Improved formulas for synthesizing multiple-mode-resonator-based UWB bandpass filters

This paper proposes improved design formulas for parallel-coupled microstrip bandpass filters with ultra-wideband multiple-mode resonators. A corrected electrical length θ_c has been introduced into the formulation for synthesizing these kinds of filters. Accurate predictions for fractional bandwidths Δ > 50% are achieved. Characteristic impedances of each coupled and connecting lines are calculated for achieving the required bandwidth and determining geometric parameters. Two filters with Δ = 70% and 90% are designed and fabricated. Measured results show a good agreement with those obtained from prediction.