damping factor and Phase margin in PLL

[flesher]

In the second order control systerm
Hclosd(s)=Wn^2/(S^2+2EWnS+Wn^2), where E=damping factor.
Normally, the larger damping factor, the more stable for the systerm.

In third order type II PLL,
Hcolsed(s)=Wn^2(1+S/Wz)/(S^2+2EWnS+Wn^2),
Here: Natural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
Damping Factor: E=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
Phase margin: PM=arcten(Wc/Wz)-arcten(Wc/Wp)
However, damping factor here increases, the PM is not necessary to increase. It looks it has a maximum PM when damping factor increases.

So I am confused about these. hope someone to explain, thank you very much.

 

[love_analog]

Yes, we deliberately limit the PM of 3rd order by bringing in a pole (to limit the phase jumps).

But its okay since we don't care about PM being too high. with 2nr order you can get 90 PM (theoretically). Not so with 3rd order.