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)?
. q6 n" S" C6 c' M2 u' ]5 u) ^; |2,
4 p, B. m3 `8 `- d  {6 \  ?$ yand I know Wc means the frequency where gain=1. W-3db means the frequency where gain decrease 3db. what does natural frequency mean?

  V0 T- {/ Q' X3, 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:

Natural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
, u# T% @. Q$ f. v( ]Damping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
4 B+ B5 i4 B5 D1 t7 t  v. BOpen loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))
' S% H% ^% D+ n3 n" \
Are these equations are correct?


! w( P& K# v) E1 URegards,

renzhq

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

gavin114

Hi, renzhq,
2 X( r7 o# R* r$ N. Q4 c
I don't think Wc=W-3db?
Assume 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?
/ t6 u$ b' r% e% r
Thank you?