In this paper, dispersion characteristics of the partial H-plane waveguides are theoretically investigated by applying Galerkin's method in Fourier domain. By extracting the dyadic Green's functions of the structure and satisfying the boundary conditions along the longitudinal slit, propagation constant and consequently, the fields in the structure are obtained. It is seen than propagation constant not only depends on the waveguide dimensions, but also on the location and dimension of the slit. A significant feature of the structure is that its first and second propagation modes can be separately controlled which is very useful in designing single-mode and multi-mode filters. Two examples are given which in the first one, the parameters of the structure are assigned in such a way the first and second cut off frequencies are at f=3.1 GHz and f=6.2 GHz respectively, but in the second example, first and second modes are degenerate. The validity of the method is confirmed by comparing our results with ones from others.
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