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We propose a general variable bandwidth filter of arbitrary even order based on the sum-difference microring filter architecture. The filter bandwidth can be varied by tuning only the resonant frequencies of the microrings and thus do not require additional controls other than those used to tune the filter center frequency. In addition, we show that there exists a bandwidth tuning range over which the filter exhibits no extra insertion loss and no degradation in the filter shape. We demonstrated a <inline-formula><tex-math notation="LaTeX">4^{\text {th}}</tex-math></inline-formula>-order variable bandwidth filter in Silicon-on-Insulator, achieving a bandwidth tuning range from 0.3 nm to 1.35 nm with a maximum in-band ripple of 3 dB. The proposed variable bandwidth filter could serve as a key element in elastic optical networks which can support variable data bandwidth allocation on demand.