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A photonic microwave true-time delay based on a tapered fiber Bragg grating (FBG) with resistive coating has been proposed and demonstrated. It features voltage-controlled continuous operation, requiring no moving parts and no mechanical perturbation. The time delay of a microwave signal carried over an optical signal is obtained by electrically controlling the reflection positions of it from the tapered FBG via the thermooptic effect. The achieved time delay was about 105 ps with the electrical power consumption of 48 mW.