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Input range of delta sigma in fractional-N synthesizer

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knights

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I got a problem when I read some paper about delta-sigma modulator in fractional-N synthesizer.

For my understanding, the input range of DSM is 0~1, because normally, N= M+k/2^K.But in some papers, it mentioned input stable range covers from 0.5 to 1.5 ( Keliu Shu, a comparative study of digital delta-sigma modulators for fractional-N synthesizer) and other input range in other papers.

Anybody can give me some explaintion about that ?

Thanks
 

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