Noise in RF Systems

Noise ultimately limits the sensitivity of any RF receiver. Understanding noise sources, how they combine in a cascaded system, and how to minimise their contribution is fundamental to receiver design.

Thermal (Johnson-Nyquist) Noise

Any resistor at temperature T generates noise power due to thermal agitation of electrons. The available noise power in bandwidth B is:

\(P_n = kTB\)

At room temperature (290 K): \(kT = -174\) dBm/Hz. This is the noise floor of any passive system at room temperature.

Noise Figure

Noise Figure (NF) is the degradation of SNR through a component, referenced to a 290 K source:

Noise figure quantifies how much a device degrades SNR. A 3 dB NF device adds as much noise as a matched resistor at 290 K.

\(NF = SNR_{in} - SNR_{out}\) (dB)

A perfect noiseless amplifier has NF = 0 dB. A 50 Ω resistive attenuator of X dB has NF = X dB.

Friis Formula for Cascaded Systems

Cascaded receiver chain. LNA noise figure dominates because later stages are divided by preceding gains.

\(F_{total} = F_1 + \dfrac{F_2-1}{G_1} + \dfrac{F_3-1}{G_1 G_2} + \cdots\)

The first stage dominates. This is why an LNA with low NF and high gain at the front of a receive chain is critical. Lossy elements (cables, switches) before the LNA directly add to system NF.

System Noise Temperature

Equivalent noise temperature \(T_e = (F-1) \times 290\) K. Useful for low-noise systems such as radio telescopes and satellite receivers where temperatures of a few kelvin are achieved.

🔧 Related Calculators

Noise Temp ↔ NF → Cascaded Noise Figure Calculator → Link Budget Calculator → dBm ↔ Watts Converter →