Higher order impedance boundary conditions for sparse wire grids

Higher order impedance boundary conditions designed for modeling wire grids of thin conducting wires are established. The derivation is based on the exact analytical summation of the individual wire fields. This allows one to write an approximate boundary condition on the grid surface, which connects the averaged electric field and the averaged current (or the electric field and the averaged magnetic fields on the two sides of the grid surface). The condition depends on the tangential derivatives of the averaged current (up to the sixth order). This approach provides an extension of the averaged boundary conditions method (well established for dense grids) to sparse grids. Numerical examples demonstrate very good accuracy of the solutions for the field reflected from grids with the wire separation as large as half of the wavelength.