Delay networks having maximally flat frequency characteristics

A lumped-constant equivalent of a transmission line can be obtained in general in the form of a symmetrical lattice, in which the series and lattice arms are inverse and approximate respectively to the short-circuit and open-circuit impedances of half the line. One such set of approximations can be derived from the infinite ladder networks (Cauer´s canonical form) equivalent to these impedances. These approximations produce all-pass constant-impedance networks (dissipation being neglected) in which the delay is maximally flat in the sense that the first 2m ¿ 1 derivatives of the delay with respect to frequency are zero at the origin; m is an integer expressing the order of the approximation.