Thermal Noise Power and Voltage Calculator: Formulas and Explanation

Thermal noise power and thermal voltage are key concepts in electrical and electronic engineering with significant practical applications. Understanding these parameters is crucial for:

• Assessing noise levels in systems to maintain a high Signal-to-Noise Ratio (SNR).
• Designing receivers and communication channels in wireless communication systems.
• Designing RF and microwave devices or components, where thermal noise is a significant factor.

Thermal Noise Power (KTB)

Thermal noise power is the random noise generated by the thermal motion of electrons within a conductor. It’s also known as Johnson-Nyquist noise.

The formula for calculating thermal noise power is:

P = K *T * B

Where:

• P = Thermal noise power
• K = Boltzmann’s constant (1.38 x 10^-23 J/K)
• T = Temperature in Kelvin
• B = Bandwidth in Hertz

Thermal Noise Power Calculator

To calculate thermal noise power, simply provide the temperature (T) in Kelvin and the bandwidth (B) in Hertz. The calculator will then output the thermal noise power. Boltzmann’s constant (K) is already pre-loaded into the calculations.

Example:

• Input: T = 300 Kelvin, BW = 1000 Hz
• Output: Thermal Noise power = -143.82 dBm

Note: To convert Celsius to Kelvin, use the formula: Temperature (Kelvin) = Temperature (Celsius) + 273.16

Thermal Noise Voltage

Thermal noise voltage is the voltage noise generated by the thermal motion of electrons in a resistor. It is also known as thermal noise voltage. By measuring the thermal noise voltage across a resistor, it’s possible to indirectly measure the temperature.

The formula for calculating thermal noise voltage is:

V_{thermal noise voltage} = √(4 * R * k T _ B)

Where:

• V_{thermal noise voltage} = Thermal noise voltage
• R = Resistance in Ohms
• K = Boltzmann’s constant (1.38 x 10^-23 J/K)
• T = Temperature in Kelvin
• B = Bandwidth in Hertz

Thermal Voltage Calculator

To calculate thermal voltage, provide the resistance of the resistor (R) in Ohms, the temperature (T) in Kelvin, and the bandwidth (B) in Hertz. The calculator will output the thermal noise voltage. Boltzmann’s constant (K) is already used in the calculations.

Example:

• Input: T = 291 Kelvin, Resistance = 50 Ohms, BW = 1 Hz
• Output: Noise voltage = 8.964e-10 volt or 0.0008964 µV

Note: Temperature (Kelvin) = Temperature (Celsius) + 273.16

Conclusion

Thermal noise power and thermal voltage formulas and calculators offer a precise way to quantify the electrical noise inherent in electronic circuits. By understanding the relationships between temperature, bandwidth, and resistance in noise generation, these tools empower engineers and technicians in various fields, from communication systems design to quantum electronics, to effectively manage and mitigate noise.