Temperature vs Noise Figure, Paul Goble (ND2X/5)


The relationship between noise figure and temperature follows a fixed formula.  Paul "did the math" for an easy cross-reference of the two!


Introduction:

In an RF receiver system, the noise figure of the first RF amplifier largely sets the noise figure for the system.  Use of a Low Noise Amplifier (LNA) is therefore imperative, especially at microwave frequencies.

Every active device such as an amplifier contributes unwanted noise that masks the incoming signal in some measure. A significant goal of RF system design is to minimize these self-inflicted contributions to noise.

The figure of merit for defining how well the design suppresses this unwanted system noise is the "noise figure" for the system. Noise figure can be applied to the system (e.g., receiver) as a whole, or to specific portions of it, such as the incoming RF amplifier or to the amplifier chain following the mixer of the receiver.

The noise emitted by a black object ("black body") at a given temperature, the "noise temperature" is used as a standard reference for noise measurement. It is measured on the Kelvin scale, in degrees K.


Conversion of Noise Figure to Noise Temperature

This table converts noise figure to noise temperature using the formula:

T(K) = 290 {10[NF(dB)/10]  - 1}

Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
0.05 3.36 1.80 148.93 3.55 366.75 5.60 762.93
0.10 6.75 1.85 154.02 3.60 374.35 5.70 787.45
0.15 10.19 1.90 159.16 3.65 382.04 5.80 812.55
0.20 13.67 1.95 164.36 3.70 389.83 5.90 838.23
0.25 17.18 2.00 169.62 3.75 397.70 6.00 864.51
0.30 20.74 2.05 174.94 3.80 405.66 6.10 891.51
0.35 24.74 2.10 180.32 3.85 413.72 6.20 918.92
0.40 27.98 2.15 185.77 3.90 421.87 6.30 947.08
0.45 31.66 2.20 191.28 3.95 430.11 6.40 975.90
0.50 35.39 2.25 196.85 4.00 438.45 6.50 1005.38
0.55 39.15 2.30 202.49 4.05 446.88 6.60 1035.56
0.60 42.96 2.35 208.19 4.10 455.41 6.70 1066.43
0.65 46.82 2.40 213.96 4.15 464.05 6.80 1098.03
0.70 50.72 2.45 219.80 4.20 472.78 6.90 1130.36
0.75 54.67 2.50 225.70 4.25 481.61 7.00 1163.44
0.80 58.66 2.55 231.67 4.30 490.55 7.10 1197.30
0.85 62.69 2.60 237.71 4.35 499.58 7.20 1231.94
0.90 66.78 2.65 243.82 4.40 508.73 7.30 1267.39
0.95 70.91 2.70 250.01 4.45 517.98 7.40 1303.67
1.00 75.09 2.75 256.26 4.50 527.33 7.50 1340.79
1.05 79.32 2.80 262.58 4.55 536.80 7.60 1378.78
1.10 83.59 2.85 268.98 4.60 546.37 7.70 1417.65
1.15 87.92 2.90 275.45 4.65 556.05 7.80 1457.42
1.20 92.29 2.95 282.00 4.70 565.85 7.90 1498.13
1.25 96.72 3.00 288.63 4.75 575.76 8.00 1539.78
1.30 101.20 3.05 295.33 4.80 585.79 8.10 1582.40
1.35 105.73 3.10 302.10 4.85 595.93 8.20 1626.01
1.40 110.31 3.15 308.96 4.90 606.19 8.30 1670.64
1.45 114.95 3.20 315.90 4.95 616.56 8.40 1716.31
1.50 119.64 3.25 322.91 5.00 627.06 8.50 1763.04
1.55 124.38 3.30 330.01 5.10 648.42 8.60 1810.86
1.60 129.18 3.35 337.19 5.20 670.28 8.70 1859.80
1.65 134.03 3.40 344.45 5.30 692.65 8.80 1909.87
1.70 138.94 3.45 351.80 5.40 715.54 8.90 1961.12
1.75 143.91 3.50 359.23 5.50 738.96 9.00 2013.55

Conversion of Noise Temperature to Noise Figure

The following table converts noise temperature to noise figure by means of the following formula:

NF(dB) = 10 log {1 + [T(K)/290]}
 
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
Noise
Temp
deg K
Noise
Figure
dB
1 0.015 51 0.704 101 1.298 151 1.820
2 0.030 52 0.716 102 1.309 152 1.830
3 0.045 53 0.729 103 1.320 153 1.840
4 0.059 54 0.742 104 1.331 154 1.850
5 0.074 55 0.754 105 1.342 155 1.860
6 0.089 56 0.767 106 1.353 156 1.869
7 0.104 57 0.779 107 1.364 157 1.879
8 0.118 58 0.792 108 1.375 158 1.889
9 0.133 59 0.804 109 1.386 159 1.898
10 0.147 60 0.817 110 1.397 160 1.908
11 0.162 61 0.829 111 1.407 161 1.918
12 0.176 62 0.841 112 1.418 162 1.927
13 0.190 63 0.854 113 1.429 163 1.937
14 0.205 64 0.866 114 1.440 164 1.947
15 0.219 65 0.878 115 1.451 165 1.956
16 0.233 66 0.891 116 1.461 166 1.966
17 0.247 67 0.903 117 1.472 167 1.975
18 0.262 68 0.915 118 1.483 168 1.985
19 0.276 69 0.927 119 1.493 169 1.994
20 0.290 70 0.939 120 1.504 170 2.004
21 0.304 71 0.951 121 1.514 171 2.013
22 0.318 72 0.963 122 1.525 172 2.022
23 0.331 73 0.975 123 1.536 173 2.032
24 0.345 74 0.987 124 1.546 174 2.041
25 0.359 75 0.999 125 1.557 175 2.051
26 0.373 76 1.011 126 1.567 176 2.060
27 0.387 77 1.023 127 1.577 177 2.069
28 0.400 78 1.034 128 1.588 178 2.078
29 0.414 79 1.046 129 1.598 179 2.088
30 0.428 80 1.058 130 1.609 180 2.097
31 0.441 81 1.070 131 1.619 181 2.106
32 0.455 82 1.081 132 1.629 182 2.115
33 0.468 83 1.093 133 1.639 183 2.125
34 0.481 84 1.105 134 1.650 184 2.133
35 0.495 85 1.116 135 1.660 185 2.143
36 0.508 86 1.128 136 1.670 186 2.152
37 0.521 87 1.139 137 1.680 187 2.161
38 0.535 88 1.151 138 1.690 188 2.170
39 0.548 89 1.162 139 1.701 189 2.179
40 0.561 90 1.174 140 1.711 190 2.188
41 0.574 91 1.185 141 1.721 191 2.197
42 0.587 92 1.197 142 1.731 192 2.206
43 0.600 93 1.208 143 1.741 193 2.215
44 0.613 94 1.219 144 1.751 194 2.224
45 0.626 95 1.231 145 1.761 195 2.233
46 0.639 96 1.242 146 1.771 196 2.242
47 0.652 97 1.253 147 1.781 197 2.251
48 0.665 98 1.264 148 1.791 198 2.260
49 0.678 99 1.276 149 1.801 199 2.269
50 0.691 100 1.287 150 1.811 200 -

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