Optimization-free design equations for narrowband equal-division filtering power divider with pre-specified filtering response and wideband isolation

In this paper, we present completely analytic design equations for a narrowband filtering power divider with an excellent isolation performance over a wide frequency range. For providing the complete design equations, the even-odd mode analysis on the circuits has been carried out. The design theory and equations allow a filtering power divider containing frequency-independent inverters to have infinite isolation over the entire frequency range. The presented design theory is significant in a sense that it enables designing a filtering power divider with a high isolation over a wide frequency range when the divider contains frequency-variant inverters in practice. Using the closed-form equations, all circuit element values and detailed physical dimensions of filtering power divider can be found based on a pre-specified filtering response. Therefore, our design method can provide a filtering power divider design guideline for the various specifications required by communications systems. For verifying the presented design method and analytic design equations, a third-order lumped-element narrowband filtering power divider has been designed, fabricated, and measured. We have also implemented a filtering power divider using microstrip resonators to verify that the presented design method and equations can be applied to distributed-element filtering power divider designs. The measured results have shown a good agreement with theoretical results.