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Shot noise factor of 2

Discussion in 'Electronic Design' started by George Herold, Jul 12, 2013.

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  1. So we know shot noise is given by the formula

    i_n^2 = 2*e*I_avg*BW

    Where e is the electron charge and BW is the bandwidth.
    I’ve been trying to derive the factor of 2 in the formula.
    But I’m not quite getting it.

    A typical derivation looks at random pulses measured over some time T.. thetricky part is relating the bandwidth to the time T. So here the author states that BW = 1/(2*T)
    and says that’s related to the Nyquist sampling theorem.

    www.physics.queensu.ca/~phys352/lect04_1.pdf

    But I don’t see it? Is that correct? Help!

    TIA
    George H.
     
  2. "Ding Ding".. (bells going off in my head)
    Thanks very much Phil.
    (I was kinda hoping you'd have the answer.)

    George H.
     
  3. Guest

    Guest Guest

    So we know shot noise is given by the formula

    i_n^2 = 2*e*I_avg*BW

    Where e is the electron charge and BW is the bandwidth.
    I’ve been trying to derive the factor of 2 in the formula.
    But I’m not quite getting it.

    A typical derivation looks at random pulses measured over some time T.. the
    tricky part is relating the bandwidth to the time T. So here the author
    states that BW = 1/(2*T)
    and says that’s related to the Nyquist sampling theorem.

    www.physics.queensu.ca/~phys352/lect04_1.pdf

    But I don’t see it? Is that correct? Help!

    TIA
    George H.

    typically one defines BW in the frequency domain (for pulses) as the amount
    between the first nulls in the spectrum, - null to + null (includes 0) this
    has 90% of the energy. the nulls are located at 1/T where T is the pulse
    width, so you get 2* delta F = 1/T where delta F is from 0 to first null.

    this is just a classic definition, which can be moved around (larger or
    smaller bandwidths) and note that the author of the reference makes note of
    that as well. the industry standardized on it ( BW => from -null to +null )
    a long while back.
     
  4. Thanks Fred, I think Phil nailed it for me.

    But other derivations are always nice to look at.

    George H.
     
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