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We describe a broad-band lightwave synthesized frequency sweeper (LSFS) that uses synchronous filtering. We control the center frequency of the bandpass filter (BPF) in the LSFS so that it tracks the frequency of the circulating pulse. In the first half of this paper, we numerically simulate the accumulation of amplified spontaneous emission (ASE) noise in the LSFS and confirm the effectiveness of synchronous filtering in suppressing the noise. We show that the frequency sweep span can be enlarged to cover the erbium-doped fiber amplifier gain bandwidth completely if ideal synchronous filtering is realized. We also describe the way in which the fluctuation of the BPF center frequency severely limits the number of pulse circulations and we estimate the accuracy required for the BPF center frequency control. In the second half, we report our experimental results. We confirmed the completion of more than 10 000 pulse circulations, which corresponded to a frequency sweep span of >1.2 THz. We also estimated the accuracy of the BPF center frequency control experimentally. As a result, the relationship between the accuracy and the number of pulse circulations was in good agreement with that obtained in the simulation.