This page computes a Friis cascade — the noise figure of a chain of up to four stages, not a single device in isolation. A single stage is simply the one-stage case, and leaving the other three switched off gives it. Every figure here uses the standard reference temperature of 290 K, the convention adopted by the IEEE and used by every noise figure specification you will read on a data sheet.
Noise figure is the amount by which a device degrades the signal-to-noise ratio passing through it, expressed in decibels. It is not a measure of how much noise a device makes in absolute terms, and that distinction is the source of most of the confusion around it. Arb Digital built this calculator around the cascade because the useful question is almost never "what is this amplifier's noise figure" but "what does my whole receiver chain do to the signal, and which stage is responsible".
What This Noise Figure Calculator Does
Enter the gain and noise figure of each stage in the order the signal meets them, and the calculator returns the noise figure of the whole cascade in dB. The grid gives the equivalent noise temperature referred to the input, the total gain, the noise floor in dBm for the bandwidth you set, and the signal-to-noise ratio that comes out for the input signal level you supply.
The subtitle names which stage contributes the most noise and what share of the total it accounts for. That is usually the answer people are actually looking for, because it tells you where a redesign would pay and where it would not.
One clarification on naming, since the site carries a similarly named tool: this page is about radio-frequency noise in a receiver chain. The noise exposure calculator is about occupational sound exposure and hearing protection, an entirely unrelated quantity that happens to share the word.
How to Use It
- Enter each stage in signal order. The order matters enormously in this calculation, unlike a gain budget where it does not.
- Enter passive losses as negative gain with a noise figure equal to the magnitude of that loss — a 3 dB cable is −3 dB gain and 3 dB noise figure at ambient temperature.
- Switch off unused stages by setting both their gain and noise figure to zero, which makes them ideal pass-throughs.
- Set the noise bandwidth to the receiver's actual equivalent noise bandwidth, not the channel spacing, to get a meaningful noise floor.
- Read the dominant stage under the headline figure before deciding what to improve.
The Formula: How It's Calculated
Work in linear terms. A noise figure NF in dB becomes a noise factor F = 10NF/10, and a gain in dB becomes a linear gain G = 10GdB/10. The Friis formula for cascaded noise then reads:
Ftotal = F1 + (F2 − 1)÷G1 + (F3 − 1)÷(G1G2) + (F4 − 1)÷(G1G2G3) + …
Converting back, NFtotal = 10 log10(Ftotal). The equivalent input noise temperature is Te = T0(F − 1) with T0 = 290 K, and the thermal noise floor referred to the input is Pn = 10 log10(kBT0B ÷ 1 mW) + NF, which is the familiar −174 dBm/Hz plus 10 log10 of the bandwidth in hertz plus the noise figure. The definitions, the 290 K convention and the measurement techniques behind them are set out in Keysight's application note Fundamentals of RF and Microwave Noise Figure Measurements, and the external noise environment a receiver actually sits in — atmospheric, galactic and man-made — is characterised in ITU-R Recommendation P.372, Radio noise.
A worked example matching the defaults here. Stage 1: 15 dB gain, 1 dB NF, so G1 = 31.62 and F1 = 1.2589. Stage 2: 20 dB, 5 dB, so G2 = 100 and F2 = 3.1623. Stage 3: 10 dB, 10 dB, so F3 = 10. The cascade gives 1.2589 + 2.1623÷31.62 + 9÷3162 = 1.2589 + 0.0684 + 0.0028 = 1.3301, which is 1.239 dB. The noise temperature is 290 × 0.3301 = 95.7 K, total gain is 45 dB, and in 1 MHz the input-referred noise floor is about −112.8 dBm. An −80 dBm signal therefore emerges with about 32.8 dB of signal-to-noise ratio.
Why the First Stage Decides Almost Everything
Look at the arithmetic above. Stage 1 contributes 1.2589 to the total. Stage 2, despite a 5 dB noise figure that looks alarming on paper, contributes 0.0684 — about a twentieth as much — because its excess noise is divided by the 31.6× gain in front of it. Stage 3, with a 10 dB noise figure, contributes 0.0028, which is under a quarter of one per cent of the total.
This is the entire reason receiver architecture looks the way it does. Put a good low-noise amplifier first, give it enough gain, and everything downstream becomes almost irrelevant to sensitivity. It is also why improving the second stage is usually wasted effort: in this example, making stage 2 noiseless would improve the system figure by roughly 0.2 dB, while improving stage 1 by half a decibel improves it by nearly half a decibel.
The corollary is the trap. There is no gain in front of stage 1, so its noise figure passes through undivided. Anything you put ahead of the amplifier — a run of coax, a filter, a switch, a connector — is now stage 1, and it is a lossy one.
Passive Losses Are Noise Figure, One for One
A passive component at ambient temperature has a noise figure numerically equal to its loss. A 3 dB attenuator has a 3 dB noise figure; 20 metres of coax with 4 dB of loss has a 4 dB noise figure. This is not a coincidence or a rule of thumb but a thermodynamic result: the component attenuates the signal and replaces the lost noise power with its own thermal noise, so the signal-to-noise ratio degrades by exactly the attenuation.
