💻

Cascaded Noise Figure Calculator (Friis Formula)

Calculate the total noise figure, noise temperature and gain of up to four cascaded RF stages (LNA, filter, mixer, IF amplifier) with the Friis formula, stage by stage.

Number of stages

Stage 1 gain

Stage 1 noise figure

Stage 2 gain

Stage 2 noise figure

Stage 3 gain

Stage 3 noise figure

Stage 4 gain

Stage 4 noise figure

Loading calculator…

How it works

F = 10^(NF/10), G = 10^(gain/10) · Friis: F_total = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁G₂) + (F₄ − 1)/(G₁G₂G₃) · NF_total = 10 log₁₀ F_total · T_e = 290 K × (F_total − 1)

Every stage of a receiver adds noise, but the noise of a later stage is divided by the total gain in front of it. That is the Friis formula for noise (Harald Friis, 1944), and it is why a receiver puts a low-noise amplifier first: with 20 dB of LNA gain, even a 10 dB-noise-figure mixer behind it adds only a fraction of a decibel. Passive losses before the LNA (cable, filter, switch) add their full loss to the noise figure. Values are referenced to the standard 290 K temperature.

Worked example

An LNA (20 dB gain, 1 dB NF), a 3 dB-loss filter (NF 3 dB) and an IF amplifier (30 dB, NF 10 dB): F = 1.259 + 0.995 ÷ 100 + 9 ÷ (100 × 0.501) = 1.448, so the total noise figure is 1.61 dB (only 0.61 dB above the LNA alone), the noise temperature is 130.1 K and the total gain is 47.00 dB.

Sources: Wikipedia — Friis formulas for noise · Keysight — Application Note 57-1: Fundamentals of RF and Microwave Noise Figure Measurements

Frequently asked questions

What is the Friis formula for noise?

F_total = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁G₂) + …, with noise factors and gains as linear ratios, not dB. The first stage dominates when its gain is high.

What noise figure does a passive filter or cable have?

At room temperature (290 K) a passive lossy component has a noise figure equal to its loss: a cable with 2 dB of loss has NF = 2 dB and gain = −2 dB.

Why put the LNA before the filter?

Every dB of loss before the LNA adds directly to the system noise figure. If out-of-band interference is strong you may still need a low-loss filter first, trading a little sensitivity for linearity.

How do noise figure and noise temperature relate?

T_e = 290 × (F − 1) kelvin. A 1 dB noise figure is 75 K, 3 dB is 289 K; noise temperature is preferred for very low-noise systems such as satellite and radio-astronomy receivers.

Related calculators

Receiver Sensitivity Calculator

Calculate a radio receiver's thermal noise floor (kTB, −174 dBm/Hz), noise floor with noise figure and sensitivity in dBm, watts, microvolts and dBµV from bandwidth, noise figure and SNR.

RF Link Budget & Fade Margin Calculator

Complete point-to-point link budget: transmit power, cable and connector losses, antenna gains, free-space path loss, extra losses and receiver sensitivity — received signal, fade margin, availability estimate and the maximum range at your target margin.

Decibel Gain Calculator (Power & Voltage)

Convert a power or voltage ratio into decibels of gain — or a loss — with the correct 10 log or 20 log rule.

dBm to Watts Calculator

Convert dBm to milliwatts and watts (or watts back to dBm) — the decibel power scale used across RF, Wi-Fi and fibre.

Signal-to-Noise Ratio Calculator

Compute the signal-to-noise ratio from a signal and noise level — as a plain ratio and in decibels, for amplitude or power quantities.

This calculator is for educational purposes. Double-check important results before acting on them.