Noise Figure
Every amplifier, every filter, and every length of cable that your signal passes through on its way from the antenna to the detector adds noise. A theoretically perfect amplifier would amplify the signal and nothing else — but no real amplifier is perfect. Every real device adds some extra noise on top of the thermal noise it receives. Noise figure (NF) is the standard way of expressing how much noise a device adds, and the Friis formula tells you how to combine the noise figures of all the stages in your receiving chain into a single number.
Understanding noise figure is essential for making intelligent decisions about your receiving setup: choosing a preamplifier, selecting a receiver, positioning a low-noise amplifier on the tower, or understanding why adding a roofing filter before the first mixer improves selectivity without hurting sensitivity.
Each stage in the signal chain adds noise. The Friis formula shows that the first stage dominates the total noise figure — which is why a low-noise preamplifier at the antenna makes such a large difference.
View LargerNoise Factor and Noise Figure Defined
Start with the concept of signal-to-noise ratio (SNR). At the input to any two-port device (an amplifier, filter, mixer, attenuator), there is a signal and there is noise. The ratio of signal power to noise power at the input is SNRin. At the output of the device, both the signal and noise have been processed — typically amplified. But if the device adds its own internal noise, the noise at the output is larger than just the amplified input noise. The result is that SNRout is worse (smaller) than SNRin.
The noise factor F is defined as the ratio of how much the SNR degrades:
F is always ≥ 1 (because SNR can only stay the same or get worse).
A perfect noiseless device has F = 1 (SNR is unchanged).
F is measured under the standard conditions of T0 = 290 K input source temperature.
Noise figure NF is simply the noise factor expressed in decibels:
Equivalently: F = 10NF/10
A perfect noiseless device has NF = 0 dB. Every real device has NF > 0 dB. Common values in amateur radio equipment:
| Device | Typical NF | Noise Factor F |
|---|---|---|
| 1 dB NF LNA (excellent VHF preamp) | 1 dB | 1.26 |
| 2 dB NF LNA (good HF preamp) | 2 dB | 1.58 |
| 3 dB NF preamplifier (typical) | 3 dB | 2.00 |
| 6 dB NF (moderate HF receiver) | 6 dB | 4.00 |
| 10 dB NF (typical HF receiver front end) | 10 dB | 10.0 |
| 15 dB NF (typical SDR dongle without LNA) | 15 dB | 31.6 |
| 3 dB attenuator (passive loss = 3 dB NF) | 3 dB | 2.00 |
| 10 dB attenuator | 10 dB | 10.0 |
Noise Figure and Noise Temperature
There is a direct relationship between noise figure and noise temperature that is very useful for understanding what a noise figure specification actually means physically. The equivalent noise temperature Te of a device is the temperature of a resistor placed at the device's input that would produce the same additional noise as the device itself:
where T0 = 290 K
Or equivalently: Te = (10NF/10 − 1) × 290 K
Noise temperature is particularly useful at low noise figures where dB differences become misleading. A difference from 0.5 dB to 1.0 dB NF sounds small, but:
- At 0.5 dB NF: Te = (1.122 − 1) × 290 = 35 K
- At 1.0 dB NF: Te = (1.259 − 1) × 290 = 75 K
The noise temperature doubles. For weak-signal work on VHF/UHF where you are competing with sky noise temperatures of 30–100 K, that difference matters enormously. This is why serious EME operators obsess over fraction-of-a-dB improvements in preamplifier noise figure.
Worked Examples
Example 1: Converting Noise Factor to Noise Figure
NF = 10 × log10(F)
NF = 10 × log10(1.58)
NF = 10 × 0.199
NF = 2.0 dB
Example 2: Converting Noise Figure to Noise Temperature
F = 106/10 = 100.6 = 3.98
Te = (F − 1) × 290
Te = (3.98 − 1) × 290
Te = 2.98 × 290
Te = 864 K
This means the receiver adds noise equivalent to a 864 K resistor at its input — three times hotter than room temperature. For HF work where external noise dominates, this is acceptable. For VHF EME where sky noise is 30 K, it is terrible.
Noise Figure Calculator
Noise Figure ↔ Noise Factor ↔ Noise Temperature
Enter any one value and calculate the other two. Noise temperature uses T₀ = 290 K.
The Friis Formula for Cascaded Stages
Real receivers are not a single stage — they are a chain of stages: perhaps a bandpass filter, a preamplifier, more filtering, a mixer, an IF amplifier, and more. Each stage adds noise. The Friis formula (developed by Harald T. Friis at Bell Labs in 1944) gives the total noise factor of a cascaded chain.
Ftotal = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1×G2) + (F4 − 1)/(G1×G2×G3) + ...
