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In this paper the most recent advances on ferromagnetic resonance (FMR)-based wideband microwave band-stop and band-pass filters using flip-chip yttrium iron garnet (YIG)/gadolinium gallium garnet (GGG)- gallium arsenide (GaAs) layer structures are reported. Specifically, simultaneous enhancement in tunable bandwidths and peak absorption levels by utilizing the meander microstrip line with step-impedance low-pass filter design together with inhomogeneous magnetic field has been accomplished. For example, an ferromagnetic resonance absorption frequency tuning range of 5 to 21 GHz, an absorption level of -35.5 dB and a corresponding 3 dB absorption bandwidth as large as 1.70 GHz, centered at 20.3 GHz, have been accomplished with the band-stop filter. For the band-pass filter large tuning ranges for the center frequency (5.90-17.80 GHz), the pass-band bandwidth (1.27-2.08 GHz) as well as the two guarding stop-bandwidths (0.45-1.70 GHz), and an out-of-band rejection of -33.5 dB were demonstrated. A good agreement between the simulation and experimental results has been achieved. Finally, some desirable measurement data on the microwave power capability and the magnetic tuning speed of the filters has also been obtained.