A comparative study on characteristics and performance of optical ring resonator architectures, i.e. circular, racetrack, and triangular-shaped optical resonators, have been carried out here. Constituent material used for designing these resonators is an silicon on insulator wafer consisting of thin silicon (Si) layer on silica (SiO 2) layer carried on a thick Si substrate having group index of 2.379. All the resonators are so designed that all provide equal free spectral range (FSR) of 25.2 THz. All these double-ring architectures have been analysed using delay line signal processing technique in z-domain and Mason's gain formula. FSR expansion has been achieved employing the Vernier principle. Various performance defining parameters have been also investigated.