Noise Figure Calculator — Friis Cascade Formula
Calculate the total noise figure and system noise temperature for a two-stage RF or microwave amplifier chain. Enter each stage's noise figure (NF in dB) and the first-stage gain to see exactly how Friis's formula combines them — and which stage dominates.
dB
dB
dB
Cascaded NF using Friis formula: F = F₁ + (F₂ − 1) / G₁
- 1
Stage 1 noise factor F₁ (linear)
10^(3 ÷ 10) = 1.9953 - 2
Stage 1 linear gain G₁
10^(20 ÷ 10) = 100High first-stage gain suppresses downstream noise in the Friis formula. - 3
Stage 2 noise factor F₂ (linear)
10^(6 ÷ 10) = 3.9811 - 4
Total noise factor (Friis)
1.9953 + (3.9811 − 1) ÷ 100 = 2.0251 - 5
Total noise figure (dB)
10 × log₁₀(2.0251) = 3.06
How does this calculator work?
The Friis formula combines two amplifier stages: F_total = F₁ + (F₂−1)/G₁, then NF (dB) = 10 × log₁₀(F_total). A high-gain LNA at the front suppresses downstream noise — a 20 dB first stage makes the second stage contribution 100× smaller. System noise temperature is Tₑ = (F−1) × 290 K.
Formula
How this is calculated
Noise figure (NF) quantifies how much a component degrades the signal-to-noise ratio (SNR). A theoretically noiseless device has NF = 0 dB (noise factor F = 1). Every real amplifier adds thermal noise, pushing F above 1. Noise figure and noise factor are related by NF = 10 × log₁₀(F). Equivalently, the same excess noise can be expressed as a noise temperature Tₑ = (F − 1) × T₀, where T₀ = 290 K is the IEEE standard reference temperature.
When two stages are cascaded — for example, a low-noise amplifier (LNA) followed by a mixer or IF amplifier — the system noise factor is given by the Friis formula: F_total = F₁ + (F₂ − 1) / G₁. Because the second stage contribution is divided by the first stage's linear gain G₁, a high-gain, low-NF LNA at the antenna input dramatically suppresses all downstream noise. A 20 dB first-stage gain reduces the second stage's excess noise contribution by a factor of 100.
The calculator assumes both stages are impedance-matched and operated at the standard reference temperature. Real systems also contend with antenna noise, feed-line losses (each decibel of loss adds 1 dB of NF), and non-linear effects at large signal levels — none of which are modelled here. For chains longer than two stages, extend Friis by adding (F₃ − 1)/(G₁G₂), and so on.
Frequently asked questions
Noise factor (F) is a dimensionless linear ratio representing how much the component degrades SNR — always ≥ 1 for a passive or active device at physical temperature. Noise figure (NF) is its decibel form: NF = 10 × log₁₀(F). An NF of 3 dB means the SNR halves through that stage.
The Friis formula divides each downstream stage's excess noise by the cumulative gain of all preceding stages. So the higher the first-stage gain, the less every subsequent stage contributes. In a well-designed receiver, an LNA with 20 dB gain and 1 dB NF reduces the second-stage contribution by 100×, making the LNA's NF almost equal to the system NF.
For n stages: F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂) + (F₄−1)/(G₁G₂G₃) + …. Each additional stage is divided by the product of all preceding linear gains. The two-stage case covers the dominant terms in most receiver chains.
Also known as
TG we-Calculate Editorial Team. (2026). Noise Figure Calculator — Friis Cascade Formula [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/noise-figure-calculator
TG we-Calculate Editorial Team. "Noise Figure Calculator — Friis Cascade Formula." TG we-Calculate. 2026. https://we-calculate.com/calculator/noise-figure-calculator.
TG we-Calculate Editorial Team, "Noise Figure Calculator — Friis Cascade Formula," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/noise-figure-calculator
@misc{wecalculate_noise_figure_calculator, title = {Noise Figure Calculator — Friis Cascade Formula}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/noise-figure-calculator}}, year = {2026}, note = {TG we-Calculate} }
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