Maximally flat approximation of attenuation characteristics of coupled-line filters

Coupled-line filters are structurally configured so that each internal line is coupled only to the two adjacent ones; the filter is thus equivalent to a cascade circuit of coupled lines connected in pairs. The transmission matrix of the entire network is found as the product of the transmission matrices of its individual cascaded sections. It is most convenient to utilize wave transmission matrices to describe the parameters of such filters. This approach is employed as the basis for a numerical method of solving the problem of approximating filter attenuation so that the response is maximally flat within the passband and isoextremal in the stopband. The derived algorithm always leads to physically feasible transmission matrix functions. The elements of the filter section conductance matrix are found by means of expanding a special form of the input conductance of the loaded network in a continued fraction.