Synthesis of series STUB-R complex gyrator circuits using halfwave long impedance transformers

The complex shunt STUB-G circuits met in the practice of three-port circulators may be matched using one eight-wave long alternate lines or quarter wave long impedance transformers. Another possibility is to employ halfwave long UEs at the characteristic planes of the junction where the complex gyrator circuit is a series STUB-R network. Although this topology is not particularly compact the impedance levels met in this solution are appropriate for the matching of junction circulators with high Q complex gyrator loads. This paper gives the-synthesis of this problem in the case of a single halfwave long UE