This paper proposed and analyzed a novel ring resonator structure with feedback Mach Zehnder based on the coupled mode theory and transfer matrix, and using the method of normalized transmission  changing with the effective refractive index to analyze the structure. By optimizing the structure parameters  it was found that the proposed structure had a sharp steep  antisymmetric Fano output spectrum. Compared with the traditional microring resonator output curve line, i.e., the symmetry Lorentz spectrum, the output light intensity is more sensitive to  perceive the external environment change. Therefore, the structure has a higher sensitivity and lower detection limit. In the 30 dB signaltonoiseratio(SNR) measuring systems, the detection limit of the structure reaches 10-9 units of the refractive index, which is one order of magnitude lower than the reported 10-8 units of refractive index.