Shot noise factor of 2

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

1. George HeroldGuest

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. George HeroldGuest

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

George H.

3. 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. George HeroldGuest

Thanks Fred, I think Phil nailed it for me.

But other derivations are always nice to look at.

George H.  