Noise Figure Calculator - SNR, dB, and Friis Cascade

A noise figure calculator converts the input and output signal-to-noise ratios of an electronic device, amplifier, or receiver chain into a single noise performance number. The result is reported both as a linear noise factor F and as a noise figure NF in decibels, so you can compare receivers, low-noise amplifiers, and cascaded front ends against published datasheet specifications.

• • RF Receiver Design: Estimate how much an LNA, mixer, or filter degrades the SNR of a radio receiver before the demodulator sees it.
• • Cascaded Amplifier Chains: Use the Friis formula idea to track how a sequence of gain stages combines into a single system noise figure, with the first stage usually dominating.
• • Communications Link Budgets: Convert a measured input and output SNR into the noise figure that feeds link-budget and sensitivity calculations in dB.

Every active electronic component adds a small amount of noise to the signal passing through it, and a noise figure calculator turns the resulting input and output SNRs into a single noise factor F and noise figure NF in dB so the device can be compared against published datasheet numbers.

When the same receiver chain is described by signal loss instead of SNR, Attenuation Calculator applies the Beer-Lambert law to the same dB scale so the two numbers can be compared on equal terms.

The calculator uses the IRE/IEEE definition of noise factor as input SNR over output SNR, then expresses that ratio in decibels using ten times the base-10 logarithm. A mode selector lets you supply the SNR values either as plain ratios or in dB.

• SNRi: Signal-to-noise ratio at the device input. In linear mode this is a unitless ratio; in dB mode it is a decibel value such as 40 dB.
• SNRo: Signal-to-noise ratio at the device output. For any physical device the output SNR is less than or equal to the input SNR, so F is always greater than or equal to 1.
• F (noise factor): Linear ratio of input SNR to output SNR. F = 1 means an ideal noiseless device; F = 2 means the device added enough noise to halve the SNR.
• NF (noise figure, dB): Noise factor expressed in decibels using 10 log10(F). An ideal device has NF = 0 dB; a typical LNA sits between 0.5 dB and 2 dB.

The decibel convention used here matches the rest of RF engineering: for power-like quantities such as signal-to-noise ratios, the decibel is 10 times the base-10 logarithm of the linear ratio, so the dB mode internally converts each input back to a linear ratio using 10^(dB/10) before applying F = SNRi / SNRo.

According to ITU-R P.341-6, For power-like quantities such as signal-to-noise ratios the decibel is defined as 10 log10(P/P0), so subtracting two decibel SNRs is exactly the same as taking 10 log10 of their linear ratio.

According to Omni Calculator noise-figure article, A noise figure calculator that uses NF = 10 log10(SNRi/SNRo) gives 0.5799 dB for SNRi=8 and SNRo=7, 3.9794 dB for SNRi=5 and SNRo=2, and 5 dB for SNRi=40 dB and SNRo=35 dB.

When you also need to translate the power values that go into the SNRi and SNRo ratios between dBm and watts, Watt Converter handles the same decibel arithmetic on a different base unit.

Four ideas show up in nearly every noise figure problem, from a single transistor to a multi-stage satellite receiver.

If you also need to check the wavelength, frequency, or wave number of the carrier the receiver is listening to, Harmonic Wave Equation Calculator gives the basic sinusoidal wave parameters that pair with noise figure analysis.

Pick the input convention that matches your numbers, type the two SNRs, and read the noise factor and noise figure from the results panel. Three quick checks below keep the answer realistic.

1. 1 Choose the SNR input mode: Select 'Linear ratio' for plain numbers or 'Decibels' for datasheet values like 40 dB and 35 dB.
2. 2 Enter the input signal-to-noise ratio: Type the SNRi value in the same convention you chose. In dB mode a typical range is 0 dB to 60 dB.
3. 3 Enter the output signal-to-noise ratio: Type the SNRo value the same way. For a real device SNRo is always less than or equal to SNRi, so F is at least 1.
4. 4 Read the noise factor F: F = SNRi / SNRo is a linear, unitless number. F = 1 means noiseless, F = 2 halves the SNR, F = 10 reduces it by a factor of 10.
5. 5 Read the noise figure NF in dB: NF = 10 log10(F). A typical LNA sits between 0.5 dB and 2 dB; a generic mixer is 6 dB to 10 dB; a poor front end can be 15 dB or more.
6. 6 Cross-check with the mode: If switching the mode selector leaves NF unchanged, your inputs are inconsistent with the chosen mode. Re-read the help text below each input.

If a spectrum analyzer shows SNRi = 40 dB at the antenna port and SNRo = 35 dB at the output of an LNA, set the mode to Decibels, type 40 and 35, and read NF = 5.00 dB. The same answer comes out in linear mode by typing 10000 and 3162.3, which represent the same 40 dB and 35 dB linear ratios.

When the noise figure you get points to an impedance-matching problem at the input, Ohm's Law Calculator gives the V = I R relationships that drive the matching network choice.

A focused noise figure calculator removes manual log conversions, keeps the linear and decibel conventions straight, and turns a two-input amplifier specification into the single number a receiver designer actually needs.

• • Skip the log conversion by hand: The calculator applies 10 log10(F) for you, so you avoid the common mistake of using 20 log10(F), which is only correct for amplitude-like fields such as voltage or pressure.
• • Use both linear and decibel inputs: A mode selector lets you enter either a linear ratio or a decibel value. The calculator handles the 10^(dB/10) conversion in the dB mode so you do not have to.
• • Get a peer-relevant RF number: The result is reported as both a linear noise factor F and a noise figure NF in dB, matching the units used in IEEE receiver definitions and most RF datasheets.
• • Check cascaded amplifier chains: Pair this calculator with the Friis formula in the key-concepts section to estimate the system noise figure of a multi-stage receiver or measurement chain.
• • Verify measurements against datasheets: Enter the measured input and output SNR from a bench setup and compare the calculated NF to the manufacturer's published number.

Acoustic noise and electrical noise both decay as exponentials, and Reverberation Time Calculator applies the same exp(-t/tau) idea to room acoustics, so it is a natural complement when you study noise behaviour in both domains.

A noise figure depends on the device under test, the input SNR you measured or assumed, and the convention you used to express that SNR. These five factors drive most of the variation you will see in practice.

• • The calculator treats the device as a single two-port with a fixed F. Real receivers have a frequency-dependent noise figure, so the result is exact only at the frequency of the input SNR measurement.
• • For cascaded stages the calculator reports the single-stage noise figure. To get the system noise figure you still need the Friis formula, which uses each stage's gain in linear units to weight the later contributions.

According to Friis, H. T. (1944) - Proceedings of the IRE, 'Noise Figures of Radio Receivers', The noise factor of M cascaded stages is F_total = F1 + (F2-1)/G1 + (F3-1)/(G1 G2) + ..., so the first stage in a receiver chain dominates the overall noise figure.

When the receiver's thermal noise contribution approaches the lossy cable loss, the equivalent noise temperature tied to the 290 K reference enters the link budget directly, and Blackbody Radiation Calculator gives the Planck spectral radiance and exitance at the operating temperature so the thermal floor lines up with the measured NF.