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A new planar slow-wave structure consisting of a planar helix with straight-edge connections is presented. It is shown that the phase velocity of the proposed structure can be much slower than that for a rectangular helix with identical cross-sectional dimensions. Further, the dispersion characteristics are obtained simply by using the effective dielectric constant method; it is shown that the method yields results which, far-from-cutoff, match very well with simulation results obtained from CST Microwave Studio. The proposed structure has the potential of easier fabrication using microfabrication techniques.