Thermal (Johnson–Nyquist) noise of a resistor: How does the generated noise power depend on temperature?

Introduction / Context:
Every resistor generates random thermal noise due to the agitation of charge carriers. Understanding how this noise scales with temperature is essential for low-noise RF and instrumentation design.

Given Data / Assumptions:

• Resistor at thermodynamic equilibrium (no shot noise source).
• Thermal noise model (Johnson–Nyquist).
• Bandwidth B is considered when converting spectral density to total noise.

Concept / Approach:

Thermal noise power spectral density at the terminals of a matched resistor is kT per hertz. The mean-square noise voltage over bandwidth B is 4kTRB. Hence noise power and voltage grow linearly with absolute temperature T (in kelvin).

Step-by-Step Solution:

Verification / Alternative check:

Cooling a low-noise amplifier or front-end (e.g., cryogenic LNAs) reduces T and thus reduces noise floor proportionally.

Why Other Options Are Wrong:

• T^2: incorrect scaling; it is linear with T.
• Independent of T: contradicted by k*T dependence.
• Inversely proportional to T: opposite of true behavior.
• Depends only on DC bias: thermal noise exists without bias.

Common Pitfalls:

• Confusing noise voltage (proportional to sqrt(T)) with noise power (proportional to T).

Final Answer:

Directly proportional to absolute temperature (T)