34 u 34 34 v 34 and 34 p 34 are selectable variables the dumbbell shape essentially corresponds to that of a rectangular waveguide having oppositely disposed ridges 22 24 which are not of the rectangular cross sectional shape shown in fig1 a 1b and 2 but instead are of a substantially bell shaped cross section which extends to generally convex ends 26 28 of the waveguide cross section defined about the major axis in the waveguide cross section shown in fig3 it should be noted that the polar equation 1 defines the contour in such a way that the upturned ends of the bell shaped ridges smoothly merge with the cross sectional ends of the waveguide thereby avoiding the presence of any corners or abrupt protrusions the contour of fig3 represents the cross sectional shape of the waveguide 20 according to a preferred embodiment where the parameters 34 u 34 34 v 34 and 34 p 34 are selected to be 0 702 34 0 128 34 and 3 40 respectively based on a dominant mode operational bandwidth of 7 5 18 0 ghz a family of curves of the type shown in fig3 can be generated by maintaining the parameters 34 u 34 and 34 v.