Low Pass Filters with Linear Phase

摘要

This report is intended as a modern sequel to Band Pass Filters with Linear Phase, published over 20 years ago. Here, the linear phase algorithms are adapted to low-pass integrated active circuit topologies for potential use as the input filter in sampled data control systems and other low-pass applications for which traditional coil-capacitor-transformer filter designs are no longer appropriate. The linear phase algorithm is applicable to a variety of circuit topologies which are not mathematically equivalent. Application to the overall transfer function (the simple approach) results in transmission that is nearly equal-ripple in both amplitude and phase, the errors being equivalent to echos in a misterminated trasmission line. The resulting filters compare favorably with modest order Tchebychef filters (lacking phase control). Application to branches of a feedback topolgy (mathematically equivalent to a lattice) leads to control of echoes and stop-band zeros at the cost of extra elements. In this case, the results compare favorably with ordinary Butterworth filters (lacking phase control) having the same total number of poles. Practical means for inserting stop band zeros without redesign of the pass-band are considered. Circuits of both the R-C and switchcap types are discussed. (Author)