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Broad-bandwidth amplification is essential for the construction of high-capacity multichannel communication systems. We describe a silica-based erbium doped fiber amplifier (EDFA) with a flat gain bandwidth exceeding 40 nm. The dual-stage EDFA includes a precisely designed inter-stage long-period fiber grating filter with more than 14-dB peak attenuation. By careful choice of the filter spectrum and fiber lengths, this EDFA is flat to within 1 dB over 40 nm while producing a noise figure below 4.0 dB and nearly +15-dBm output power.