Resistor Noise Calculator
Calculate thermal noise voltage, current, and power in resistors with temperature and bandwidth analysis
Resistor Parameters
Resistance value of the noisy resistor
Operating temperature of the resistor
Frequency bandwidth of interest
Thermal Noise Results
Johnson-Nyquist Formula: V_n = √(4kTRΔf)
Parameters: k = 1.381e-23 J/K, T = 298.15 K
Bandwidth: Δf = 1.000e+3 Hz, R = 1.000e+4 Ω
Temperature vs Noise Analysis
| Temperature (°C) | Temperature (K) | Noise Voltage | Relative to 25°C |
|---|---|---|---|
| -40°C | 233.15 K | 358.830 nV | 0.0% |
| 0°C | 273.15 K | 388.394 nV | 0.0% |
| 20°C | 293.15 K | 402.362 nV | 0.0% |
| 40°C | 313.15 K | 415.861 nV | 0.0% |
| 80°C | 353.15 K | 441.623 nV | 0.0% |
Higher temperatures increase thermal agitation and noise voltage proportionally to √T
Bandwidth vs Noise Analysis
| Bandwidth (Hz) | Noise Voltage | √Bandwidth Factor |
|---|---|---|
| 1.0e+2 Hz | 128.318 nV | 0.32× |
| 1.0e+3 Hz | 405.779 nV | 1.00× |
| 1.0e+4 Hz | 1.283 μV | 3.16× |
| 1.0e+5 Hz | 4.058 μV | 10.00× |
| 1.0e+6 Hz | 12.832 μV | 31.62× |
Noise voltage increases proportionally to √(bandwidth). Wider bandwidth captures more noise.
Types of Resistor Noise
Thermal Noise
Johnson-Nyquist noise from electron motion
Frequency-independent, temperature-dependent
Current Noise
1/f noise from material imperfections
Low-frequency, inversely proportional to frequency
Shot Noise
Quantum nature of current flow
DC current dependent, white noise spectrum
Physical Constants
Low Noise Design Tips
Use metal film or thin film resistors
Minimize bandwidth to reduce noise
Keep resistors at low temperatures
Use lower resistance values when possible
Avoid carbon composition resistors
Consider wire-wound for ultra-low noise
Understanding Resistor Thermal Noise
What is Thermal Noise?
Thermal noise, also known as Johnson-Nyquist noise, is the electronic noise generated by the thermal agitation of electrons in an electrical conductor at thermal equilibrium. This fundamental noise source is present in all resistive elements and sets the ultimate limit for noise performance in electronic circuits.
Key Characteristics
- •White noise spectrum (frequency-independent)
- •Gaussian amplitude distribution
- •Proportional to √(temperature)
- •Proportional to √(resistance)
- •Proportional to √(bandwidth)
Mathematical Formulas
Voltage Noise:
V_n = √(4kTRΔf)
e_n = √(4kTR) [V/√Hz]
Current Noise:
I_n = √(4kTΔf/R)
i_n = √(4kT/R) [A/√Hz]
Power Noise:
P_n = kTΔf
Practical Applications
- •Low-noise amplifier design
- •Precision measurement systems
- •RF circuit noise budget analysis
- •Signal-to-noise ratio optimization
- •Thermal noise floor determination