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We have experimentally demonstrated and characterized the generation of tunable and ultra-broadband microwave frequency combs (MFCs) based on a slave laser (SL) subject to regular pulse injection from a current modulated master laser (ML). Under modulation frequency f_m = 1.2 GHz and modulation power P_m = 22 dBm, the current modulated ML is driven into a regular pulse state, and a seed MFC with 14.4 GHz bandwidth within a ±5 dB amplitude variation can be obtained. Such a seed MFC is then injected into the SL for producing final MFC with higher performances. For a fixed detuning frequency f_i = 0 GHz and optimized injection power P_i = 2060 μW, the bandwidth of the final MFC is increased to 33.6 GHz, and the single-sideband phase noises of all comb lines of the MFC within the bandwidth can be decreased to below -90.9 dBc/Hz@10 kHz. Additionally, the influences of P_i and f_m on the MFC bandwidth are also analyzed. The experimental results are in agreement with numerical simulations to a certain extent.