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Any formula about settling time and loop-filter bandwidth?

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settling time formula

As we can see, the wider the loop-filter's bandwidth,the shorter the settling time.
Now I want to know the exact formula revealing this relative!
Thank you!
 

loop bandwidth formula

Please refer to Dean's PLL book which you can get it free from National Semiconductor website. In the book, you will definitely find the formulae you want.

For quick estimation, lock time is about 2.5 times of the inverse of your loop bandwidth.
 

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