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Noise temperature, Noise Figure (NF) and noise factor (f)

This is noise-version-2, with the red reference point located at the antenna output / waveguide input.

For the noise-version-1, the reference point is at the waveguide output / LNA input. Go to "https://www.satsig.net/noise-version-1.htm".

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)

System noise temperature calculation
Example figures - same as the defaults below

		Noise contribution
Antenna gain G ant	dBi
Antenna temp T ant	K

Waveguide loss L wg	dB
Waveguide temp T wg	K

LNA/LNB gain	dB
* LNA/LNB noise factor f or	num
* LNA/LNB Noise Figure NF or	dB
* LNA/LNB Temp	K	including Waveguide

Cable loss L cable	dB
* Modem noise factor f or	num
* Modem Noise Fig NF or	dB
* Modem temp T3	K	including Cable

System noise temp, referred to waveguide input	Total K
Gain, referred to Antenna output	Gain dB
System G/T	G/T dB/K

* 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.

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.372-16-202208-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)'.

31 May 2024: I've been working on this to move my reference point (marked in RED) to the interface between the antenna and the waveguide/diplexer/filter which often precede an LNA/LNB. The result will be a physical reference point closer to the 'not physically existing' ITU standard.

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. All html code upgraded to HTML5
11 Feb 2018 formula for the cable contribution changed again.
5 Oct 2017 formula for the cable contribution changed.
3 Oct 2017 waveguide contribution formula changed
21 April 2017 to alter formula for the cable contribution. ref: http://www.sm5bsz.com/pcdsp/ntemp.htm 5 decimal places for some outputs.
6 Feb 2014: Column format in table amended, centering NF and inserting black background columns to clarify the pairings. Font size increased for improved readability on tablet devices. 3 decimal places for outputs.
15 June 2013 to include a calculator.
25 March 2007 to alter formula for cable noise temperature back to what is was in April 2004 !.
2 Feb 2007
16 March 2005
18 Apr 2004 to correct formula for cable noise temperature.
2 Sept to further correct result for cable noise temperature and add details about G/T.
17th Aug to clarify terms: cable gain and cable loss.
16 Aug to further correct result for cable noise temperature.
24 July 2001 to correct error in cable loss (20 dB=0.01), plus text clarifications
31 May 2024: Moved reference point to close to antenna as possible and red mark in images changed. Calculations changed, so, if problems, please tell me.
28 July 2024: Two different pages now made. This page, noise-version-2, has reference point at antenna output / waveguide input. Loss of the waveguide added to the total. noise-version-1 has the reference point at the waveguide/LNB junction.