Filter with periodic phase delay and insertion-loss ripple

An analytical design procedure is presented for the lowpass prototype selective linear phase filter, from which bandpass-channel filters may be deduced, whose insertion-loss and phase-delay-error functions vanish at an optimum number of equidistant points in the passband. Synthesis is performed using an even-and-odd-mode decomposition for a symmetrical filter comprising capacitors and impedance invertors. Finally, explicit formulas are given for element values in the 2nd-, 4th- and 6th-degree networks from which a simple realisability condition is deduced for all positive coupling elements, and numerical results on a 12th-degree filter are presented to illustrate the typical response characteristics. The main application of the design technique is in the construction of channel filters in high-capacity communication systems which use frequency modulation, particularly at microwave frequencies where the compact physical devices are readily constructed