Closed-Form Equations for Substrate Integrated Coaxial Lines and Its Application to Dual-Frequency Coupler With Wide Bandwidth and Out-of-Band Rejection

This article presents the design and fabrication of self-packaged, self-shielded substrate integrated coaxial lines (SICL). The study introduces a closed-form equation for the characteristic impedance of SICL, emphasizing the effect of the outer conductor width and substrate thickness on this parameter. The robustness of the proposed formula is confirmed through testing of four distinct SICL transmission lines, each with varying dielectric constants and substrate thicknesses. A novel dual-band SICL transmission line is developed using short-circuited planar coaxial stubs, which serves as an alternative to the conventional quarter-wavelength transmission line design. The performance of this dual-band line is analyzed across different characteristic impedances, and the range of achievable frequency ratios is determined analytically. The resulting SICL-based rat-race coupler, fabricated using standard PCB processes, demonstrates a measured fractional bandwidth of 26.69% at 10.83 GHz and 11.29% at 22.94 GHz. It achieves low amplitude and phase imbalances, with values of $\pm$ 1 dB and less than $\pm$ 4°, respectively. Owing to the filtering response provided by short circuited coaxial stubs, the third harmonic of proposed coupler is suppressed and spurious rejection better than 22 dB is achieved up to 40 GHz.