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What is Noise figure (NF)?

A measure of how much a circuit such as an amplifier or receiver degrades the signal-to-noise ratio (S/N) through its own noise. The input S/N divided by the output S/N (the noise factor), expressed in dB, is called the noise figure (NF). It is defined with thermal noise at 290 K as the reference. The value for cascaded circuits is found with Friis's formula and is set mainly by the first stage's noise figure and gain.

Japanese name: 雑音指数(NF)

Noise figure (NF) appears in 3 practice questions across 1 topic, including Wireless Communication Basics.

Field: Wireless Communication Basics

Definition and noise temperature

The noise factor F is the input S/N divided by the output S/N, defined with the input noise being thermal noise at 290 K. An ideal noiseless circuit has F = 1 (0 dB), and NF = 10·log₁₀ F. The same performance can be expressed as the circuit's noise referred to the input as a temperature; the equivalent noise temperature is Te = 290 × (F − 1) K. For example, an NF of 1 dB corresponds to about 75 K and 3 dB to about 290 K, and noise temperature is often used in the low-noise regime, such as satellite communication receivers.

Friis's formula

When a circuit with noise factor F1 and gain G1 is followed by circuits with noise factor F2 and gain G2, and F3, the overall noise factor is F = F1 + (F2 − 1)/G1 + (F3 − 1)/(G1·G2) + … (all linear). Noise from later stages is divided by the gain before them, so it is important to place an LNA with a low noise figure and high gain at the first stage. Conversely, the loss (L dB) of a cable or filter between the antenna and the LNA worsens the noise figure directly by that amount.

Relation to semiconductor devices

An LNA's noise figure is set by the transistor's thermal noise, shot noise, gate or base resistance and similar factors. For applications requiring especially low noise figures at high frequencies, GaAs and InP HEMTs, with their high electron mobility, have been used. Meanwhile, scaled CMOS LNAs have come to deliver sufficient performance for mobile phones and wireless LANs up to several GHz and are integrated in transceivers.

Try it: questions about Noise figure (NF)

An LNA with a noise figure of 1.5 dB and a gain of 15 dB is placed at the first stage of a receiver, followed by a circuit with a noise figure of 10 dB. Which is closest to the noise figure of the two stages together?

  1. A1.5 dB
  2. B2.3 dB
  3. C11.5 dB
Show answer and explanation

Answer: B. 2.3 dB

The noise figure of cascaded circuits is found with Friis's formula F = F1 + (F2 − 1)/G1, using linear values for F (noise figure) and G (gain). F1 = 10^0.15 ≈ 1.41, F2 = 10 and G1 = 10^1.5 ≈ 31.6, so F ≈ 1.41 + 9/31.6 ≈ 1.70, which is 10·log₁₀(1.70) ≈ 2.3 dB. The noise of later stages is divided by the first stage's gain, so the larger that gain, the smaller their effect. For this reason, a receiver's noise performance is set mainly by the first-stage LNA.

Take the thermal noise power density at 290 K as −174 dBm/Hz. For a receiver with a bandwidth of 1 MHz and a noise figure of 6 dB that needs an S/N of 10 dB to demodulate, which is closest to the receiver sensitivity (the minimum signal power that can be received)?

  1. A−114 dBm
  2. B−108 dBm
  3. C−98 dBm
Show answer and explanation

Answer: C. −98 dBm

The thermal noise power in a 1 MHz bandwidth is −174 + 10·log₁₀(10⁶) = −174 + 60 = −114 dBm. Treating the receiver's noise figure as increasing the noise by that amount, the input-referred noise power is −114 + 6 = −108 dBm. A signal 10 dB above that is needed for the required S/N, so the sensitivity is −108 + 10 = −98 dBm. Narrowing the bandwidth or lowering the noise figure or required S/N improves (lowers) the sensitivity.

FAQ

What does a noise figure of 3 dB mean?

It means that passing through the circuit worsens S/N by 3 dB (about half). Referred to the input, the circuit adds noise equal to the input thermal noise. Lowering a receiver's noise figure by 3 dB improves its sensitivity by 3 dB.

Do the losses of mixers and filters also affect the noise figure?

Yes. A matched passive loss (a filter or cable) has a noise figure roughly equal to its loss in dB. Placed before the LNA, that loss adds directly to the overall noise figure. Placed after the LNA, it is divided by the LNA's gain according to Friis's formula, and its effect is small.

Noise figure (NF) in the explanations

Questions that mention Noise figure (NF) (3)

  1. An LNA with a noise figure of 1.5 dB and a gain of 15 dB is placed at the first stage of a receiver, followed by a circuit with a noise figure of 10 dB. Which is closest to the noise figure of the two stages together?
  2. Take the thermal noise power density at 290 K as −174 dBm/Hz. For a receiver with a bandwidth of 1 MHz and a noise figure of 6 dB that needs an S/N of 10 dB to demodulate, which is closest to the receiver sensitivity (the minimum signal power that can be received)?
  3. In a radio receiver, which circuit is placed right after the antenna and amplifies the weak received signal while adding as little of its own noise as possible?

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Related terms

Thermal noise (Johnson noise) Beamforming Bluetooth Low Energy (BLE) Direct-conversion receiver Fading Free-space path loss (FSPL) Hidden node problem Link budget LPWA (low-power wide-area) MIMO (multiple-input multiple-output)

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