Calculator Inputs
Choose a method, enter bandwidth and load, then calculate shot noise.
Formula Used
Shot noise arises from discrete charge carriers in a steady current. For an ideal Poisson process, the (white) current noise density is:
- Current noise density:
in = √(2·q·I·F)in A/√Hz - RMS noise current:
irms = in·√(Δfeff) - Voltage noise across load:
vrms = irms·RL
Here q is the electron charge (1.602176634×10⁻¹⁹ C),
I is the mean current, F is an optional excess noise factor,
and Δfeff is your effective noise bandwidth.
How to Use This Calculator
- Select a method: DC current, photodiode, or electron rate.
- Enter your current inputs for the selected method.
- Enter the bandwidth and (optional) bandwidth factor.
- Enter the load resistance to compute voltage and power noise.
- Press Calculate Shot Noise to view results above.
- Use Download CSV or Download PDF for reports.
Example Data Table
| Mean Current (I) | Bandwidth (Δf) | Load (RL) | Noise Current (irms) | Noise Voltage (vrms) |
|---|---|---|---|---|
| 1 mA | 10 kHz | 1 kΩ | ≈ 1.79 nA | ≈ 1.79 µV |
| 100 µA | 100 kHz | 10 kΩ | ≈ 5.66 nA | ≈ 56.6 µV |
| 10 µA | 1 MHz | 1 kΩ | ≈ 5.66 nA | ≈ 5.66 µV |
| 1 µA | 10 MHz | 50 Ω | ≈ 5.66 nA | ≈ 0.283 µV |
| 0.5 mA | 1 kHz | 100 kΩ | ≈ 0.401 nA | ≈ 40.1 µV |
Values are illustrative and assume F = 1 and ideal shot noise only.
What shot noise measures
Shot noise is the random fluctuation created by discrete charge arrival. In many devices, arrivals are well modeled by Poisson statistics, producing nearly white noise versus frequency. This calculator reports noise density (per √Hz) and integrated RMS noise over your selected bandwidth. It sets a fundamental floor for current-based sensing and counting.
Key constants and units
The electron charge is q = 1.602176634×10⁻¹⁹ C. Enter mean current using A through pA, and enter bandwidth from Hz to GHz. Results are displayed with engineering prefixes to keep numbers readable, such as nA or µV. Common lab currents from microamps to milliamps produce picoamp-per-root-hertz densities.
Current-based calculation
If you know the device DC current, select the DC current method. The noise density is in = √(2qIF), where F is an optional excess factor. Increasing current raises noise, but only with the square root, which is why doubling current is a modest change.
Photodiode and responsivity pathway
Optical detectors often start from power rather than current. With responsivity R (A/W), the photocurrent is I = R·P, and dark current can be added. Use datasheet responsivity at your wavelength for best accuracy, because R can change significantly across spectra.
Bandwidth and filter effects
RMS noise over a band is irms = in·√(Δfeff). A 100× wider effective bandwidth produces 10× more RMS noise. Real filters rarely behave like perfect rectangles, so the bandwidth factor lets you apply an equivalent‑noise‑bandwidth correction. If you average N samples, effective bandwidth usually falls, improving noise.
Converting to voltage and power
Many front ends sense voltage, so the calculator converts to vrms = irms·RL. Noise power into the load is Pn = irms2RL. RL does not change the shot noise current, but it does scale the voltage you observe.
Interpreting SNR and dB
A convenient current‑domain SNR is SNR = I / irms. When shot noise dominates, irms grows with √I, so SNR improves only with √I. The dB figure uses 20·log10(SNR), matching amplitude‑ratio practice in electronics and optics.
Practical notes and limitations
Real measurements also include thermal noise, amplifier noise, and low‑frequency 1/f noise. Avalanche gain can add extra noise, which is why the excess factor is editable. Treat these results as the shot‑noise contribution, then combine other independent sources by RMS summation for a complete budget.
FAQs
1) Why does shot noise increase with current?
More current means more carriers per second. Poisson statistics give variance proportional to the mean rate, so current noise density scales as √I and RMS noise rises with √I and √bandwidth.
2) What is effective noise bandwidth?
It is the bandwidth of an ideal rectangular filter that passes the same total noise power as your real filter. It can differ from the -3 dB bandwidth, especially for higher‑order filters.
3) When should I set the excess noise factor above 1?
Use F > 1 for devices with internal gain noise, such as avalanche photodiodes or multiplication processes. If you only need ideal shot noise, keep F = 1.
4) Does load resistance change shot noise current?
No. Shot noise current depends on q, I, F, and bandwidth. The load resistance only converts that current noise into voltage and power noise, which is often what you measure.
5) How do I estimate photodiode responsivity?
Check the datasheet at your wavelength. Responsivity varies with material and wavelength, so using the closest curve point is better than guessing. You can also back‑calculate R from measured photocurrent and power.
6) Can shot noise dominate over thermal noise?
Yes, especially at higher currents or in low‑resistance, wide‑bandwidth receivers. Thermal noise depends on temperature, resistance, and bandwidth, while shot noise depends on current and bandwidth.
7) How can I reduce shot noise in my measurement?
You cannot remove it without reducing current or bandwidth, because it is fundamental to discrete charge flow. Practical strategies include narrowing bandwidth, averaging, increasing signal gain before noisy stages, or using higher quantum efficiency.