Parametric Modeling of Coupled Stripline Coupler With Arbitrary Operating Frequency and Coupling Coefficient in Silicon-Based 3-D RF Integration

A parametric model is proposed for the coupled stripline coupler with arbitrary operating frequency and coupling coefficient in silicon-based 3-D RF integration. All the three parts of the coupler configuration, including the coupled stripline section, the coupled bends, and the stripline to grounded coplanar waveguide (GCPW) transitions, are modeled and then constructed. The conformal mapping (CM) method is employed to establish the relationship between the key geometrical parameters and the eigenmode characteristic impedances of coupled striplines. The analytical model is validated with high accuracy and the error is less than 4% when compared with the full-wave simulations. A scalable equivalent circuit model is established for the coupled bends with the arbitrary bend angle between 0° and 90°, which is formed by the integration of subregions. An equivalent circuit model is proposed for the stripline-to-GCPW transition and validated by full-wave simulation. Nine coupler prototypes are synthesized and fabricated with three typical coupling coefficients (7, 8, and 11 dB) and three central frequencies (10, 20, and 26.5 GHz). Good agreement is achieved among the S-parameters obtained by the proposed circuit model, full-wave simulations, and on-wafer measurements. The return loss and isolation of the couplers are better than 15 and 20 dB, respectively.