The coherent population trapping (CPT) atomic clock is very promising for use in next-generation spaceborne applications owing to its compactness and high performance. In this paper, we propose and implement a CPT atomic clock based on the direct modulation of a large-modulation-bandwidth and narrow-linewidth distributed Bragg reflector laser, which replaces the usually used external bulk modulator in the high-performance CPT clock. Our method retains the high performance while significantly reducing the size. Using this highly compact bichromatic light source and simplest CPT configuration, in which a circularly polarized bichromatic laser interrogates the ^{87}Rb atom system, a CPT signal of clock transition with a narrow linewidth and high contrast is observed. We then lock the local oscillator frequency to the CPT error signal and demonstrate a short-term frequency stability of 3.6 times 10^{-13} {tau}^{-1/2} (4 s le {tau} le 200 s). We attribute it to the ultralow laser frequency and intensity noise as well as to the high-quality-factor CPT signal. This study can pave the way for the development of compact high-performance CPT clocks based on our scheme.
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