Figure 1: Every amplifier adds noise, degrading the SNR. Noise figure measures this degradation. In a cascade, the first stage dominates because subsequent noise is divided by the preceding gain (Friis formula).
Table of Contents
What Is Noise Figure?
Noise figure (NF) measures the degradation of signal-to-noise ratio caused by a component or system. A perfect noiseless device would have NF = 0 dB — the SNR at its output would match the SNR at its input. In practice every amplifier, mixer, filter, and cable adds noise, so the output SNR is always worse. The noise figure quantifies exactly how much worse.
The related quantity noise factor (F) is the linear ratio: F = SNRin / SNRout. Noise figure is that ratio in decibels: NF = 10 × log₁₀(F). A noise factor of 2 (NF = 3 dB) means the device doubles the noise power — half the output noise comes from the input, half from the device itself. The Decibel Calculator handles the dB-to-ratio conversion if you need to work with the linear values directly.
Noise Temperature
Noise temperature is an alternative way to express the same information, widely used in satellite communications and radio astronomy. Instead of stating SNR degradation as a ratio, noise temperature states the equivalent thermal source (in kelvins) that would produce the same added noise:
Te = T₀ × (F − 1) where T₀ = 290 KTemperature to NF:
F = 1 + Te/T₀ → NF = 10 log₁₀(F)
A 1 dB noise figure corresponds to about 75 K. A 3 dB NF corresponds to 290 K — the device adds as much noise as a resistor at room temperature. Cryogenic LNAs used in radio telescopes achieve noise temperatures below 10 K (NF < 0.15 dB).
The Formulas
NF (dB) = 10 log₁₀(F) | F = 10(NF/10)Friis cascade:
Ftotal = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁×G₂) + …Sensitivity:
MDS = kTB + NF + SNRmin (all dBm)Thermal floor:
kTB = −174 + 10 log₁₀(BW) dBm
Mode 1 — NF ↔ Temperature Conversion
Enter noise figure in dB or noise temperature in kelvin — the calculator converts bidirectionally. This is the starting point for any noise analysis: you need the NF or temperature of each component before cascading them.
Example: 1 dB Low-Noise Amplifier
F = 10(1/10) = 1.259
Te = 290 × (1.259 − 1) = 75.1 K
System temp = 75.1 + 290 = 365.1 K
The LNA adds 25.9% more noise than a matched 290 K termination. SNR degrades by exactly 1 dB.
Example: 6 dB Mixer
F = 10(6/10) = 3.981
Te = 290 × (3.981 − 1) = 864.5 K
The mixer adds nearly three times the room-temperature noise. This is why mixers are never placed at the front of a receiver chain. The Gain Calculator can size the LNA that must precede the mixer to suppress its noise contribution.
Mode 2 — Cascaded Noise Figure (Friis Formula)
This is the mode that matters most for RF system design. Real receivers are chains of amplifiers, mixers, filters, and cables, each adding noise. The Friis formula calculates the total system noise figure from up to 6 stages, each with its own NF (dB) and gain (dB). Each stage’s noise contribution is divided by all preceding gain, which is why the first stage dominates.
Example: LNA + Mixer + IF Amplifier
Stage 1: LNA — NF 1 dB, Gain +20 dB (F=1.259, G=100)
Stage 2: Mixer — NF 6 dB, Gain −6 dB (F=3.981, G=0.251)
Stage 3: IF Amp — NF 3 dB, Gain +15 dB (F=1.995, G=31.62)
Ftotal = 1.259 + (3.981−1)/100 + (1.995−1)/(100×0.251)
= 1.259 + 0.0298 + 0.0396 = 1.329
System NF = 10 log₁₀(1.329) = 1.23 dB
Total gain: +20 − 6 + 15 = +29 dB
The 6 dB mixer adds only 0.23 dB to the system NF because the LNA’s 20 dB gain divides the mixer’s noise by 100.
Example: Full 4-Stage Receiver
Stage 1: NF 2 dB, Gain +30 dB (F=1.585, G=1000)
Stage 2: NF 8 dB, Gain −8 dB (F=6.310, G=0.158)
Stage 3: NF 4 dB, Gain +20 dB (F=2.512, G=100)
Stage 4: NF 3 dB, Gain +15 dB (F=1.995, G=31.62)
Ftotal = 1.585 + 0.00531 + 0.00957 + 0.0000630 = 1.600
System NF = 2.04 dB | Total gain: +57 dB
Stage 1 contributes 1.585 of the total 1.600 noise factor — that is 99.1% of the total. The 8 dB mixer’s contribution is negligible because the LNA’s 30 dB gain divides it by 1,000.
Mode 3 — Sensitivity and MDS
Once you know the system noise figure, the next question is: what is the weakest signal this receiver can detect? The minimum detectable signal (MDS) depends on three things: the thermal noise floor, the system NF, and the minimum SNR required for reliable demodulation.
Example: Narrowband Receiver
kTB = −174 + 10 log₁₀(10,000) = −174 + 40 = −134 dBm
Noise floor = −134 + 3 = −131 dBm
MDS = −131 + 10 = −121 dBm (7.94 × 10−16 W)
Any signal above −121 dBm will be detected with at least 10 dB SNR. The Signal Attenuation Calculator can then check whether the signal arrives above this threshold after cable and path losses.
Example: Wideband Receiver
kTB = −174 + 60 = −114 dBm
Noise floor = −114 + 5 = −109 dBm
MDS = −109 + 10 = −99 dBm
22 dB worse than the narrowband receiver, almost entirely because the 100× wider bandwidth raises the thermal noise floor by 20 dB. The Bandwidth Calculator quantifies this relationship and shows the Shannon capacity limit at the resulting SNR.
Why the First Stage Dominates
The Friis formula divides each stage’s noise contribution by all preceding gain. If the first stage has 20 dB gain (linear 100), the second stage’s noise is divided by 100. Only the first stage’s noise passes through at full strength.
Consider swapping an LNA (1 dB NF, +20 dB gain) and a mixer (6 dB NF): LNA first gives system NF = 1.10 dB. Mixer first gives system NF = 7.0 dB. The order changed the system NF by nearly 6 dB — that is a 4× difference in sensitivity. This is the single most important lesson in receiver design: always put the lowest-noise, highest-gain stage first.
Losses Before the LNA
Any loss between the antenna and the LNA adds directly to the system noise figure. A 1 dB cable loss before the LNA adds a full 1 dB to the system NF. This is why satellite dishes mount the LNB directly at the feed — the cable runs after the amplifier, where its loss merely reduces signal level without degrading the noise figure.
A 10-metre cable at 12 GHz could easily have 3 dB of loss. Placing that cable before the LNA would double the system noise temperature. After the LNA (with 20 dB gain), the same 3 dB cable loss reduces signal by 3 dB but adds virtually nothing to the system noise figure.
Practical Design Guidelines
Losses before LNA: Minimise ruthlessly — every dB of pre-LNA loss adds directly to system NF.
Sensitivity vs bandwidth: MDS improves by 3 dB every time bandwidth is halved. Narrow the bandwidth if you need better sensitivity.
Margin: Design for 6–10 dB above MDS to account for fading, interference, and component aging.
Frequently Asked Questions
What is a good noise figure?
Why does the first stage dominate system noise figure?
What is MDS and how does it differ from noise floor?
What is noise temperature and when should I use it?
Can noise figure be negative?
How does bandwidth affect sensitivity?
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