A Sensitivity Study of Butler Matrices: Application to an SIW Extended Beam Matrix at 28 GHz

In this paper, a detailed sensitivity study of Butler matrices is proposed. In particular, a Monte Carlo analysis is carried out on each block constituting the matrix to estimate its impact on the overall performance. The isolation level of the crossover transmission path is hence proved to be a critical part of the Butler matrix design. As it will be shown using both full-wave analysis and analytical equations, an isolation of 30 dB should be reached in order to guarantee proper operation of the matrix. These outcomes were experimentally proved by designing two 28 GHz Substrate Integrated Waveguide (SIW) $4\times 4$ Butler matrices as a demonstrator in the framework of the extended beam concept. Thanks to the crossover transmission path high isolation, the measured results show an insertion loss of 2.13±0.7 dB and a maximum output progressive phase deviation of −15.5° and +16.9°. Based on 0.5 $\lambda $ _0 evenly spaced isotropic antennas, those results enable a spatial coverage from −89.4° to 83.1° with a maximum loss of 2.2 dB and a ripple of 1.1 dB for the array factor as compared to the −48.6°/+48.6° spatial coverage, 3.7-dB of ripple of the conventional $4\times 4$ Butler matrix array.