Diophantine Frequency Synthesis A Number Theory Approach to Fine Frequency Synthesis

Abstract

Diophantine frequency synthesis is a new approach to fine-step, fast-hopping, low-spurs frequency synthesis that is based on mathematical properties of integer numbers and linear Diophantine equations. Diophantine frequency synthesis overcomes the constraining relation 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 in the vicinity of the carrier