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A method for synthesizing bandpass microring filters constructed of N serially coupled microring resonators is presented. The approach is based on the reduction of a chain of N serially coupled microrings to an equivalent prototype baseband LC ladder network. Standard analog-filter-synthesis techniques can then be applied to realize a desired filter transfer function. The proposed method is valid in the narrowband approximation and can be used to synthesize both amplitude and phase filters with the coupled resonators in either the add-drop or allpass configuration. The robustness of the proposed circuit-based method will be demonstrated by two examples: The first is the design of a transitional Chebyshev-Bessel filter, illustrating the useful technique of manipulating filter poles to achieve desired amplitude and phase responses; the second example is the synthesis of an Nth-order maximally flat delay allpass filter. The proposed method can also be applied to other types of serially coupled resonators such as Fabry-Perot cavities and photonic crystal nanocavities to explore novel amplitude and phase filter applications.