Circular helix is a very popular slow-wave structure (SWS) for application in traveling-wave tubes (TWTs). But it is not easy to be fabricated using printed-circuit or microfabrication techniques which are important for low-cost fabrication and high frequency applications. In this context, during the last few years, a planar helix SWS with straight-edge connections (PH-SEC) has been proposed and studied. Unlike the circular helix, the PH-SEC is suitable to be fabricated using printed circuit or microfabrication techniques. However, there are still some issues and problems that need to be addressed for the PH-SEC when used in millimeter wave TWTs. First of all, there can be backward wave oscillations when the TWT is working at high voltages. Secondly, the size of the SWS, the electron beam tunnel, and the beam get very small, causing difficulty in fabrication, alignment, and focusing of the electron beam. Thirdly, at millimeter wave frequencies, it is more likely that the electrons hit the supporting dielectric, causing dielectric charging which will affect the performance of the TWT adversely. Moreover, PH-SEC can be dispersive in the presence of dielectric loading, reducing the bandwidth of operation. This thesis presents novel SWSs which are based on the PH-SEC and solve some of these problems. First of all, two types of coupled planar helices, an unconnected pair of PH-SECs and a coaxial pair of PH-SECs, are proposed. Their dispersion characteristics are derived from analysis based on field-theory. The characteristic equations and field expressions are obtained to explain the nature of different modes that propagate in the coupled structures. Coupling impedance is also calculated. Effects of variations in dimensions are studied. The analysis results match well with simulations. Simulation results are presented to show that the unconnected pair of planar helices has a reduced interaction with backward waves as compared to that for a corresponding single PH-SEC. Based on the above knowledge of various modes, an unconnected pair of PH-SECs has been designed together with a stripline power divider in order to provide input signals with equal magnitude and phase. Also proposed is a connected pair of PHvi SECs which can be fed in a much simpler way by a coplanar waveguide (CPW) feed. The latter structure offers a larger electron-beam tunnel and lower risk of backward wave oscillation compared to the single PH-SEC. Moreover, the connected pair of PH-SECs has a higher gain growth rate than that for the single PH-SEC. The connected pair also shows a significantly higher coupling impedance compared to a recently reported meander-line based SWS. Both the unconnected and the connected pair of PH-SECs have been designed and fabricated using printed circuit techniques. The measurement results match well with the simulation results.