Shot Noise Current Calculator

Formula used

This calculator uses a generalized shot-noise model, useful for diodes and photodetectors. The current-noise power spectral density is:

in2 = 2 q I · F · M2 · E · B

• q is electron charge (1.602176634×10^-19 C).
• I is average current (A).
• F is the Fano factor (dimensionless).
• M is multiplication gain (dimensionless).
• E is an excess-noise factor (dimensionless).
• B is noise bandwidth (Hz).

Noise current density: in,ρ = √(2 q I · F · M2 · E) in A/√Hz. RMS noise current over bandwidth: in,rms = in,ρ · √B.

How to use this calculator

1. Select RMS if you know the measurement bandwidth.
2. Enter the device average current and pick units.
3. Set Fano, gain, and excess as needed.
4. Optionally add a load resistance to estimate voltage noise.
5. Press Calculate to see results above the form.
6. Use the Download buttons to export CSV or PDF.

Tip: If you only need noise per √Hz, choose density mode.

Example data table

Values are rounded for illustration; your results depend on inputs.

Shot noise current in practical measurements

1) Why shot noise exists

Shot noise comes from discrete charge carriers crossing a potential barrier. Even with steady average current, electrons arrive randomly, producing current fluctuations whose statistics are often close to Poisson for many junction devices. In precision electronics, it sets a fundamental noise floor.

2) The core scaling law

For an ideal Poisson process, the single-sided current-noise density is √(2qI) in A/√Hz, where q = 1.602176634×10^-19 C. Doubling average current increases noise density by √2, not by two.

3) Bandwidth turns density into RMS

Instruments integrate noise across an effective bandwidth B. The RMS noise current is i_n,rms = i_n,ρ·√B. For example, at I = 1 mA and B = 1 MHz, i_n,ρ ≈ 17.9 pA/√Hz and i_n,rms ≈ 17.9 nA. With B = 10 kHz, RMS noise becomes about 1.79 nA.

4) Fano factor for non‑ideal sources

Some transport mechanisms suppress or enhance fluctuations. The Fano factor F rescales noise power, so i_n,ρ ∝ √F. Setting F = 0.5 reduces noise by about 29%, while F = 2 increases it by about 41%.

5) Gain and excess noise in detectors

Avalanche photodiodes and multiplication regions amplify current by a gain M. Noise power grows with M², and an excess noise factor E captures additional multiplication randomness. The calculator applies the combined factor F·M²·E for a realistic estimate.

6) Converting to voltage and power

When a load resistance R is used, voltage noise follows v_n,rms = i_n,rms·R. With R = 50 Ω and i_n,rms = 17.9 nA, v_n,rms is about 0.895 µV. Noise power in the resistor is i_n,rms²·R.

7) Using the results for design decisions

Compare shot noise to other sources such as Johnson noise, amplifier input noise, and 1/f noise. If shot noise dominates, improving SNR usually requires increasing signal current, narrowing bandwidth, or using averaging, rather than changing resistor value. In photodiode systems, more optical power raises current and improves relative noise.

8) Common sanity checks

Check unit consistency (A, Hz, Ω), confirm bandwidth is the measurement’s noise-equivalent bandwidth, and keep gains realistic. As a quick reference, I = 100 µA gives i_n,ρ ≈ 5.66 pA/√Hz; I = 10 nA gives about 0.0566 pA/√Hz at F = 1. Verify results scale with √I and √B.

FAQs

1) What is the difference between noise density and RMS noise?

Noise density is the current noise per √Hz (A/√Hz). RMS noise is the integrated noise over a bandwidth B, computed as density multiplied by √B, assuming a flat spectrum in that band.

2) When should I change the Fano factor?

Use F = 1 for ideal shot noise. Adjust F when a datasheet, model, or measurement indicates suppressed or excess fluctuations, such as in certain semiconductor transport regimes or devices with correlated carrier flow.

3) Do I need gain M and excess factor E for normal diodes?

Usually no. For standard diodes and most photodiodes without multiplication, set M = 1 and E = 1. Use M>1 and an appropriate E mainly for avalanche or multiplication detectors.

4) What bandwidth should I enter?

Enter your measurement’s noise-equivalent bandwidth. If you have a simple low-pass filter, it may be close to its cutoff, but instrument manuals often specify NEB or effective bandwidth more accurately than the −3 dB point.

5) Why does increasing resistance change voltage noise?

The current noise is set by charge statistics, but voltage noise across a resistor is v = i·R. A larger R produces a larger voltage noise for the same RMS current noise, which matters for amplifier and ADC input limits.

6) Can this replace a full noise budget?

It covers shot noise and optional resistor conversion, but a full budget should also include thermal (Johnson) noise, amplifier voltage/current noise, 1/f noise, and any bandwidth shaping from filters or sampling.

7) What common mistakes cause unrealistic results?

Mixing units (mA vs A), entering the wrong bandwidth, and using gain factors that don’t match the device are typical issues. Also ensure the average current is the DC or mean value, not a peak signal current.

Notes and interpretation

• Shot noise increases with the square root of average current.
• Doubling bandwidth increases RMS noise by √2.
• Fano factors below 1 model suppressed noise in some devices.
• With multiplication, noise rises roughly with M when E≈1.

Accurate noise estimates improve designs, testing, reliability, and performance.