Phase accumulator quantization of a digital to time conversion (DTC) direct frequency synthesizer is analyzed for a fixed output frequency. This paper applies the time/ frequency axis scaling property of the discrete Fourier transform (DFT) to the analysis of the phase accumulator quantization error of a DTC synthesizer. It is shown, using a close approximation, that the quantization spectra associated with all possible output frequencies can be divided into a very small number of classes. The spectra within each class are predictably scaled and rearranged versions of each other. For a DTC that has a phase accumulator with integer and fractional bits, this result simplifies the number of DTC output spectra from to less than classes. Spur values predicted based on the analysis match closely with measurements performed on a 90 nm CMOS DTC synthesizer. It is shown that the choice of specific method of quantization (truncation or round) does not affect non-dc subharmonic spurs. The analysis also applies to a flying adder (FA) synthesizer.Index Terms-DFT axis scaling, digital-to-time converter (DTC) synthesizer, flying adder, quantization error spectra.
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