Table of Contents
What Is Thermal Noise?
Thermal noise (Johnson-Nyquist noise) is the electronic noise generated by the random thermal motion of charge carriers inside a resistor, regardless of any applied voltage. First measured by John B. Johnson in 1926 and theoretically explained by Harry Nyquist in 1928, it sets a fundamental lower limit on the noise in electronic circuits.
Thermal noise is white noise -- it has a flat power spectral density across all frequencies up to quantum limits. It is present in every resistor and cannot be eliminated, only minimized by reducing resistance, temperature, or bandwidth. It is the dominant noise source in many precision measurement and communication systems.
Johnson-Nyquist Formulas
Noise Levels by Resistance
| Resistance | Vn (10kHz BW, 300K) | Application |
|---|---|---|
| 50 Ω | 90 nV | RF systems |
| 1 kΩ | 405 nV | Audio preamps |
| 10 kΩ | 1.28 μV | Sensor interfaces |
| 1 MΩ | 12.8 μV | High-impedance circuits |
Low-Noise Design
- Minimize resistance: Noise voltage scales with sqrt(R).
- Limit bandwidth: Only measure the bandwidth you need.
- Cool components: Cryogenic cooling at 77K reduces noise by factor of 2 vs room temperature.
- Use metal film resistors: Lower excess noise than carbon composition types.
Frequently Asked Questions
Does thermal noise depend on resistor type?
The Johnson-Nyquist thermal noise depends only on resistance, temperature, and bandwidth -- it is the same for all resistor types. However, resistors also generate excess noise (1/f noise) when current flows, and this does depend on construction. Carbon composition resistors have the highest excess noise; metal film and wirewound have the lowest.
How do resistors in series affect noise?
Noise voltages from uncorrelated sources add in quadrature (root sum of squares). For n identical resistors in series, the total resistance is nR and the noise is sqrt(n) times the single resistor noise. You can also calculate noise for the total series resistance directly.
What is the noise floor of a 50-ohm system?
At room temperature with 1 Hz bandwidth, a 50-ohm resistor generates about 0.9 nV of noise. The thermal noise power in a 50-ohm system is -174 dBm/Hz, which is the fundamental noise floor reference used in RF engineering.