The mathematical model of an optical ring resonator (RR) configuration using a single directional optical coupler (DOC) with a uniform fiber Bragg grating (FBG) incorporated and an RR configuration using two DOCs with an FBG incorporated is developed in the Z-domain. The developed mathematical model is used for the evaluation of transmission response. Spectral characteristics in terms of peak transmittance, resonant frequency, and free spectral range are determined for a single fiber ring configuration using two DOCs with an FBG incorporated. The results are found to be in very close agreement with measured values. The transmission characteristic of the single waveguide structure comprising a ring of length 2 mm enclosing a Bragg grating is analyzed. By properly optimizing the grating reflectivity and power coupling ratios of the coupler, a narrow full width at half maximum of 4.72 GHz that is around 78 times sharper than the normal FBG resonance is obtained. Further narrowing of the spectral width is achieved by increasing the RR length. The grating lengths are chosen judiciously to minimize the side peaks. The group delay and dispersion characteristics are addressed.