Flatness and Symmetric Low-Pass Lossless Filters

Subsequent to a review of flat transfer functions and maximally flat functions with transmission zeros on one or both of the two axes in particular, characteristics of lossless symmetric networks with equal resistance terminations are given. Several theorems pertaining to the order of flatness for such filters are presented and specific design examples are given. The theorems, along with the representative examples, provide a basis for development of an extensive approximate graphical cascading design technique which gives better results than image-matching methods for unbalanced filters. In the method, control of phase is possible while maintaining known flat gain characteristics. Also, existence of and design methods for approximately all-pass phase-equalizing networks which allow for shunt capacitance are demonstrated.