  We study theoretically an influence of the near-interfacial insulator traps
and electron-hole puddles on the small-signal capacitance and conductance
characteristics of the gated graphene structures. Based on the self-consistent
electrostatic consideration and taking into account the interface trap
capacitance the explicit analytic expressions for charge carrier density and
the quantum capacitance as functions of the gate voltage were obtained. This
allows to extract the interface trap capacitance and density of interface
states from the gate capacitance measurements. It has shown that
self-consistent account of the interface trap capacitance enables to reconcile
discrepancies in universal quantum capacitance vs the Fermi energy extracted
for different samples. The electron-hole puddles and the interface traps impact
on transfer I-V characteristics and conductivity has been investigated. It has
been shown that variety of widths of resistivity peaks in various samples could
be explained by different interface trap capacitance values.
