Insertion loss function synthesis of maximally flat parallel-coupled line bandpass filters

Insertion loss (IL) functions are derived for synthesis of microstrip parallel-coupled line bandpass filters with maximally flat responses. The derivation is performed by successively multiplying the ABCD matrices of all coupled stages. Simultaneous equations for determining linewidth and line spacing of the coupled stages are established by total Q (Q_T) of the filter specification and comparing the IL function with the canonical form. The results are provided for filters of order N≤6. Two filters with fractional bandwidths Δ=30% are synthesized and demonstrated by simulation using a full-wave software package. In addition, two filters with Δ=40% and 50% are fabricated. Tapped line inputs are employed to these two circuits since some linewidths or gaps are beyond the fabrication resolution. The measured results show very good agreement with the theoretical responses.