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Relationship between Phase margin and zero frequency

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promach

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I am reading the paper "A Design Procedure for All-Digital Phase-Locked Loops Based on a Charge-Pump Phase-Locked-Loop Analogy"

why is phase margin related to zero frequency ? I mean I am not convinced with equation (9). I usually used bode plot, but here how do I derive equation (9) analytically from the transfer function given at equation (7) ?

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