How to Compute Cascaded Noise Figure

Friis Cascade Formula

  F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂) + (F₄−1)/(G₁G₂G₃) + ...
  
  where F = noise factor (linear, F = 10^(NF_dB/10))
        G = linear gain (G = 10^(G_dB/10))

Step-by-Step Example

  RF receive chain:  
  Stage 1: Pre-select filter: NF=2.0 dB, G=−2.0 dB
  Stage 2: LNA: NF=1.5 dB, G=+18.0 dB
  Stage 3: 2nd filter: NF=1.0 dB, G=−1.0 dB
  Stage 4: Mixer: NF=8.0 dB, G=−6.0 dB

  Convert to linear:
  F₁=1.585, G₁=0.631
  F₂=1.413, G₂=63.1
  F₃=1.259, G₃=0.794
  F₄=6.310

  Apply Friis:
  F_total = 1.585 + (1.413−1)/0.631 + (1.259−1)/(0.631×63.1) + (6.310−1)/(0.631×63.1×0.794)
          = 1.585 + 0.655 + 0.0065 + 0.168
          = 2.414
  NF_sys = 10·log₁₀(2.414) = 3.83 dB

  Sensitivity at 10 MHz BW, SNR_min=−1 dB:
  S = −174 + 3.83 + 70 + (−1) = −101.2 dBm

Key Insights from This Example

• Filter before LNA contributes 2.0 dB → directly adds to NF (most impactful)
• LNA contributes only 0.655 dB (attenuated by filter before it)
• 2nd filter and mixer contribute tiny amounts (suppressed by LNA gain)
• Moving LNA before filter: NF_sys drops from 3.83 to ~1.76 dB (+1.7 dB sensitivity improvement)

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