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Periodic guiding or radiating structures at microwave frequencies frequently possess symmetry properties in addition to their axial periodicity. These include rotation and reflection symmetries, wither occurring alone or in conjunction with translations. These symmetries influence the characteristics of the electromagnetic fields associated with the structures.Therefore, useful information concerning the fields can be obtained from the symmetry properties without resorting to detailed field solutions or to equivalent circuit analogs. These symmetry properties are conveniently analyzed by introducing symmetry operators under which the structure is invariant.This paper showsthat two symmetries, the screw and the glide, are particularly important in determining the characteristics of the fields. Some of the implications of these symmetries for leaky wave antennas and microwave tube interaction circuits are explored. The consequences of screw and glide symmetries, together with five other possible symmetries, are examined to facilitate the analysis and synthesis of periodic microwave structures.

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