A Rigorous Multimodal Analysis and Design Procedure of a Uniplanar 180 $^{\circ}$ Hybrid

Uniplanar 180deg hybrids are basic building blocks in uniplanar technology. In this paper, a new rigorous analysis of a uniplanar 180deg magic-T hybrid based on an air-bridged coplanar cross is performed. The analysis proposed is multimodal since it takes into account the coplanar even and odd fundamental modes simultaneously. From this analysis, a complete circuit model for the hybrid is extracted, and the conditions for ideal performance are derived. This new multimodal model is necessary for the design of the hybrid, and allows a quantitative analysis of its performance, notably bandwidth, isolation, and return loss under any actual loading condition. It has been used to design and implement a 180deg hybrid on alumina with a working frequency of 15 GHz. A very good agreement between simulation and measurement is obtained. The experimental results prove a frequency-independent phase-shift behavior with a measured phase error less than plusmn 2deg.