PLL Bandwidth definition and calculation?

gavin114

1,
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)?
2,
" v, q  I7 H" p7 Q; j0 G3 n* t0 h4 yand 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,
5 b: ?* w6 g- v0 f$ C$ oW-3db, Phase Margin, Damping factor. can anyone give the formulars ? I found some thing for internet:

% Q6 ?4 @/ f' R' b' QNatural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
& @  B. p4 p% e; j: m% b# DDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
1 y, J8 c8 m; XOpen loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
: Z3 {# a3 T5 \; \3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))
5 ?5 }' Y: }0 Y# Y0 g: T
  L; t/ w( y$ b& OAre these equations are correct?
& p9 c- j% V+ |) y8 W# I9 |

Regards,

renzhq

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

gavin114

Hi, renzhq,
! M2 H) ^1 {+ r/ Y1 j. J; Y
; K9 _) R2 q) p( M  fI don't think Wc=W-3db?
1 m1 ]* R* C- k5 \" D4 qAssume forward transfer is H(s), Closed loop transfer is Close(s), feedback divider ratio is N.
% ]5 o0 [/ _& M" I! f3 B
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?

7 e+ }3 H! f, ~) KThank you?