Frequency-Variant Phase-Shifters in Bandstop Extracted-Pole Cascade Synthesis

Microwave bandstop filters several finite transmission zeros are commonly synthesized as a sequence of frequency-invariant phase shifters followed by hung resonators. The physical realization however often involves transmission lines, whose phase delay introduces a linear variation with frequency and hence limit the design effectiveness to narrow band and heavy subsequent optimization. Leveraging a revisited version of classical cascade synthesis, the formulation presented here allows to include the known frequency variation of such components at synthesis time. The resulting compound technique yields a synthesized circuit much closer to its physical implementation up to relative bandwidth 13%.