Where:
Fn = noise factor of stage n (linear, not dB)
Gn = power gain of stage n (linear, not dB — a 10 dB gain stage has G = 10)
The most important insight from the Friis formula is that the first stage dominates the total noise figure. The noise contribution of each subsequent stage is divided by the cumulative gain of all the preceding stages. A second stage with gain G1 = 100 (20 dB) before it contributes only 1/100 as much noise as it would if it were first. This is why:
- The LNA (low-noise amplifier) at the antenna input is the most critical component for receiver sensitivity
- Feedline loss before the first active stage is doubly damaging — it attenuates the signal AND adds noise with a gain of less than 1
- A high-gain, low-noise preamplifier placed before a lossy cable makes the cable's noise contribution negligible
Worked Example: Three-Stage Receive Chain
LNA: Gain = 20 dB (G = 100), NF = 2 dB (F = 1.585)
RG-8X, 50 ft at 14 MHz: Loss = 1.5 dB, so gain G = 0.708 (less than 1), NF = 1.5 dB (F = 1.413)
Receiver: NF = 10 dB (F = 10.0)
Applying the Friis formula:
Ftotal = FLNA + (Fcable − 1)/GLNA + (Frcvr − 1)/(GLNA × Gcable)
Ftotal = 1.585 + (1.413 − 1)/100 + (10.0 − 1)/(100 × 0.708)
Ftotal = 1.585 + 0.00413 + 9.0/70.8
Ftotal = 1.585 + 0.00413 + 0.127
Ftotal = 1.716
NFtotal = 10 × log10(1.716) = 2.35 dB
Without the LNA:
Ftotal = Fcable + (Frcvr − 1)/Gcable
Ftotal = 1.413 + (10.0 − 1)/0.708 = 1.413 + 12.71 = 14.12
NFtotal = 10 × log10(14.12) = 11.5 dB
Conclusion: Adding the 2 dB NF LNA at the tower reduces the system noise figure from 11.5 dB to 2.35 dB — a 9.2 dB improvement in sensitivity.
Cascaded Noise Figure Calculator (Friis Formula)
Cascaded Noise Figure — Up to 4 Stages
Enter NF and gain for each stage in dB. Leave unused stages blank. Stages are numbered in signal flow order (Stage 1 is first in the chain).
Noise Figure in Practice
A few practical rules flow directly from the Friis formula and noise figure theory:
The First Stage Is Everything
The Friis formula makes it clear that the first stage in the signal chain determines system noise figure almost entirely, provided that stage has sufficient gain. If the first stage is a 20 dB, 2 dB NF preamplifier, the system NF will be approximately 2 dB no matter what comes after it. If the first stage is 3 dB of feedline loss, the system NF starts at 3 dB before the first amplifier even contributes.
When Noise Figure Matters on HF
On frequencies below about 20 MHz, external noise arriving at the antenna (atmospheric noise, galactic noise, man-made noise) is often much greater than the receiver's internal noise floor. In this situation, improving the receiver noise figure from 10 dB to 5 dB makes essentially no difference — the antenna is already delivering far more noise than the receiver's internal noise. Noise figure matters most on VHF and above where the external noise environment is quiet and the receiver's own noise is the limiting factor.
SDR Dongles and Their Limitations
Inexpensive RTL-SDR dongles typically have noise figures of 15–20 dB. By adding a quality LNA (1–3 dB NF, 20 dB gain) at the antenna, the system noise figure improves to approximately 2–4 dB — a dramatic improvement that makes the SDR perform like a much more expensive receiver for weak-signal work. This is exactly what the Friis formula predicts: the high-gain, low-noise first stage overwhelms the dongle's own noise contribution.
Effect of Attenuators and Feedline on Noise Figure
A passive attenuator at room temperature has a noise figure exactly equal to its loss. A 10 dB attenuator has a noise figure of 10 dB (F = 10). This is true whether the "attenuator" is a deliberate pad, a length of lossy cable, or a lossy filter. The attenuator absorbs some of the signal, and in place of what it absorbed it generates thermal noise from its own resistive elements. The result is that the SNR degrades by exactly the amount of the loss.
This has a critical implication: any loss before the first amplifier directly adds to the system noise figure, decibel for decibel. A bandpass filter at the antenna input with 2 dB of insertion loss adds 2 dB to the system noise figure. A connector with 0.5 dB of loss adds 0.5 dB to system noise figure. Every decibel of loss ahead of the LNA costs a decibel of sensitivity.
The Friis formula applied to a typical station receive chain. The first-stage contribution dominates; each subsequent stage contributes only 1/Gpreceding as much noise as it would if placed first.
View LargerFrequently Asked Questions
Can noise figure ever be less than 0 dB?
No. A noise figure of 0 dB (noise factor F = 1) means the device is perfectly noiseless — it passes the signal through without adding any noise. This is a theoretical limit that no real device achieves. Real devices always add some noise, so NF is always greater than 0 dB in practice. Specifications claiming 0 dB NF are either theoretical or contain measurement error.
My SDR has a 15 dB NF but I can hear signals fine. Do I need a preamplifier?
It depends on the frequency and the external noise environment. On HF (below 20 MHz), external noise from atmospheric and man-made sources typically exceeds the SDR's internal noise, so the high NF is not the limiting factor. On VHF (144 MHz) and above, the external noise is much lower and the SDR's 15 dB NF significantly limits sensitivity. A good LNA before a 15 dB NF SDR on 2 meters can improve reception by 10–13 dB — the difference between hearing a signal and not hearing it.
Does connecting a preamplifier to a good receiver always improve reception?
Not always. If your station has significant external noise (common on HF in urban areas), adding a preamplifier only amplifies the noise along with the signal — no improvement. And if the preamplifier is overloaded by strong signals, it can degrade performance by generating intermodulation products (covered in lessons M19F and M19G). Preamplifiers are most beneficial on VHF and above with directional antennas, or on HF in very quiet rural locations with no strong nearby transmitters.
What is the difference between sensitivity and noise figure?
Noise figure is an intrinsic property of a device — it measures how much noise the device itself adds. Sensitivity is the complete system performance — the minimum signal power that produces a usable output. Sensitivity depends on noise figure, bandwidth, and the required SNR for the mode being used. A 3 dB NF receiver in a 2.4 kHz SSB bandwidth has a noise floor (minimum detectable signal) of about −137 dBm.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.