Design of Transmission-Type $N$th-Order Differentiators in Planar Microwave Technology

In this paper, we propose and demonstrate a new technique for the design of arbitrary-order differentiators, intended for ultra-wideband (UWB) applications in microwave coupled-line technology. The technique employs an exact analytical series solution for the synthesis problem derived by the authors from the coupled-mode theory. This solution allows for the synthesis of microwave devices with arbitrary frequency responses, only limited by the principles of causality, passivity, and stability. The method has been successfully applied in the past to the design of two-port waveguide and transmission-line components operating in a reflection-type configuration. Here, the synthesis technique is extended to coupled-line structures, where the input port is matched at all frequencies and the reflected signal is redirected to the coupled port, enabling an effective transmission-type operation for the device. First-, second-, third-, and fourth-order UWB differentiators have been successfully designed, fabricated, and measured, validating the general design technique proposed.