The consequence for system design is stark. Put 4 dB of feeder in front of a 1 dB amplifier and the system noise figure is not 1 dB, and not 5 dB either — it is the cascade of a 4 dB loss followed by a 1 dB amplifier, which works out at 5.0 dB. The entire benefit of the low-noise amplifier has been thrown away before the signal reached it. Move the amplifier to the antenna end of the same feeder and the system figure drops to about 1.1 dB, because the cable's loss is now divided by the amplifier's gain. Nothing changed except the order, and the ordering rule is the whole practical content of the Friis formula. Cable and component losses themselves are handled by the insertion loss calculator, and the free-space part of the link budget by the free space path loss calculator.
What 290 K Actually Means, and When It Is the Wrong Reference
Noise figure is defined against a source termination at a standard temperature of 290 K — about 17 °C, chosen because it makes kT0 a convenient round number and it approximates a terrestrial environment. It is a definition, not a measurement of your equipment room, and a device's noise figure does not change because the lab is warm.
The convention becomes actively misleading for systems whose real source is much colder than 290 K. A satellite ground station or a radio telescope points its antenna at a sky whose brightness temperature may be a few tens of kelvin, and there the meaningful comparison is between the receiver's noise temperature and the antenna's. Noise figure compresses that range badly: the difference between a 0.5 dB and a 0.3 dB receiver looks trivial in decibels but is 35 K against 21 K in temperature, a 40% improvement in a system whose total might be 60 K. This is why deep-space and radio-astronomy work quotes noise temperature and terrestrial communications quotes noise figure, and why the calculator reports both.
Noise Bandwidth Is Not Channel Bandwidth
The noise floor depends on bandwidth, and the bandwidth that belongs in the formula is the equivalent noise bandwidth — the width of an ideal brick-wall filter that would pass the same noise power as your real filter. For a real filter with sloping skirts, that is wider than the 3 dB bandwidth, typically by ten to twenty per cent for a multi-pole design, and it is not the channel spacing.
Using channel spacing instead of noise bandwidth is a common and quietly optimistic error, because it usually understates the noise. Halving the noise bandwidth improves the noise floor by 3 dB, which is often a cheaper sensitivity gain than improving the front end. Bandwidth arithmetic is covered by the bandwidth and frequency calculator, the dB conversions by the decibel calculator, and the thermal noise of a resistor in its own right by the resistor noise calculator.
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Browse All Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Adding noise figures in dB — the Friis formula works on linear noise factors and linear gains, and adding decibels gives a much worse answer than the real one.
- Putting the low-noise amplifier after the feeder — whatever comes first sets the floor, and a lossy cable in front of an LNA discards its entire benefit.
- Giving a passive component a low noise figure — at ambient temperature its noise figure equals its loss exactly, so a 4 dB cable is a 4 dB noise figure.
- Using channel spacing as the noise bandwidth — the correct figure is the equivalent noise bandwidth, which is wider than the 3 dB bandwidth of a real filter.
- Quoting noise figure for a cryogenic or sky-facing system — noise temperature resolves differences that decibels compress into invisibility.
Related Free Tools From Arb Digital
Build the rest of a link budget with the EIRP calculator for radiated power and the free space path loss calculator for propagation loss. Component and cable losses go through the insertion loss calculator, dB conversions through the decibel calculator, and thermal noise from a resistance through the resistor noise calculator. Set filter widths with the bandwidth and frequency calculator, and check occupied bandwidth on the transmit side with the modulation index calculator. Everything else is in the free online tools hub.
Frequently Asked Questions
The amount by which a device degrades the signal-to-noise ratio passing through it, in decibels, measured with the input terminated at the standard reference temperature of 290 K. It is a ratio of ratios, not an absolute noise level, which is why an amplifier with high output noise can still have a low noise figure.
It is the standard adopted by the IEEE and used throughout the industry. It corresponds to about 17 degrees Celsius, approximates a terrestrial environment, and makes the thermal noise density a convenient round figure of roughly minus 174 dBm per hertz. It is a definition rather than an assumption about your operating conditions.
No. The Friis formula works on linear noise factors, and each stage after the first has its excess noise divided by all the gain preceding it. Adding decibels would give a far worse figure than reality, because it ignores the fact that early gain suppresses later noise contributions.
Numerically equal to its loss, at ambient temperature. A 3 dB attenuator has a 3 dB noise figure and a feeder with 4 dB of loss has a 4 dB noise figure. The component attenuates the signal and substitutes its own thermal noise, so the signal-to-noise ratio degrades by exactly the attenuation.
Because the first stage sets the floor and everything after it is divided by the gain in front. Four decibels of cable ahead of a 1 dB amplifier gives a system figure of about 5 dB; the same amplifier placed before the same cable gives about 1.1 dB. Only the order changed.
Whenever the source is much colder than 290 K, such as a satellite ground station or a radio telescope pointed at the sky. In decibels the difference between an excellent and a merely good receiver looks negligible, while in kelvin the same difference can be tens of per cent of the system total.
The equivalent noise bandwidth of the receiver, which is the width of an ideal rectangular filter passing the same noise power as your real one. It is wider than the 3 dB bandwidth, often by ten to twenty per cent, and it is not the channel spacing.
This tool is provided for educational and engineering-estimate use. It applies the Friis cascade relation at the 290 K reference temperature and assumes matched impedances, linear operation and stages specified at the same frequency. It does not account for impedance mismatch, image response, phase noise, non-linearity or interference, so measured system performance should be verified against a calibrated noise figure measurement.
