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A digital ΔΣ fractional-N frequency synthesizer for 4G communication standards is presented which is able to achieve wide loop bandwidth while producing low fractional spurs. The loop adopts a fractional-N divider based on a phase interpolator, allowing to shrink the TDC dynamic range and to improve its linearity. A dynamic-element matching algorithm is employed to further improve TDC linearity and an original correlation algorithm is used to correct for the phase interpolator mismatches. Both digital algorithms operate in background and they are demonstrated to be concurrently effective in reducing in-band fractional spurs below -57 dBc. The circuit is fully integrated in a 65 nm CMOS process and it synthesizes a carrier in the 3.0-3.6 GHz range from a 40 MHz crystal reference with 40 Hz resolution. It achieves -104-dBc/Hz phase noise at 400-kHz offset and a 3.2-MHz maximum loop bandwidth. The synthesizer dissipates 80 mW and occupies 0.4 mm2.