|
Home: |
Noise temperature, Noise Figure (NF) and noise factor (f)
Calculates System Noise Temperature for receive satellite system comprising a series of cascaded gain/loss blocks. Enables the expected G/T result to be calculated.
For each 'block', you must supply Gains or Losses in dB and Noise
characteristic Noise temp, Noise Figure (NF) or noise factor (f).
For attenuators you need to know the actual Kelvin temperature of the attenuator (e.g 290 deg K).
If you know Noise Figure (NF) or noise factor (f) then the
calculator will convert these to noise temperature (K).
There are two columns of results, using two different red reference points. Popular reference points are the exact antenna output or the waveguide to LNA/LNB junction, as illustrated below:
* Enter values for either item noise factor (f number), or Noise Factor (NF dB) or Noise Temperature (K). Select using the radio button. The unselected values will be ignored.
The initial formulae to get noise temperature are:
Noise temperature (T) = 290 * (10^(Noise Figure/10)-1) K
Noise Figure (NF) = 10 * log (noise factor) dB
Note that log must be to base 10. When using calculators and spreadsheets make sure that base 10 is selected. As a test, 10 * log(2) should give an answer of +3 dB. Noise temperature is measured in units called Kelvin (K) and these are like Celsius (C) temperature degrees but start at zero for absolute zero temperature so 0 K = -273 deg C, 273 K = 0 deg C (ice melts) and 290 K = 17 deg C (typical ambient temperature of a waveguide or cable)
Table to convert Noise Figure (NF dB) to Noise Temperature (T).
This is useful for working out LNA or LNB noise temperatures from advertised Noise Figures.
| NF(dB) | T (K) | NF(dB) | T (K) |
| 0.1 | 7 | 2.1 | 180 |
| 0.2 | 14 | 2.2 | 191 |
| 0.3 | 21 | 2.3 | 202 |
| 0.4 | 28 | 2.4 | 214 |
| 0.5 | 35 | 2.5 | 226 |
| 0.6 | 43 | 2.6 | 238 |
| 0.7 | 51 | 2.7 | 250 |
| 0.8 | 59 | 2.8 | 263 |
| 0.9 | 67 | 2.9 | 275 |
| 1.0 | 75 | 3.0 | 289 |
| 1.1 | 84 | 3.1 | 302 |
| 1.2 | 92 | 3.2 | 316 |
| 1.3 | 101 | 3.3 | 330 |
| 1.4 | 110 | 3.4 | 344 |
| 1.5 | 120 | 3.5 | 359 |
| 1.6 | 129 | 3.6 | 374 |
| 1.7 | 139 | 3.7 | 390 |
| 1.8 | 149 | 3.8 | 406 |
| 1.9 | 159 | 3.9 | 422 |
| 2.0 | 170 | 4.0 | 438 |
Procedure for adding up noise temperatures for antenna, waveguide, LNA, cable and indoor receiver in series:
Notes:
System noise temperature (T system) is referred to the reference point. Two possible reference points are illustrated.
Antenna noise temperature is provided by the manufacturer. It will be at the output end of the feed
or waveguide OMT/diplexer/filter assembly. Complex diplexer/filters will have slightly higher antenna noise temp specs. The
Antenna Noise temperature also changes with beam elevation angle and goes up when the lower beam sidelobes start receiving noise from the warm ground.
The noise temperature of the LNA refers to the input of the LNA.
The noise temperature of the receiver refers to the input of the receiver.
Cascaded calculation components:
Tant = 35 K
Gwg = -0.25 dB = 10 ^ (-0.25/10) = 0.944061
Twg = 290 * (-1 + 1/0.944061) = 17.183580 K
Tlna = 75 K
Tcable = 290 * (-1 +1/0.01) = 28710 K
Glnb = 10 ^(60 / 10) = 1000000
Moden NF = 9 dB
Tmodem = 290 * (10^(9/10)-1) = 2013.5519 K
Gcable = 10 ^ (-20/10) = 0.01
Cascaded calculation 1: Reference point 1 is exactly at the antenna output.
Tsys = Tant + Twg + Tlna/Gwg + Tcable/(Gwg*Glnb) + Tmodem/(Gwg*Glnb*Gcable)
Tsys = 35 + 17.18358 + 79.444019 + 0.03 + 0.21 = 131.87 K
Gain = Gant = 55 dBi
Cascaded calculation 2: Reference point 2 is at the LNA/LNB input.
Tsys = Tant * Gwg + Twg * (Gwg -1)/Gwg + Tlna + Tcable/Glnb + Tmodem/(Glnb*Gcable)
Tsys = 33.042135 + 16.22 + 75 + 0.03 + 0.2 = 124.49 K
Gain = Gant - Lwg(dB) = 55 - 0.25 = 54.75 dBi
Note that LNA noise temperature, the antenna noise temperature and waveguide loss are the main factors.
Some examples of antenna noise temperature versus elevation angle are shown on page antnoise.htm. At lower elevation angles where more of the sidelobes hit the ground and receive ground noise (~290K). The antenna noise temperature increases. The same applies if the main beam partially hits the ground (terrestrial radio link) or entirely hits the earth in the case of a uplink receive antenna on a satellite with is beam pointed down at the land, clouds, sea.
To calculate the G/T of a receive system we need to compare the gain and system noise temperature, both referenced to the same place. In example 1, the Gain (G) referenced to the antenna output. In the case of example 2, the Gain is referenced to the waveguide output/input to the LNA. System noise temperature (T) is similarly referenced to the same points.
G/T = Gain in dBi - 10 log ( system noise temperature T ).
See the general purpose link budget calculator.
Useful link: Y factor method of noise figure measurement method.
If you find similar calculators on the internet or have your own method, please compare the results with this one. If different results, please tell me. If you can offer explanation that would help me. Comments welcome.
Reference point 1 has been added in response to a question received May 2024:
Why don't you use the reference point according to current ITU standard (08/2022)?
https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.372-17-202408-I!!PDF-E.pdf
:
'The only appropriate reference point for the overall operating noise for a radio receiving system is the input of an equivalent loss-free receiving
antenna. (The terminals of this lossless antenna do not exist physically)'.
The antenna output is the nearest I could get to the non-existing physically "input of an equivalent loss-free receiving antenna".
This page replaces two separate pages, both controversial, which were here for many years and which were revised many times in response to suggestions and comments.
Constructive comments are welcome on this new combined page. If you think something is wrong please suggest precise changes. Email me Eric Johnston
Useful references:
Attenuator and amplifier noise (Reeve)
Cascaded Noise Figure (NF) and noise factor (nf) calculations (recafe)
|
This combined page, last amended 3 March 2025 Older versions from 24 July 2001...
|