Diophantine Frequency Synthesis The Mathematical Principles

Diophantine Frequency Synthesis1 is a new approach to fine-step and fast-hopping frequency synthesis that is based on mathematical properties of integer numbers and Diophantine equations. Diophantine Frequency Synthesis overcomes the constraining relationship between frequency step and phase-comparator frequency inherent in conventional phase-locked loops. It leads to fine-step, fast-hopping, modular-structured frequency synthesizers with potentially very low spurs, especially near the carrier.