Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses

In this paper, a novel technique to synthesize microwave filters by inverse scattering is proposed. It provides an exact solution for the synthesis problem, by means of a closed-form expression, with very low computational cost. The technique is valid when the target frequency response can be expressed as a rational function. The coupled-mode theory is used to model microwave propagation along the filter, and therefore, the synthesis technique is applicable to filters implemented in a wide range of technologies, such as planar and nonplanar transmission lines, and many waveguides. The synthesis method is exact for all the frequency range of interest, preventing the degradation of the frequency response that can be troublesome for wideband applications or to satisfy the out-of-band requirements of the filter. The resulting synthesized filter is, in general, a nonuniform transmission line or waveguide that features a continuously varying smooth profile, avoiding the presence of sharp discontinuities and their detrimental effects. To demonstrate the potential of the proposed synthesis technique, a multiband microwave filter, fulfilling stringent specifications, will be designed in rectangular waveguide technology. The prototype will be fabricated by electroforming and carefully measured with a vector network analyzer, confirming the accuracy of the novel synthesis method reported.