Thermal Noise

Thermal noise arises from the random motion of electrons inside any resistive component above absolute zero. A simple 50 ohm resistor generates measurable noise power at room temperature.

Core Concept

Heat causes electrons inside conductors to jiggle randomly in all directions. This microscopic movement creates tiny, random voltage fluctuations. We officially call this Johnson-Nyquist noise or thermal noise.

This fundamental noise appears in absolutely every passive resistor. It has a completely flat power spectral density across all typical radio and audio frequencies used in engineering.

Engineers cleanly model this physical reality as an ideal noiseless resistor in series with a voltage source. This lets them use standard circuit analysis laws to calculate total noise.

Key Equations

RMS Noise Voltage: Vn = √(4 * k * T * R * B)

Maximum Available Power: Pn = k * T * B

Here, k is Boltzmann's constant (1.38e-23 J/K). The temperature T must be in Kelvin, often 300K for room temperature. The resistance R is in ohms.

Given:
Resistance R = 50 ohms
Temperature T = 300 K
Bandwidth B = 1 MHz
Boltzmann k = 1.38e-23 J/K

Why this formula:
Calculate the RMS open-circuit noise voltage for a standard RF resistor.

Formula:
Vn = √(4 * k * T * R * B)

Substitution:
Vn = √(4 * 1.38e-23 * 300 * 50 * 1e6)

Calculation:
Vn = √(8.28e-13)

Final Answer:
The RMS thermal noise voltage is 0.91 uV.

Exam Tip: Thermal noise power depends only on absolute temperature and bandwidth. The resistance value determines the actual noise voltage, but absolutely never the available noise power.

Key Properties

• Considered entirely white noise because its power density is flat across the spectrum.
• Increases directly with the square root of both temperature and resistance.
• Purely reactive components like ideal capacitors and inductors generate zero thermal noise.
• Limits the ultimate sensitivity of deep space receivers and radar systems.
• Engineers cool LNA amplifiers with liquid nitrogen to physically reduce this noise.

Quick Revision

• Thermal noise is also called Johnson noise.
• It requires absolute temperatures above zero Kelvin.
• Noise power is completely independent of resistance.
• Noise voltage scales with resistance.
• Capacitors only filter noise, they never generate it.
• Exam trap: Trying to calculate noise power using resistance instead of just kT.