Friis Noise Figure (3-stage)

NFtotal = NF1 + (NF2−1)/G1 + (NF3−1)/(G1×G2)

Quick answer

This calculator solves NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2) for NFtotal. With Stage 1 Noise Factor 0.5, Stage 1 Gain (linear) 1.1, Stage 2 Noise Factor 2.35, Stage 2 Gain (linear) 0.235, Stage 3 Noise Factor 5, the result is 17.2 linear.

Calculator

Result
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Formula

NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2)

Description

Friis' formula calculates the total noise factor of cascaded amplifier stages, showing that the first stage dominates the system noise performance. Each subsequent stage's noise contribution is divided by the cumulative gain of all preceding stages. This is why low-noise amplifiers (LNAs) are placed first in receiver chains: their high gain makes the noise of following stages negligible. The noise factor is the linear (not dB) ratio of output SNR to input SNR. Convert noise figure (dB) to noise factor: F = 10^(NF_dB/10).

Variables

  • NFtotal — System noise factor (linear)
  • NF1, NF2, NF3 — Individual stage noise factors (linear)
  • G1, G2 — Stage gains (linear power ratio)

Practical Notes

A 1 dB noise figure LNA with 20 dB gain followed by a 10 dB noise figure mixer gives system NF ≈ 1.36 dB. Without the LNA, system NF would be 10 dB. Losses before the LNA (cables, filters) add directly to the system noise figure: a 1 dB cable loss adds 1 dB to the noise figure. This is why LNAs are placed at the antenna.

Symbols and units

Symbol Meaning Default unit Accepted units
NF1 Stage 1 Noise Factor — —
G1 Stage 1 Gain (linear) — —
NF2 Stage 2 Noise Factor — —
G2 Stage 2 Gain (linear) — —
NF3 Stage 3 Noise Factor — —

Step by step

  1. 1. What you know: Stage 1 Noise Factor 0.5, Stage 1 Gain (linear) 1.1, Stage 2 Noise Factor 2.35, Stage 2 Gain (linear) 0.235, Stage 3 Noise Factor 5
  2. 2. The relation: NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2)
  3. 3. Substitute: NF1 = 0.5, G1 = 1.1, NF2 = 2.35, G2 = 0.235, NF3 = 5
  4. 4. Result: NFtotal = 17.2 linear

Worked examples

Minimum range

Given: Stage 1 Noise Factor 0.025, Stage 1 Gain (linear) 0.055, Stage 2 Noise Factor 0.118, Stage 2 Gain (linear) 0.0118, Stage 3 Noise Factor 0.25

Result: NFtotal = -1172 linear

Low range

Given: Stage 1 Noise Factor 0.25, Stage 1 Gain (linear) 0.55, Stage 2 Noise Factor 1.18, Stage 2 Gain (linear) 0.118, Stage 3 Noise Factor 2.5

Result: NFtotal = 23.69 linear

Typical

Given: Stage 1 Noise Factor 0.5, Stage 1 Gain (linear) 1.1, Stage 2 Noise Factor 2.35, Stage 2 Gain (linear) 0.235, Stage 3 Noise Factor 5

Result: NFtotal = 17.2 linear

High range

Given: Stage 1 Noise Factor 0.8, Stage 1 Gain (linear) 1.76, Stage 2 Noise Factor 3.76, Stage 2 Gain (linear) 0.376, Stage 3 Noise Factor 8

Result: NFtotal = 12.95 linear

Maximum range

Given: Stage 1 Noise Factor 8, Stage 1 Gain (linear) 17.6, Stage 2 Noise Factor 37.6, Stage 2 Gain (linear) 3.76, Stage 3 Noise Factor 80

Result: NFtotal = 11.27 linear

How NFtotal changes with Stage 1 Noise Factor

Stage 1 Noise Factor (input) NFtotal (result)
0.05 16.75 linear
0.125 16.83 linear
0.25 16.95 linear
0.375 17.08 linear
0.5 17.2 linear
0.75 17.45 linear
1 17.7 linear
2 18.7 linear
3.5 20.2 linear
5 21.7 linear

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Frequently asked questions

How do you calculate Friis Noise Figure (3-stage)?

Use NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2). With Stage 1 Noise Factor 0.5, Stage 1 Gain (linear) 1.1, Stage 2 Noise Factor 2.35, Stage 2 Gain (linear) 0.235, Stage 3 Noise Factor 5, NFtotal works out to 17.2 linear.

What is the formula for Friis Noise Figure (3-stage)?

The formula is NFtotal = NF1 + (NF2 − 1)/G1 + (NF3 − 1)/(G1 × G2). Friis' formula calculates the total noise factor of cascaded amplifier stages, showing that the first stage dominates the system noise performance.

Related Concepts

All Signal & RF formulas →
Wavelength Free Space Path Loss Signal-to-Noise Ratio Nyquist Sampling Rate Link Budget Antenna Gain Skin Depth Friis Noise Figure (3-stage)

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