Microwave Hilbert Transformer and Its Applications in Real-Time Analog Processing

A microwave Hilbert transformer is introduced as a new component for real-time analog processing (RAP). In contrast to its optical counterpart that resorts to optical fiber gratings, this Hilbert transformer is based on the combination of a branch-line coupler and a loop resonator. The transfer function of the transformer is derived using signal flow graphs, and two figures of merits are introduced to effectively characterize the device: the rotated phase and the transition bandwidth. Moreover, a detailed physical explanation of its physical operation is given, using both a steady-state regime perspective and a transient regime perspective. The microwave RAP Hilbert transformer is demonstrated experimentally and demonstrated in three applications: edge detection, peak suppression, and single-sideband modulation.