the coherent summation of all of the spatial domain Green's function's becomes infinite, so that any finite current produces an infinite field on the surface of the FSS. As a result, all currents must be zero under this condition. This example illustrates the usefulness and shortcomings of the simple equivalent circuit model. The equivalent circuit only includes features related to the individual scattering element, not features related to the periodic array, such as interactions between the scatterers. FSS duality versus circuit duality FSS duality If a mesh type FSS is created from a patch type FSS in such a way that the metal portions or the former are replaced by aperture portions of the latter, then the two FSS are said to be duals of one another. Duality only strictly applies when no dielectric substrates are present, therefore it is only approximately satisfied in practice, though even when dielectric substrates are present, duality can be useful in FSS design. As a side note, Pathological FSS patterns such as a checkerboard FSS may be treated as the limit of the patch and mesh as the patch (and aperture) size approaches the unit cell size, with electrical connections of the mesh retained in the limit. For dual FSS, the reflection coefficient of the patch will be equal to the transmission coefficient of the mesh. Circuit duality The dual circuit of the bandstop filter can be obtained simply equating the reflection coefficient of the bandstop FSS to the transmission coefficient of the bandpass FSS to obtain (if we use L1, C1 for the bandstop patch FSS and L2, C2 for the bandpass mesh FSS): This produces a bandpass circuit (with parameters L2, C2) which is the dual of the bandstop circuit (with parameters L1, C1). FSS equivalent circuits - applications to FSS design Once the transmission line equivalent circuit has been determined, multi-layer FSS design becomes much simpler and more intuitive - like ordinary filter analysis and design. Now while it is certainly possible to design multi-layer FSS structures using first principles codes and generalized scattering matrices (GSM), it is far easier, quicker and more intuitive to use equivalent circuit models for FSS design, since it is possible to leverage decades' worth of research performed on electrical filter analysis and design and bring it to bear on FSS structures. And, FSS filters are even easier to design than waveguide filters since the incidence