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

Frequently Asked Questions

Why is the first stage so important?

Noise from later stages is divided by the gain of preceding stages. High first-stage gain makes subsequent noise negligible.

What is a good LNA noise figure?

Below 1 dB for satellite receivers. 1-3 dB for typical RF systems. Above 3 dB is considered noisy.

Loss before the LNA?

Any loss (cable, filter) before the LNA adds directly to the noise figure. A 3 dB cable loss adds 3 dB to system NF.

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