Cascade Noise Figure
Two-stage Friis cascade — why the LNA wins.
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The engineering
Stage two's noise arrives divided by stage one's gain — so a 1 dB LNA with 20 dB of gain in front of a noisy 10 dB mixer yields a 1.35 dB system, not 11. Put the good part first and give it gain.
Corollary: any loss *before* the LNA (cable, filter, switch) adds dB-for-dB to system NF. The antenna-mounted preamp exists because of this equation.
Where this math comes from
The cascade formula is the second half of Friis's 1944 noise paper, and it reorganized receiver design permanently: sensitivity became a question of what touches the antenna first.
It's also why radio telescopes cool their first amplifier to 15 K while the racks behind run warm — everything after the first stage is nearly free.
- 1944Harald FriisCascade formula — first-stage dominance proven.
- 1963Maser/paramp eraCryogenic first stages exploit the formula for radio astronomy.
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