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Optical frequency synthesis (OFS) based on self-referenced optical combs has enabled a variety of applications including absolute optical frequency measurements, optical spectroscopy, gas sensing, light detection and ranging (LiDAR), and optical frequency metrology. Arbitrary OFS can be achieved by locking a Continuous-Wave (CW) tunable laser to a programmable offset across multiple comb teeth. This report describes the design of a Radio Frequency (RF) frequency synthesizer that will generate this programmable offset, enabling the optical synthesizer to span frequencies between the comb lines with 1Hz tuning resolution and 10^{-13}/tau Allan deviation. The RF-synth tuning range requirement is 1GHz as dictated by the distance of adjacent optical comb teeth. To satisfy these specs, a Flying Adder frequency synthesis topology is selected. A simulation framework that evaluates the effect of different synthesizer variants on the spectral content and stability of the synthesized output has been implemented in MATLAB Simulink. Simulations of this model are used as a guide for actual circuit design choices. Finally, measurement results of the synthesizer that has been built in silicon are presented.

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