1. What is Johnson-Nyquist Noise?

Johnson-Nyquist noise (thermal noise) is the electronic noise generated by the thermal agitation of charge carriers inside an electrical conductor at equilibrium. It's a fundamental noise source in electronic circuits.

2. How Does the Calculator Work?

The calculator uses the Johnson-Nyquist noise equation:

Where:

• \( V_n \) — Noise voltage (V)
• \( k \) — Boltzmann constant (1.38 × 10^-23 J/K)
• \( T \) — Temperature (K)
• \( R \) — Resistance (Ω)
• \( \Delta f \) — Bandwidth (Hz)

Explanation: The equation shows that thermal noise power is proportional to temperature and bandwidth, and independent of resistance, while noise voltage is proportional to the square root of resistance.

3. Importance of Noise Calculation

Details: Understanding thermal noise is crucial for designing sensitive electronic equipment, communication systems, and scientific instruments where signal-to-noise ratio is important.

4. Using the Calculator

Tips: Enter temperature in Kelvin, resistance in ohms, and bandwidth in Hertz. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this noise depend on the material?
A: No, Johnson-Nyquist noise is independent of the material as long as it's a conductor. It depends only on resistance, temperature, and bandwidth.

Q2: How does temperature affect the noise?
A: Noise voltage increases with the square root of temperature. Doubling the temperature increases noise voltage by √2 (about 41%).

Q3: What's the noise power spectral density?
A: The power spectral density is 4kTR (V²/Hz) or simply kT (J) per hertz of bandwidth.

Q4: Can this noise be eliminated?
A: No, it's a fundamental physical limit. However, cooling components reduces thermal noise significantly.

Q5: How does this relate to the Nyquist theorem?
A: The same Harry Nyquist derived this noise formula while studying thermal agitation in conductors, related to his sampling theorem work.