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system designintermediateFriis, H.T., "Noise Figures of Radio Receivers", 1944

Friis Cascade Noise Formula

#cascade#noise figure#friis#LNA#receiver design#system noise

Friis Cascade Noise Formula

When multiple amplifier stages are cascaded, the overall noise figure depends on each stage's noise figure and gain. This formula shows why the first stage (usually an LNA) dominates system noise performance.

Ftotal=F1+F2−1G1+F3−1G1G2+⋯F_{total} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \cdots

Alternative Forms

Two-Stage
Ftotal=F1+F2−1G1F_{total} = F_1 + \frac{F_2 - 1}{G_1}
Simplified form for two stages
In dB (Two-Stage)
NFtotal=10log⁡10(10NF1/10+10NF2/10−110G1/10)NF_{total} = 10\log_{10}\left(10^{NF_1/10} + \frac{10^{NF_2/10} - 1}{10^{G_1/10}}\right)
Convert each stage to linear first, then back to dB

Input Variables

dB

Noise figure of first stage (LNA)(Range: 0 – 20 dB)

dB

Gain of first stage(Range: -10 – 50 dB)

dB

Noise figure of second stage(Range: 0 – 20 dB)

dB

Gain of second stage(Range: -10 – 50 dB)

dB

Noise figure of third stage (optional, 0 to ignore)(Range: 0 – 30 dB)

Results

Total Noise Figure (NF_{total})
—

📖 Example: Receiver Front-End

Calculate total NF: LNA (1dB NF, 20dB gain) → Mixer (6dB NF, 10dB gain) → IF Amp (10dB NF)

Reference: Friis, H.T., "Noise Figures of Radio Receivers", 1944

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