Frequency‐periodic microwave passive circuits and their digital matching

Abstract

Frequency-periodic microwave passive devices can be analysed in such a way that the coefficients of their digital counterparts can be extracted. In this study, this analysis procedure is exploited with the aim of providing a new theoretical framework to model these circuits, which could hopefully make their synthesis easier in the future. Interesting results observed from the application of this method to three examples of passive devices are as follows: (i) the appearance of zero-pole cancelations (ZPCs), (ii) the explanation of the required redundancy in certain microwave structures, and (iii) some difficulties observed in the synthesis of some frequency-periodic circuits, given a predefined digital design as a single starting point. The ZPCs appearing for the first example corresponding to a stepped-impedance-stub-based lowpass filter explain its inherent structure redundancy. Next, the analysis performed for a frequency-periodic wide-band matching network as second example also reveals the ZPC phenomenon, which justifies the existence of difficulties in its theoretical synthesis starting from a prefixed digital design. Finally, the third example consists in the application of the procedure to the well-known 3-dB branch-line hybrid, for which no ZPCs arise.