General Synthesis of Tapered Matching Sections for Single-Mode Operation Using the Coupled-Mode Theory

In this paper, a novel and general method to synthetize microwave waveguide tapers intended for single-mode operation is proposed. The technique is based on the use of an exact series solution of the inverse scattering synthesis problem. An additional strategy necessary for dealing with waveguides where the propagation constant varies with the position is included. The coupled-mode theory is employed to model the electromagnetic behavior of the taper with the inherent mismatch caused by the connection of the waveguides with different cross sections. The novel method allows us to synthesize the (classical) transmission line taper functions of Klopfenstein and Hecken, making them suitable for general waveguide tapers with single-mode operation. Additionally, a new type of taper functions, also suitable for general waveguide tapers, is presented. The novel functions are obtained by partially employing the frequency response of multisection transformers, resulting in fully smooth tapers that can offer shorter lengths than the classical proposals. The taper synthesis procedure is demonstrated in rectangular waveguide technology, by requiring realistic and challenging specifications for different cases with different waveguide cross sections to be matched: height mismatch, width mismatch, and simultaneous height and width mismatch. Several prototypes of Klopfenstein, Hecken, and novel function tapers have been fabricated in an aluminum alloy by means of an Additive Manufacturing technique (Direct Metal Laser Sintering). The simulation and measurement results obtained for the rectangular waveguide taper prototypes confirm the accuracy of the novel synthesis technique proposed.