Thermal Noise Calculator

Formula

The formula to calculate the Thermal Noise Power (Vn²) is:

\[ Vn² = 4 \cdot k \cdot T \cdot B \cdot R \]

Where:

\( Vn² \) is the thermal noise power in volts squared (V²).
\( k \) is the Boltzmann constant (1.380649e-23 J/K).
\( T \) is the absolute temperature in Kelvin (K).
\( B \) is the bandwidth in Hertz (Hz).
\( R \) is the resistor value in Ohms (Ω).

What is Thermal Noise?

Thermal noise, also known as Johnson-Nyquist noise, is the electronic noise generated by the thermal agitation of charge carriers (usually electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is a fundamental limitation in the sensitivity of electronic equipment and is directly proportional to the temperature and bandwidth of the system.

Example Calculation

Consider an example where:

Absolute Temperature (T): 300 K
Bandwidth (B): 1000 Hz
Resistor Value (R): 100 Ω

Using the formula to calculate the Thermal Noise Power:

\[ Vn² = 4 \cdot 1.380649e-23 \cdot 300 \cdot 1000 \cdot 100 \approx 1.65678e-15 \text{ V²} \]

This means that the thermal noise power for this example is approximately \(1.65678 \times 10^{-15}\) V².