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

Abstract

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.

Synthesis of Rectangular Waveguide Filters With Smooth Profile Oriented to Direct Metal Additive Manufacturing

“…The new inverse scattering technique, known as ILP, allows us to synthesize filters with very high rejection levels, as customarily required in rectangular waveguide, without experiencing numerical problems. Although the methodology has been formulated for rectangular waveguide with variations in height, it could also be extended to variations in width by applying the technique developed in [48], and even to other waveguide technologies.…”

“…As it was demonstrated in [41], the coupling coefficient, K (z), required to obtain a target frequency response, S 11 (β), can also be calculated through the kernel functions A 1 (z, τ ) and A 2 (z, τ ) of the GLM equations (50). Formulating the problem in the τ domain, by taking the inverse Fourier transform of the coupled-mode equations (32), substituting the solutions obtained (46), (48), (49), expressed also in the τ domain, and taking into account causality considerations (52), it can be deduced after several mathematical manipulations [41]…”

“…In this case, proper tapers should be added at the input and output ports of the filter to keep the standard port dimensions, as it was done in [42]. The taper design procedure is thoroughly explained in [48]. Another important advantage of growing the filter following its propagation axis is that the classical staircase effects experienced in SLM fabrications are reduced and optimum manufacturing accuracy is achieved, as it was discussed in Section I.…”

Advanced Modeling of Rectangular Waveguide Devices With Smooth Profiles by Hierarchical Model Reduction

“…6 by setting a 0 = 22.86 mm, b 0 = 10.16 mm, a L = 22.86 mm, b L = 5.08 mm and length L = 47.08 mm = 1.41λ 0 , being f 0 = 10 GHz. The profile synthesis was done by the procedure described in [31] for a Hecken taper [32], which exhibits a quasi-optimal response for the given set of input parameters (i.e., a return loss lower than 40 dB for the WR90 frequency range, between 8.2 GHz and 12.4 GHz). The b(z) dependence does not have an explicit form but can be expressed as…”

New insights from broadband simulations into small overmoded smooth and corrugated terahertz waveguides and transitions for NMR-DNP

“…These referenced loss studies did not investigate tapered transitions, perhaps because such were not needed in their primary application – plasma heating of the ITER reactor, where a large corrugated waveguide of constant size (60–90 mm ID) could be used from the beginning to the end of the waveguide run. There is indeed considerable literature on tapered overmoded transitions [ 30 , 34 ], including a nice recent addition [ 38 ]; but the prior literature on such has generally been focused on cases where the number of propagating modes may be perhaps a dozen, not hundreds, and the frequencies are much lower.…”