Abstract: A waveguide structure composed of circular waveguide cavities resonant in the TE.sub.011 mode is capable of realizing the most general bandpass filter characteristics with significant decreases in filter loss and gain slope. In addition to the commonly used Tchebychev and Butterworth functions, the structure can realize general transfer functions including the elliptic function. In its simplest form, the structure is composed of four cylindrical cavities which form a building block for more complex filters. The first and second cavities and the third and fourth cavities each have their side walls in contact and their end walls in common planes. The third and fourth cavities are superposed to the first and second cavities with their adjacent end walls in a common plane, but the second and third cavities are offset so that they overlap at one-half diameters. The first and second cavities are coupled by means of a centrally located side wall slot, as are the third and fourth cavities.