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Two different types of coupled planar helix structures with straight-edge connections (PH-SECs), namely, an unconnected pair and a coaxial pair of planar helices, are proposed and analyzed in the context of application in millimeter-wave traveling-wave tubes. It is shown that the nature of the propagating modes, dispersion characteristics, field distribution, and coupling impedance for the proposed structures can be obtained as special cases of a generic structure that consists of four parallel infinite unidirectionally conducting screens. For both the coupled planar helix structures, the results based on simple analytical approximations of the generic structure match well with the simulation results. As an application of these structures, simulation results are presented to show that the unconnected pair of planar helices has a reduced interaction with backward waves compared with that for a corresponding single planar helix. The proposed PH-SECs offer easier fabrication using printed-circuit or microfabrication techniques compared with their circular counterparts.