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We present a systematic study of two-ring-one-bus (2R1B) and two-ring Mach-Zehnder interferometer (2RMZI). By exciting the cavity modes in certain ways, it is possible to shape the transmission spectrum that may be suitable for specific applications, such as relaxation of critical coupling for the case of 2R1B or finesse enhancement for the case of 2RMZI. The deteriorating effects of resonator self-coupling known as coupling-induced resonance frequency shift is quantized. The two-ring structures are demonstrated on a silicon-on-insulator platform where good agreement is obtained between the experiment and the theory.