Planar compact ellipticfunction low-pass filter using high-permittivity ceramics substrate

A component elliptic-function low-pass filter using microstrip stepped-impedance hairpin resonators and their equivalent-circuit models is developed. The prototype filters are synthesized from the equivalent-circuit model using available element value tables. To optimize the performance of the filters, electro-magnetic simulation is used to tune the dimensions of the prototype filters. The filter using multiple cascaded hairpin resonators provides a very sharp cutoff-frequency response with low insertion loss. The full-wave simulator IE3D is used to design the elliptic-function low-pass filter. The response of the fabricated filter using Al₂O₃ (ε_r = 9.7, Q × f = 350,000 GHz) and La(Mg _1/2Ti_1/2)O₃ (ε_r = 28.6 Q × f = 60,000 GHz).