PLL Bandwidth definition and calculation?

gavin114

1,
' u/ @6 q- a' t  ]When designing PLL, it is always said that PLL's bandwidth should be set to be smaller than Fref/10. what's the PLL bandwidth? Is it Wc(open loop unit gain bandwidth), Wn( Natural frequency) or W-3db ( closed loop -3db frequency)?
" B1 j8 p1 y; I- y, i3 w, ^2,
7 [, p. N2 \& G( o) cand I know Wc means the frequency where gain=1. W-3db means the frequency where gain decrease 3db. what does natural frequency mean?

3, If all the parameters are know, like Ich, Kvco, R,C1,C2. How to get Wc, Wn,
W-3db, Phase Margin, Damping factor. can anyone give the formulars ? I found some thing for internet:

0 F3 H, ?/ V9 k; E" z, INatural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
5 w9 c' x' w* D7 v2 K$ `* sDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
+ V$ C4 a  \8 K4 p  ^! U( a) _Open loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
( N; C, _* M8 k8 o1 T* M2 [% V3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))

1 [3 c5 q& X% j1 ]Are these equations are correct?
  w+ V7 H8 o8 T0 ^% |4 k2 g
9 b5 q7 l2 B8 a) ?
Regards,

renzhq

it is Wc, if we make an approximate，it equals W-3db

gavin114

Hi, renzhq,
+ ]$ c# X2 n/ v0 W0 H4 W
; l3 N/ X' m8 S) [4 E+ lI don't think Wc=W-3db?
$ R3 T" f+ D3 o% W, o% l" Y7 DAssume forward transfer is H(s), Closed loop transfer is Close(s), feedback divider ratio is N.

So Closed(s)=H(s)/(1+H(s)/N),  W-3db is the root when 1+H(s)/N=0, and Wc is the root when |H(s)/N/=1. Are their roots same?

Thank you?