On the Design of $n$ th-Order Polyphase All-Pass Filters

A structure for nth-order polyphase all-pass filters (PAFs) is proposed that improves the tradeoff between output phase accuracy and filter loss. The filter also has a well-defined input impedance, which is independent of the phase accuracy and can generate the exact desired phase at n distinct frequencies. The proposed structure along with its design approach is analyzed. The design procedure to design a second, third, and fourth-order PAFs is presented. It is shown that by increasing the order of the PAF structure, one can either improve the phase accuracy of the structure over the same bandwidth of interest or achieve the same phase accuracy over a wider bandwidth. Practical design considerations, including the effect of the parasitic capacitances, component tolerance, and inductor quality factors on the output amplitude imbalance and input impedance, are analyzed and discussed. As a proof-of-concept, experimental results are presented to show that the fourth-order structure is able to generate quadrature signals at four distinct frequencies.