Chirped fiber Bragg gratings can straightforwardly and efficiently be fabricated onto microfibers with a uniform phase mask. Due to the variation of the propagating constant, which depends on the fiber diameter, the broadband spectrum of the grating can be formed. Depending on the different responses to the ambient refractive index in different parts of the grating, the bandwidth of the grating can be tuned by changing the surrounding solution. In addition, by being partly immersed in a liquid, the diameter-chirped Bragg grating can act as a broadband Fabry-Perot interferometer, whose spectrum can be tuned by means of controlling the liquid level and ambient refractive index.