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Noise temperature, Noise Figure (NF) and noise factor (f)
The basic formulae 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 (ambient temperature of a waveguide, for example)
Example figures - same as the defaults 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.
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 input of the LNA.
Antenna noise temperature is referenced to the flange specified by the manufacturer.
The calculations below assume you add some length of waveguide between the above flange and the LNA.
The noise temperature of the LNA refers to the input of the LNA.
The noise temperature of the cable after the LNA refers to the input of the cable.
The noise temperature of the receiver refers to the input of the receiver.
You need to convert gains in dB to numbers. Number = 10 ^(dB/10)
T system = Noise contribution from antenna = Antenna noise temp * waveguide gain
+ noise contribution of the waveguide = 290 * (1-waveguide gain)
+ noise contribution of the LNA = the LNA noise temp
+ noise contribution of the cable = cable temp * (1/attenuation -1) / LNA gain
+ noise contribution of the indoor receiver = indoor receiver input noise temp / (LNA gain * cable gain)
Antenna noise temperature = 35 K (mainly ground pick up noise)
Waveguide feeder gain = -0.25 dB (0.944), temperature = 290K
LNA gain = 60 dB (1,000,000), input noise temperature = 75 K
Cable loss or attenuation = 20 dB or 100 or cable gain = -20 dB (0.01)
Cable temp= 290 K
Cable noise temp = 290 * ( 1/0.01 -1) = 28710 K
Indoor receiver noise figure
NF = 9 dB
Indoor receiver input noise temperature = 290 *
(10^(9/10)-1) = 2013.5519 K
Tsystem = 35 * 0.944 = 33.042
Noise contribution of the antenna
+ 290 ( 1 - 1 / (1/0.994)) = 16.222 Noise contribution of the
waveguide (new formula 11 Feb 2018)
+ 75
Noise contribution of the LNA
+ 290 * (100 -1) /1,000,000 = 0.02871 Noise contribution of the
cable (new formula 7 Jan 2019)
+ 2013.5519 /(1,000,000 * 0.01) = 0.20135519
Noise contribution of the indoor receiver.
Total = 124.494 K
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 the noise temperature increases. The same applies if the main beam partially hits the ground or entirely hits the ground in the case of a satellite uplink receive antenna on a satellite.
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 this case the Gain (G) referenced to the input to the LNB is = Antenna gain (dBi) minus Waveguide loss (dB). System noise temperature (T) is as per the calculation above, referenced to the input to the LNB. G/T = Gain in dBi - 10 log ( system noise temperature T ). See the general purpose link budget calculator and use the final section which relates to the receive antenna.
Useful link: Y factor method of noise 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.
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Any questions, errors you have found that need fixing or comments your help is appreciated, please e-mail Eric Johnston Amendments: 7 Jan 2019 formula in text above for the cable contribution changed yet again.
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