  We generalize the derivation of dynamo coefficient $\alpha$ of Field et al
(1999) to include the following two aspects: first, the de-correlation times of
velocity field and magnetic field are different; second, the magnetic Prandtl
number can be arbitrary. We find that the contributions of velocity field and
magnetic field to the $\alpha$ effect are not equal, but affected by their
different statistical properties. In the limit of large kinetic Reynolds number
and large magnetic Reynolds number, $\alpha$-coefficient may not be small if
the de-correlation times of velocity field and magnetic field are shorter than
the eddy turn-over time of the MHD turbulence. We also show that under certain
circumstances, for example if the kinetic helicity and current helicity are
comparable, $\alpha$ depends insensitively on magnetic Prandtl number, while if
either the kinetic helicity or the current helicity is dominated by the other
one, a different magnetic Prandtl number will significantly change the dynamo
$\alpha$ effect.
