Loop Filter for PLL

Hello to All

I have a question concerning the phase lock loop,

I could not understand the Loop filter:


in Wikipedia :https://en.wikipedia.org/wiki/Phase-locked_loop#Li...

the where two types of Filter:

1. one-pole RC circuit
2.the lag-lead filter with one pole and one zero.


i have also read , that the Filter can be realized with a Pi-Controller.
But the Transferfuntion of a Pi Controller is not equal with the two type of filters above,
and is a Pi Controller also an Low pass filter?
So how to use a Pi controller as the loop Filter?

Thx

The loop filter is simply an integrator, a device that changes the rectangular error pulse coming from the phase comparator into an analog voltage that is used as the input to the voltage-controlled oscillator (VCO). As long as the component values are selected so that the integrator works correctly within the desired range of frequencies either should work. You simply connect the input of the PI controller to the output of the phase comparator, and connect the output of the PI controller to the input of the VCO.