  This paper introduces simple analytical formulas for the grid impedance of
electrically dense arrays of square patches and for the surface impedance of
high-impedance surfaces based on the dense arrays of metal strips or square
patches over ground planes. Emphasis is on the oblique-incidence excitation.
The approach is based on the known analytical models for strip grids combined
with the approximate Babinet principle for planar grids located at a dielectric
interface. Analytical expressions for the surface impedance and reflection
coefficient resulting from our analysis are thoroughly verified by full-wave
simulations and compared with available data in open literature for particular
cases. The results can be used in the design of various antennas and microwave
or millimeter wave devices which use artificial impedance surfaces and
artificial magnetic conductors (reflect-array antennas, tunable phase shifters,
etc.), as well as for the derivation of accurate higher-order impedance
boundary conditions for artificial (high-) impedance surfaces. As an example,
the propagation properties of surface waves along the high-impedance surfaces
are studied.
