why CT delta-sigma modulator needs a DFF at its output?

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sapphire

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Looks like if there is not the DFF, the output will enter a limited-cycle osicllation? I am not sure how to express that meaning in a formal language. Thanks

Edward
 

the comparator is not clocked, so the book is telling you that you need a clocked comparator to create a known delay in the loop.
 

after the clock introduced, the system becomes a 'controlled' sampling system, and the output is meaningful. it also has limited-cycle osicllation, cant avoid.
 

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