Calculation of Thermal Noise

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Thermal Noise (also known as Johnson-Nyquist noise) refers to the random fluctuations in electrical current or voltage that arise from the thermal motion of charge carriers (such as electrons) inside a conductor or resistor. These fluctuations are always present in any conductor at non-zero temperature and are a fundamental limit in many electrical systems, particularly in sensitive electronic devices.

The magnitude of thermal noise can be calculated using Johnson-Nyquist noise formula:

Formula for Thermal Noise Voltage:

The thermal noise voltage across a resistor Rat a temperature Tover a bandwidth Bis given by:

Where:

Vnoise = Noise voltage (in volts, V)
kB = Boltzmann constant = 1.38×10−23 J/K
T= Temperature (in Kelvin, K)
R= Resistance (in ohms, Ω)
B= Bandwidth (in Hz)

Formula for Thermal Noise Current:

Similarly, the thermal noise current Inoise through a resistor R is:

Where:

Inoise= Noise current (in amperes, A)

Example Calculation:

Let's calculate the thermal noise voltage for a resistor with the following conditions:

Resistance: R=1000 Ω(1 kΩ)
Temperature: T=300 K(room temperature)
Bandwidth: B=1 MHz=10⁶ Hz

Using the thermal noise voltage formula:

So, the thermal noise voltage for this resistor is approximately 1.29 μV.

Applications of Thermal Noise Calculation:

Electronic Devices: Understanding thermal noise is critical for designing sensitive amplifiers, receivers, and other electronic circuits where noise limits performance.
Communication Systems: In radio frequency and communication systems, thermal noise contributes to the overall noise floor, affecting signal-to-noise ratio (SNR).
Instrumentation: High-precision measurement systems need to account for thermal noise to ensure accurate readings.