A system of an add-drop microring resonator integrated with a sampled grating distributed feedback (SG-DFB) is investigated via modeling and simulation with the time-domain traveling wave (TDTW) method. The proposed microring resonator comprises a ${\mathrm{SiO}}_2$ waveguide integrated with an InGaAsP/InP SG-DFB, and the ${\mathrm{SiO}}_2$ waveguide consists of a silicon core having a refractive index of 3.48 and Kerr coefficient of $4.5\times {10}^{18}{\mathrm{m}}^2/\mathrm{W}$. The SG-DFB consists of a series of grating bursts that are constructed using a periodic apodization function with a burst spacing in the grating of 45 μm, a burst length of 5 μm, and 10 bursts across the total length of the SG-DBR. Transmission results of the through and drop port of the microring resonator show the significant capacity enhancement of the generated center wavelengths. The $Q$-factor of the microring resonator system, defined as the center wavelength (${\lambda }_0$) divided by 3 dB FWHM, without and with integration with the SG-DFB is calculated as $1.93\times {10}^5$ and $2.87\times {10}^5$, respectively. Analysis of the dispersion of the system reveals that increasing the wavelength results in a decrease of the dispersion. The higher capacity and efficiency are the advantages of integrating the microring resonator and the InGaAsP/InP SG-DFB.