Quantization Error Spectra Structure of a DTC Synthesizer via the DFT Axis Scaling Property

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 I integer and M fractional bits, this result simplifies the number of DTC output spectra from 2^I+M to less than M 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.