Resistor Noise Calculator

Thermal noise voltage is driven by random electronic motion governed by thermodynamic principles. The primary equation used to compute the root-mean-square (RMS) noise voltage ($v_n$) is derived from the fluctuation-dissipation theorem:

noise = 2 * (resistance * temperature * 1.380649e-23 * bandwidth) ^ 0.5

Where resistance is measured in ohms ($\Omega$), temperature is in Kelvin (K), bandwidth is in Hertz (Hz), and $1.380649 \times 10^{-23}$ J/K is the Boltzmann constant. Additionally, the calculator translates this RMS voltage into decibel units relative to reference standards: noise level in dBu (noise_Lu = 20 * log10(noise / 0.774596670)) and noise level relative to one volt (noise_Lv = 20 * log10(noise)).

Imagine you are designing a front-end amplifier stage using a high-value feedback resistor. Let us run a calculation with the following parameters:

• Resistance ($R$): $10,000\ \Omega$ ($10\text{ k}\Omega$)
• Temperature ($T$): $293.15\text{ K}$ (approx. $20\,^{\circ}\text{C}$)
• Bandwidth ($B$): $20,000\text{ Hz}$ ($20\text{ kHz}$, standard audio range)
• Boltzmann Constant ($k$): $1.380649 \times 10^{-23}\text{ J/K}$

Step 1: Multiply the variables together inside the radical: $10000 \times 293.15 \times 1.380649 \times 10^{-23} \times 20000 = 8.125\times 10^{-14}$.
Step 2: Multiply by $4$ (represented as squaring the factor $2$ outside the root): $4 \times 8.125\times 10^{-14} = 3.25\times 10^{-13}$.
Step 3: Take the square root to find the RMS noise voltage: $\sqrt{3.25\times 10^{-13}} \approx 5.70\times 10^{-7}\text{ V}$, or $0.57\text{ }\mu\text{V}$.
Step 4: Convert this voltage into logarithmic decibel formats such as dBu and dBV for audio system integration.

Minimizing thermal noise requires careful component selection. First, keep operating temperatures low; enclosing sensitive analog stages away from high-heat power supplies significantly reduces thermal agitation. Second, use lower resistance values where circuit topology allows, because thermal noise scales proportionally with the square root of resistance. Finally, limit unnecessary system bandwidth using low-pass filters to prevent high-frequency noise from corrupting your signal.