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A continuously tunable photonic microwave bandpass filter with positive and negative coefficients implemented using an optical phase modulator and chirped fiber Bragg gratings (FBGs) is proposed and experimentally demonstrated. The positive and negative coefficients are generated through optical phase-modulation to intensity-modulation conversion by reflecting the phase-modulated optical carrier from linearly chirped FBGs (LCFBGs) with positive and negative dispersions. The tunability of the filter is realized by changing the wavelength of the optical carrier such that it is reflected at different physical locations in the LCFBGs. A two-tap microwave bandpass filter with a free spectral range tunable from 1.14 to 4.55 GHz is experimentally demonstrated.