An LNA with a noise figure of 1.5 dB and a gain of 15 dB is placed at the first stage of a receiver, followed by a circuit with a noise figure of 10 dB. Which is closest to the noise figure of the two stages together?

Answer: B. 2.3 dB

The noise figure of cascaded circuits is found with Friis's formula F = F1 + (F2 − 1)/G1, using linear values for F (noise figure) and G (gain). F1 = 10^0.15 ≈ 1.41, F2 = 10 and G1 = 10^1.5 ≈ 31.6, so F ≈ 1.41 + 9/31.6 ≈ 1.70, which is 10·log₁₀(1.70) ≈ 2.3 dB. The noise of later stages is divided by the first stage's gain, so the larger that gain, the smaller their effect. For this reason, a receiver's noise performance is set mainly by the first-stage LNA.

• A. This looks only at the noise figure of the first-stage LNA. The later stage's noise is also added, divided by the first stage's gain.
• B. Correct. 1.41 + 9/31.6 ≈ 1.70, about 2.3 dB.
• C. This adds the two noise figures in dB. Friis's formula uses linear values.