Transmission characteristics of a folded waveguide structure, which consists a bifurcating metal plate with finite thickness between the lower and the upper metal plate guides and being placed unsymmetrically in the cross-sectional plane in general, are investigated theoretically by using mode matching technique for the application as a feeder for any planar radiating structure. A novel technique is proposed in which the inclusion of step junctions in the folded waveguide portion play an essential role in minimizing reflections caused by the presence of finite thickness of the bifurcating metal plate as well as the unsymmetry in the folded portion and hence, a complete power transmission could be achieved. Based on the numerical computations some practical structures which could be applied as feeders for plasma generating devices are designed and the perfect matching performances are demonstrated.