature

**T**(an equivalent temperature such that the same noise power is delivered to the load).

_{e}**T _{e} = P_{s}/(kB)**

where,

- k = 1.380 x 10
^{-23}J/K is Boltzmann’s constant - B is the system bandwidth in Hz

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

**T _{e} = P_{0}/(GkB)**

where **P _{0}** is the output noise power

**Example Calculation**

The default value of **Tref** in the calculator is the room temperature or 290 K. If the noise temperature measurement of a Low Noise Amplifier is 82 K, then its noise figure is calculated to be 1.08 dB.

**Application**

**How is Noise Temperature Measured?**

Noise temperature is measured using the **Y Factor Method** [3, 4]. The noise temperature of a component is determined by measuring the output power when a matched load at 0 K is connected at the input of the component (such as an amplifier).

Since 0 K cannot be realized, a practical alternative is to use to matched loads at different temperatures. The input is connected to only one of the two at a time.

The Y factor is determined from the ratio of the output powers in each case [5].

**Y (dB) = P _{1} (dBm) – P_{2} (dBm) **

and the equivalent noise temperature is

**T _{e} = (T_{1}-Y*T_{2})/(Y-1)**

Note that Y in the above equation is a linear number. Use this calculator to convert from Y in dB to a linear quantity.

**How is Noise Temperature Converted to Noise Figure?**

Noise temperature T_{Noise} (expressed in Kelvin) is converted to to noise figure by the following formula:

**Noise Figure (dB) = 10*Log _{10}(T_{Noise}/T_{Ref }+ 1)**

Note that the Noise Figure is in deciBels (dB).

**Why is Noise Temperature Converted to Noise Figure?**

Noise figure is very useful parameter for a number of RF system calculations and as such can be plugged in directly to calculate the sensitivity of a radio receiver. This number in addition to others impacts the range of a radio system.

It is an important specification for a low noise amplifier – a component that is used to improve signal reception.

**Why is Noise Temperature Important?**

The noise figure of an amplifier is related to its noise temperature as per the equation above.

**???? A lower noise temperature translates directly to lower noise figure**

This indicates better amplifier performance as in, the amplifier adds a minimal amount of noise to the receiver or signal chain after the amplifier.

Let’s use T_{Noise} = 0 Kelvin. This gives F = 1 and NF = 0 dB. It’s not possible to achieve this value practically. The plot below shows practical values for a LNA.

**References**

[2] Wikipedia post on Noise Temperature

[3] Microwave Engineering by David M. Pozar

[4] Y-Factor Method on Wikipedia