Resistor Noise Calculator

Resistance (R):

Temperature (T):

Bandwidth (ΔF):

Resistor Noise (E):

Noise Level (Lu):

Noise Level (Lv):

1. What is a Resistor Noise Calculator?

Definition: This calculator computes the thermal noise voltage (E), noise level (Lu), and noise level (Lv) generated by a resistor due to the thermal agitation of electrons.

Purpose: It is used in electronics to evaluate the noise performance of resistors in circuits, crucial for low-noise amplifier design and signal integrity.

2. How Does the Calculator Work?

The calculator uses the following equations:

\( E = \sqrt{4 \cdot R \cdot k \cdot T \cdot \Delta F} \)
\( L_u = 20 \cdot \log_{10} \left( \frac{E}{0.77459667} \right) \)
\( L_v = 20 \cdot \log_{10} \left( \frac{E}{1} \right) \)

Where:

\( E \) is the RMS noise voltage (V)
\( R \) is the resistance (Ω)
\( k \) is Boltzmann’s constant (\( 1.380649 \times 10^{-23} \, \text{J/K} \))
\( T \) is the temperature (K)
\( \Delta F \) is the bandwidth (Hz)
\( L_u \) and \( L_v \) are noise levels in dB with reference voltages 0.77459667 V and 1 V, respectively

Steps:

Enter resistance (R), temperature (T), and bandwidth (ΔF)
Convert inputs to base units (Ω, K, Hz)
Calculate \( E \), \( L_u \), and \( L_v \) using the formulas
Display \( E \) in nV, µV, mV, or V based on magnitude

3. Importance of Resistor Noise Calculation

Thermal noise sets the baseline noise floor in electronic circuits, affecting the signal-to-noise ratio and limiting the sensitivity of amplifiers and receivers.

4. Using the Calculator

Examples:

For \( R = 20 \, \text{kΩ} \), \( T = 20 \, \text{°C} \), \( \Delta F = 1 \, \text{kHz} \):
- \( E = 569.15515 \, \text{nV} \)
- \( L_u = -62.33658 \, \text{dB} \)
- \( L_v = -64.89631 \, \text{dB} \)
For \( R = 1 \, \text{MΩ} \), \( T = 25 \, \text{°C} \), \( \Delta F = 1 \, \text{MHz} \):
- \( E = 128.30078 \, \text{µV} \)
- \( L_u = -15.61304 \, \text{dB} \)
- \( L_v = -17.83849 \, \text{dB} \)

5. Frequently Asked Questions (FAQ)

Q: What is thermal noise?
A: Thermal noise, or Johnson-Nyquist noise, is the random voltage generated by electron movement in a resistor due to temperature, independent of applied voltage.

Q: Why are Lu and Lv different?
A: They use different reference voltages (0.77459667 V for Lu, 1 V for Lv), reflecting different standards for noise measurement.

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