Resistor Thermal Noise (Johnson–Nyquist)

Formula

Description

Johnson–Nyquist noise is the thermal noise voltage generated by any resistor due to random thermal motion of charge carriers. It is a fundamental physical limit that cannot be eliminated by better manufacturing. The noise is white (flat across frequency) and sets the noise floor in precision analog circuits. At room temperature (25 °C), a 1 kΩ resistor generates about 4 nV/√Hz. This noise is critical in low-noise amplifier design, sensor front-ends, and audio preamplifiers.

Variables

• Vn — RMS noise voltage (V)
• T — Temperature (°C, converted to Kelvin internally)
• R — Resistance (Ω)
• BW — Measurement bandwidth (Hz)

Practical Notes

k = 1.380649 × 10⁻²³ J/K (Boltzmann constant). Temperature is entered in °C and internally converted to Kelvin (T_K = T_°C + 273.15). To minimize noise, use the lowest resistance that meets circuit requirements, reduce bandwidth with filtering, and cool the circuit if necessary. Metal-film resistors have lower excess noise (current noise) than carbon resistors, but thermal noise is identical for all resistor types at the same resistance.