Compact 94-GHz 4×4 Butler Matrix Design in IPD Technology

In this work, we designed 94-GHz $4\times 4$ Butler matrix circuits in glass-based integrated-passive-device (IPD) technology. Given the design rule constraints, the inevitable crossover structure is carefully planned as a miniature low-pass filter carrying simulated 0.2 dB insertion loss, successfully incorporating parasitics with good matching. The fabricated standard Butler circuit exhibits insertion loss of 8 dB, with mismatch less than 1 dB and phase difference less than 10 degrees at 94 GHz. Size reduced by 34%, the miniaturized circuit shows insertion loss about 1 dB worse but phase mismatch improved by 3 degrees. The core areas of the standard and miniaturized circuits are $1.42\times 1.22 mm^{2}$ and $1.04\times 1.08 mm^{2}$, respectively. The designs are applicable to beamforming phased arrays in the W band.