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Noise Figure ⇄ Noise Temperature

Convert between NF in dB and equivalent noise temperature in kelvin.

InputTe = (F − 1) · 290 K

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The engineering

Same degradation, two dialects: terrestrial folks quote NF in dB, satellite and radio-astronomy folks quote kelvin because their antennas see cold sky, not a 290 K room. A 1 dB LNA is 75 K; a 3 dB one is 289 K.

Below ~1 dB, kelvin resolves differences the dB scale compresses — which is exactly why the deep-space people use it.

Where this math comes from

Harald Friis defined noise figure in 1944 to score receiver front ends fairly, referencing everything to a 290 K source. The cascade formula that goes with it explains the eternal rule: the first amplifier decides the system.

When Penzias and Wilson chased a stubborn 3.5 K excess in their horn antenna's noise-temperature budget in 1964, the leftover turned out to be the Big Bang — the most famous noise-temperature measurement ever made.

  1. 1944Harald FriisNoise figure defined; 290 K reference set.
  2. 1964Penzias & WilsonA 3.5 K unexplained noise temperature = the cosmic microwave background.

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