Photomultiplier Tube (PMT)

PMT gain, signal current, excess noise factor, and SNR from dynode parameters.

Number of DynodesSecondary Emission Ratio (δ)Quantum EfficiencyAnode Dark Current (nA)Photon Rate (photons/s)Bandwidth (MHz)

Gain (δⁿ)

2.76e+5

Signal Current

1.10e-8 A

Photoelectrons/s

2.50e+5

Excess Noise Factor F

1.4000

δ/(δ−1) = 1.4000 for infinitely many stages

Dark Electrons/s at Cathode

2.26e+4

Anode dark current / (e·G)

SNR

0.0286

100 MHz bandwidth

Gain G = δⁿ

I_signal = R_ph · QE · e · G

F = 1 + 1/δ + 1/δ² + … + 1/δⁿ → δ/(δ−1) (Poisson secondary emission at every dynode)

SNR = R_pe / √(2·B·(R_pe + R_dark)·F), with R_dark = I_dark/(e·G)

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Equal dynodes, Poisson secondary emission, full interstage collection and shot noise only. All anode dark current is taken as cathode emission (no leakage) and the dark level as known, with no subtraction term.

Hamamatsu Photonics (2017). Photomultiplier Tubes: Basics and Applications, 4th ed., §4.3.7, Eq. 4-25 to 4-32. Noise figure of a dynode chain, F = 1 + 1/δ₁ + 1/(δ₁δ₂) + … → δ/(δ − 1), and the shot-noise SNR. hamamatsu.com

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