New Synthesis of Parallel-Coupled Line Bandpass Filters With Chebyshev Responses

Parallel-coupled line filters with Chebyshev passbands are synthesized based on the insertion-loss functions derived by converting the composite $ABCD$ matrices of all coupled stages. With the synthesis, both the electromagnetic simulation and measurement results have accurate in-band response and bandwidth. Simultaneous equations for Chebyshev filters of order $N leq 9$ are derived for determining geometric parameters of the coupled stages. The tradeoff between circuit bandwidth and ripple level is discussed. In experiments, three planar or quasi-planar structures, including the coupled-line with aperture in the ground plane, the three-line microstrip, and the broadside-coupled lines, are employed to realize the end stages for implementing the high coupling levels. Experimental filters of order up to nine with fractional bandwidth of 30% or 40% are fabricated and measured. The results show good agreement with predictions by the theory and simulation.