# 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. ### GuestGuest

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.  