For given intrinsic losses of a single ring resonator sensor, there exists the maximum sharpness, at the extinction ratio of -6dB. However, the maximum sharpness of a single ring resonator sensor is sensitive for the coupling coefficient. In order to obtain the maximum sharpness, the coupling region of the single rings must have a higher precision of manufacture. To solve this problem, this paper proposed eye-like resonator which is formed by a ring resonator (named inner loop) embedd in the dual-bus-coupled ring resonator (named outer loop). Eye-like resonators can generate the asymmetric Fano-resonance spectra of the drop port, numerical calculation of spectra on the drop port is utilized by the transfer matrix method. As the round trip loss varies, the maximum value of sharpness and the corresponding transmission at the resonant point can be obtained by tuning the phase ratio of the outer loop to the inner loop. The maximum value of sharpness increases with the round trip loss, as the outer loop and inner loop coupling coefficient changing, the maximum value of sharpness of Fano-resonance change slowly in a wide range. As the round trip loss and coupling coefficients of the outer loop and inner loop varies, the corresponding transmission at the resonant point remains almost the same, about -6dB. The sharpness of Fano resonant peak is insensitive for the coupling coefficients, which can reduce the requirements of manufacture of coupling region.