Direct digital frequency synthesizers with the /spl Sigma/-/spl Delta/ arrangement in the PLL systems

Discussed generation of spurious signals in phase locked (PLL) fractional-N direct digital frequency synthesizers (DDS), with different numbers of DDS accumulators in the auxiliary feedback path. We started with discussion of the simple arrangements with one DDS accumulator. However, main attention was paid to the systems with three accumulators since they exhibit very low level of spurious signals close to the carrier which is of advantage in PLL systems. Since we have experienced difficulties with the generally used relation for the spurious spectral level, based on the application of the Z-transform, we have revised the problem with inspection of the pulse swallowing process. With the assistance of the Fourier series we have computed spectral components due to the imposed frequency modulation, investigated power of the spurious signals in respect of the number of bits in the used E-A accumulators and corrected the formula for expected spurs power.