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The spectral characteristics of a ring resonator made of Si photonic wires are modeled using mode expansion of supermodes of the directional coupler. The influence of the coupling coefficient, loss factor and waveguide dispersion on the spectral features are analyzed in detail. The model is then compared with the experimental data of a ring resonator designed for sensing purposes. The model that includes a wavelength dependence on coupling length reproduces the large variations of the envelope of the experimental spectrum, when coupling coefficient cover its full range from 0 to 1. Fitting parameters explain the details of the experimental spectrum and contribute to the sensor optimization, as well as illustrating general guidelines for ring resonator design.