Behavioral model for DPLL

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jihrenee

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i'm doing behavioral model (MATLAB) for digital PLL
the most significant difference between DPLL and analog PLL is the filter
where digital loop filter of DPLL is consists of a proportional path and integral path (2nd-order system)
my problem is, for propotional path and integral path
should i use a PI controller rather than the realization as the picture shown?

Where the PI controller is in the discrete domain, and the picture shown is in s-domain (continuous)
2 methods come different results.
 

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