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Noise temperature, Noise Figure (NF) and noise factor

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)

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) NF(dB) T (K) NF(dB) T (K)
0.1 7 1.1 84 2.1 180 3.1 302
0.2 14 1.2 92 2.2 191 3.2 316
0.3 21 1.3 101 2.3 202 3.3 330
0.4 28 1.4 110 2.4 214 3.4 344
0.5 35 1.5 120 2.5 226 3.5 359
0.6 43 1.6 129 2.6 238 3.6 374
0.7 51 1.7 139 2.7 250 3.7 390
0.8 59 1.8 149 2.8 263 3.8 406
0.9 67 1.9 159 2.9 275 3.9 422
1.0 75 2.0 170 3.0 289 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 noise temp / LNA gain
 + noise contribution of the indoor receiver = indoor receiver input noise temp / (LNA gain * cable gain)

Example:

Antenna noise temperature = 35 K  (mainly ground pick up noise)
Waveguide feeder gain = -0.25 dB  (0.944),  temperature = 290K
LNA gain = 50 dB  (100000),   input noise temperature = 75 K
Cable loss or attenuation = 20 dB or cable gain = -20 dB (0.01)
Cable noise temp= 290  K
Indoor receiver noise figure NF = 9 dB
Indoor receiver input noise temperature = 290 * (10^(9/10)-1) =  2013.5519 K

Tsystem = 35 * 0.94406 =  33.042  Noise contribution of the antenna
 + 290 ( 1 - 0.94406) = 16.2226  Noise contribution of the waveguide
 + 75                             Noise contribution of the LNA
 + (290 * (1-0.01)/0.01) /100000 = 0.2871  Noise contribution of the cable 
 + 2013.5519 /(100000 * 0.01)  = 2.0135519 Noise contribution of the indoor receiver.
Total  = 126.56  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

To calculate the G/T of a receive system :    G/T = Receive 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 links: Y factor method of noise measurement method.

Any questions, errors you have found that need fixing or comments your help is appreciated, please e-mail Eric Johnston

Amended 15 June 2013 to include a calculator.
Amended 25 March 2007 to alter  formula for cable noise temperature back to what is was in April 2004 !.
Amended 24 July 2001 to correct error in cable loss (20 dB=0.01), plus text clarifications Amended 18 Apr 2004 to correct formula for cable noise temperature.
Amended 16 Aug to further correct result for cable noise temperature.
Amended 17th Aug to clarify terms: cable gain and cable loss. Amended 2 Sept to further correct result for cable noise temperature and add details about G/T.
Amended 16 March 2005, amended 2 Feb 2007, amended 25 March 2007

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.

More ideas welcome please on the controversial cable noise calculations .... Copyright 2000 Satellite Signals Ltd 
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Example figures only - not same as defaults below 

Noise contribution
Antenna gain Ga dBi  
Antenna temp Ta K
Waveguide loss Gw dB  
Waveguide temp Tw K
LNB gain G1 dB  
 * LNB noise factor f or num  
LNB Noise Figure NF or dB  
LNB Temp T1 K
Cable loss G2 dB  
Cable temp T2 K
 * Modem noise factor f or num  
Modem Noise Fig NF or dB  
Modem temp T3 K
System noise temp   Total K
System G/T dBK  
* Enter values for either item noise factor (f  num), or Noise Factor (NF dB) or Noise Temperature (K).  Select using the radio button. The unselected values will be ignored.