  We report a detailed analytic investigation of the interplay between size
quantization and local scattering centers in armchair graphene nanoribbons, as
seen in the conductance. The scattering property of a local scattering center
is dependent on if it is located on one sublattice (A-site impurity) or both
(impurity situated at neighboring carbon atoms, A-B-site impurity). The A-site
impurity scatters in a similar way as a localized impurity in a one-dimensional
channel made from a two-dimensional electron gas. On the other hand, the
A-B-site impurity introduces A- to B-sublattice scattering, which knows about
the chirality of Dirac electrons, and heavily influence the conductance. For
A-site impurities, interplay between evanescent waves at the impurity and the
propagating modes contributing to the conductance, leads to scattering
resonances that generate either dips in the conductance or render the impurity
completely transparent. The latter occurs at subband bottom energies where the
wave vector of the opening mode is zero. The conductance of defect free
graphene therefore remains at these energies. This is analagous to the case of
a scattering center in a quantum channel made from a two-dimensional electron
gas. The conductance dips occur at energies $\Delta E$ away from the
conductance steps and their location depend directly on the impurity strength.
In particular, for repulsive impurities the dips occur for hole-doping, while
for attractive impurities for electron doping. For an A-B-site impurity, the A-
to B-sublattice scattering interferes with the transmission resonance at the
energies of the subband bottoms and the impurity is never transparent and the
conductance steps of defect free graphene ribbons are always lost. We derive a
generalized Fisher-Lee formula for graphene leads that holds for arbitrary
scattering region and arbitrary number of leads.
