Skip to Main Content
Cascaded diophantine frequency synthesis (CDFS) is an approach to high-resolution frequency synthesis based on the mathematical properties of integer numbers and diophantine equations. CDFS can be implemented using two or more phase-locked loops (PLLs) and frequency mixing stages in a cascade topology. CDFS achieves frequency resolution arbitrarily finer than that of the constituent PLLs while maintaining their loop bandwidths and frequency hopping agility. CDFS results in intermediate signals with minimal frequency ranges in all frequency mixing stages, allowing for improved spectral purity and lower design complexity compared to the parallel form of its predecessor, diophantine frequency synthesis (DFS). CDFS architectures are modularly structured and expandable. The paper introduces CDFS focusing on the mathematical and algorithmic aspects.