Noise Figure Calculator Formula

Understand the math behind the noise figure calculator. Each variable explained with a worked example.

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Formulas Used

Cascaded Noise Figure

cascaded_nf_db = 10 * log10(f1 + (f2 - 1) / g1 + (f3 - 1) / (g1 * g2))

Total Gain

total_gain_db = gain1_db + gain2_db

Noise Temperature

noise_temp_k = 290 * (pow(10, (10 * log10(f1 + (f2 - 1) / g1 + (f3 - 1) / (g1 * g2))) / 10) - 1)

Variables

VariableDescriptionDefault
nf1_dbStage 1 Noise Figure(dB)1.5
gain1_dbStage 1 Gain(dB)20
nf2_dbStage 2 Noise Figure(dB)10
gain2_dbStage 2 Gain(dB)15
nf3_dbStage 3 Noise Figure(dB)15
f1Derived value= pow(10, nf1_db / 10)calculated
f2Derived value= pow(10, nf2_db / 10)calculated
f3Derived value= pow(10, nf3_db / 10)calculated
g1Derived value= pow(10, gain1_db / 10)calculated
g2Derived value= pow(10, gain2_db / 10)calculated

How It Works

Friis Noise Figure Formula

Formula

F_total = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1 x G2) + ...

All values in linear (not dB). The first stage dominates overall noise figure. Use a low-noise amplifier (LNA) first for best sensitivity.

Worked Example

LNA (1.5 dB NF, 20 dB gain) followed by mixer (10 dB NF, 15 dB gain) and IF amp (15 dB NF).

nf1_db = 1.5gain1_db = 20nf2_db = 10gain2_db = 15nf3_db = 15
  1. 01F1 = 10^(1.5/10) = 1.413
  2. 02F2 = 10^(10/10) = 10, G1 = 10^(20/10) = 100
  3. 03F3 = 10^(15/10) = 31.62, G2 = 10^(15/10) = 31.62
  4. 04F_total = 1.413 + (10-1)/100 + (31.62-1)/(100x31.62) = 1.413 + 0.09 + 0.0097 = 1.513
  5. 05NF = 10 x log10(1.513) = 1.80 dB

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