A series-coupled double-ring resonator with asymmetric radii is analyzed to achieve a filter response with a large free spectral range (FSR), a narrow passband of tens of MHz and a small shape factor simultaneously for use in microwave photonic channelizer. By introducing difference to the two radii, based on the vernier effect, the FSR of the resonator filter can be extended while maintaining the narrow passband and the small shape factor. A filter response with a FSR of 29.444 GHz, a 3-dB bandwidth of 96 MHz and a shape factor of 3.17 is realized by numerical analysis.