Noise Figure

Noise Figure (NF) is the standard measure of how much a two-port network, such as an amplifier or mixer, degrades the signal-to-noise ratio of a signal passing through it. While SNR tells us the quality at a given point, noise figure tells us how much worse the quality becomes due to the device itself.

For GATE aspirants, noise figure is one of the most tested topics in RF and communication systems. It connects directly to system sensitivity, amplifier noise performance, and the Friis formula for cascaded stages.

Core Concept Explanation

Every real amplifier or receiver component introduces noise in addition to amplifying the input signal and its accompanying noise. The noise figure F is defined as the ratio of input SNR to output SNR when the input is driven by a source at the standard temperature T0 = 290 K.

Because every real device adds noise, SNRo is always less than or equal to SNRi, so F is always greater than or equal to 1. An ideal noiseless device would have F = 1, meaning 0 dB noise figure. In practice, low-noise amplifiers (LNAs) used at the front end of receivers typically have noise figures of 0.5 dB to 3 dB.

The specification of a standard input temperature T0 = 290 K is important. Noise figure is only defined under this condition because the amount of noise added by the device relative to the input noise depends on the input noise level. Changing the source temperature changes the SNR ratio, so T0 must be fixed for comparison.

Mathematical Expression

The noise factor F (linear) is defined as: F = SNRi / SNRo. The noise figure NF in decibels is: NF = 10 log10(F). Expanding the definition using input and output powers: F = (Si/Ni) / (So/No).

For an amplifier with gain G, So = G x Si, and the output noise No = G x Ni + Na, where Na is the amplifier's own added noise referred to input. Therefore: F = (G x Ni + Na) / (G x Ni) = 1 + Na/(G x Ni). This shows that F depends on how much additional noise Na the amplifier adds compared to the amplified input noise G x Ni.

An alternative and equivalent definition uses equivalent noise temperature Te: the device is modeled as noiseless with an equivalent input noise source at temperature Te. The relationship is: F = 1 + Te/T0, or equivalently Te = (F - 1) x T0. For T0 = 290 K, a noise figure of 1 dB (F = 1.26) gives Te = 0.26 x 290 = 75.4 K.

Practical Understanding

In receiver design, the noise figure of the first stage dominates the overall system noise figure. This is why the LNA in a satellite receiver or radio telescope is designed for the lowest possible noise figure, often using cooled amplifiers. The Friis formula (covered separately) formalizes this dominance.

Noise temperature Te is more convenient when the operating temperature differs significantly from T0 = 290 K, such as in satellite communication, where sky noise temperatures can be as low as 10 to 50 K. In such cases, expressing noise as a temperature Te allows direct addition of source temperature and amplifier noise temperature to find total system noise.

Given:
Amplifier noise figure NF = 3 dB, standard temperature T0 = 290 K

Why this formula applies:
Equivalent noise temperature Te relates to noise factor F by Te = (F-1) x T0

Formula:
F = 10^(NF/10)
Te = (F - 1) x T0

Substitution:
F = 10^(3/10) = 10^0.3 = 2
Te = (2 - 1) x 290

Calculation:
Te = 1 x 290 = 290 K

Final Answer with units:
Te = 290 K (a 3 dB NF amplifier adds noise equivalent to a 290 K source)

Exam Tip: Memorize the key pair: NF = 3 dB means F = 2 and Te = 290 K. Also, NF = 0 dB means F = 1 and Te = 0 K (ideal noiseless). These two anchor points solve many GATE substitution problems quickly.

Key Relationships Summary

• Noise factor F = SNRi / SNRo, always greater than or equal to 1 for real devices.
• Noise figure NF (dB) = 10 log10(F). NF = 0 dB means ideal noiseless device.
• Equivalent noise temperature Te = (F - 1) x T0, where T0 = 290 K.
• For F = 2 (NF = 3 dB): Te = 290 K. For F = 1.26 (NF = 1 dB): Te = 75 K.
• Te is preferred in satellite and space systems where ambient temperatures differ from 290 K.

Quick Revision

• Noise figure F = SNRi/SNRo, measured with source at T0 = 290 K.
• NF(dB) = 10 log10(F). F is always greater than or equal to 1.
• Equivalent noise temperature Te = (F-1) x 290 K.
• NF = 3 dB is the anchor point: F = 2, Te = 290 K.
• Noise figure definition requires input source at standard temperature T0 = 290 K.
• Exam trap: Noise figure is not simply the dB of added noise power — it is the ratio of input to output SNR.
• First-stage NF dominates overall receiver noise figure — motivates LNA placement at receiver front end.