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Does positive clock skew only tightens the hold time and there is no change on setup time, similarly does negative skew only tightens setup time and there is no change in hold time.

Is this right?

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The diagrams below with the setup and hold requirement inequalities, illustrate how clock skew helps or hurts meeting hold or setup

Illustrating clock tree buffers that help or hurt setup and hold

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Clock skew will effect both setup and hold.

On a hold path, clock skew directly influences your hold time margins because you must hold to the slowest possible receiver clock wrt launching clock.

On a setup path, clock skew directly influences your setup margins because you must setup to the fastest possible receiver clock wrt to launching clock.

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