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*Log10(TNoise/TRef + 1)
where
TRef is the reference noise temperature (reference usually refers to room temperature which is 293 K [1] but is often taken as 290 K).
TNoise is the noise temperature in Kelvin
This formula is derived from the definition of Noise factor F
F = (TNoise+TRef)/TRef
and Noise Figure (NF)
NF (dB) = 10*Log10(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 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)
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
Te = P0/(GkB)
where P0 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) = P1 (dBm) – P2 (dBm)
and the equivalent noise temperature is
Te = (T1-Y*T2)/(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 TNoise (expressed in Kelvin) is converted to to noise figure by the following formula:
Noise Figure (dB) = 10*Log10(TNoise/TRef + 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 TNoise = 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