  We present several new results, extending our recent proposal of a spin
filter based on a tight-binding model for a periodic chain of diamond-like
loops [Phys. Rev. B {\bf 78}, 125328 (2008)]. In this filter, the Rashba
spin-orbit interaction (which can be tuned by a perpendicular gate voltage) and
the Aharonov-Bohm flux (due to a perpendicular magnetic field) combine to
select only one propagating ballistic mode. For this mode, the electronic spins
are fully polarized along a direction that can be controlled by the electric
and magnetic fields and by the electron energy. All the other modes are
evanescent. Generalizing the square diamonds into rhombi with arbitrary opening
angles, we find that increasing these angles widens the parameter range for
efficient filtering. A different gate voltage on the two sides of each rhombus
is found to delocalize the electrons for energies on one side of the band
center. We also compare our tight-binding model with models which use
continuous quantum networks of one-dimensional wires, and find coincidence only
when one chooses particular site energies at the nodes of the network.
