Noise Figure (NF)

Noise Figure (NF) quantifies how much an electronic device degrades the signal-to-noise ratio (SNR) compared to an ideal, noise-free system. It is expressed in decibels (dB) and is a key parameter in evaluating the sensitivity and performance of RF and microwave components.

Noise Factor and Noise Figure

• The Noise Factor (F) is the linear ratio of input SNR to output SNR:

  F = (Sᵢ/Nᵢ) / (Sₒ/Nₒ)

• The Noise Figure (NF) is the noise factor expressed in logarithmic form:

  NF = 10 log₁₀(F)

where:

• Sᵢ: Input signal power

• Nᵢ: Input noise power

• Sₒ: Output signal power

• Nₒ: Output noise power

Example

If a receiver has:

• Input SNR = 20 dB

• Output SNR = 15 dB

Then:

• F = 10^((20 − 15)/10) = 3.16

• NF = 10 log₁₀(3.16) ≈ 5 dB

Measurement Methods

Noise Figure is typically measured using:

• Y-Factor Method: Based on a known excess noise ratio (ENR) from a calibrated noise source

• Gain Method: Derived from gain and output noise power measurements

Cascaded System Noise Figure

In multi-stage systems, the overall noise factor is calculated using the Friis formula:

F_total = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁G₂) + …

where:

• F₁, F₂, F₃: Noise factors of individual stages

• G₁, G₂: Linear gains of preceding stages

This emphasizes the importance of low-noise components in early stages of the signal chain.

Applications

• Wireless and satellite communications: Determines receiver sensitivity

• Microwave engineering: Critical in low-noise amplifier (LNA) design

• Radar systems: Helps detect weak reflected signals

• Radio astronomy: Enables observation of low-level cosmic signals

• Electronic instrumentation: Characterizes internal noise behavior of measurement equipment