[Aavso-photometry] Converting Std Deviation in electrons to magnitudes

[Brad Walter]

I have been perusing Handbook of CCD Astronomy by Steve Howell and came
across a formula in Section 4.4 (page 78 in my paperback version) that
mystifies me. Steve uses a conversion factor of 1.0857 as a conversion
factor from Sigma = 1/SNR in electrons to sigma in magnitudes. With a little
fiddling I was able to deduce that the conversion factor equals (to the
least significant digit given) 2.5/LN(10). I don't understand how a constant
conversion factor can be correct. It seems to me that the conversion would
be more like the following 

Sigma(mag)= -2.5*Log(1 + 1/SNR)/2 + 2.5*Log(1 - 1/SNR)/2 

where using Steve Howell's terminology
  SNR = Nstar/SQRT(Nstar + P)
  Nstar is the signal in electrons
  P is made up of the noise terms other than the Poisson noise of the flux
from the star.

Can anyone explain Steve's conversion formula? I can't find the reference he
cites on-line