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Continuous tuning of the frequency of laser light is the cornerstone for a plethora of applications in basic science as well as in the industrial environment. They range from the hunt for gravitational waves, the realization of optical clocks over health and environmental monitoring to distance measurements. So far, it is difficult to combine a wide tuning range (> 100 GHz) with sub-microsecond tuning times, intrinsic tuning linearity and coherence lengths beyond 10 m. We show that electro-optically driven adiabatic frequency converters using high Q microresonators made of lithium niobate are able to transfer arbitrary voltage signals into frequency chirps on time scales far below 1 {\mu}s. The temporal variation of the frequency nicely agrees with the one of the voltage applied. Superimposing the converted light with the unconverted one, we derived from the beat signal that 200-ns-long linear frequency chirps deviate less than 1 % from perfectness without any additional measures. The Coefficient of Determination is R2 > 0.999. The coherence length of the emitted light is of the order of 100 m. In order to prove these findings, we apply linear frequency sweeps for FMCW LiDAR for distances between 0.5 and 10 m without any signs of nonlinearity. Combined with the demonstrated ns tuning, with the potential to tune the eigenfrequency of lithiumniobate-based resonators by several 100 GHz, our results show that electro-optically driven adiabatic frequency converters can be used in applications that require ultrafast and flexible continuous frequency tuning with intrinsic linearity and large coherence length.