A Lumped Element Filtering Rat-Race Coupler on Self-Packaged SISL Platform

This article proposes a lumped element filtering rat-race coupler (FRC) and its detailed analysis. In addition to the basic filtering and coupling function of general FRCs, the proposed FRC design can generate additional transmission zeros, and the FRC circuit is analyzed as an overall circuit rather than separated resonators and coupler. To provide an insight into their filtering and coupling mechanism, the proposed FRC is analyzed by equating the FRCs to the circuits with immittance inverters and admittance topology. All of the used lumped elements, as well as external quality factor and coupling coefficients, can be calculated by the given formulas. According to the given design process, two compact FRCs with lumped element are designed as design cases and implemented based on the substrate integrated suspended line (SISL) platform. The overall area of core circuits is only
$0.117\lambda _{\mathrm {g}}\,\,\times \,\,0.054\lambda _{\mathrm {g}}$
and
$0.091\lambda _{\mathrm {g}}\,\,\times \,\,0.054\lambda _{\mathrm {g}}$
, which is much smaller than other designs. The simulated results are confirmed via experiment, showing good coupling and filtering performance, which demonstrates that the proposed lumped element FRC circuits are feasible.