PLL Bandwidth definition and calculation?

gavin114

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. x4 g, a, C4 R7 b8 g1 T5 p1 TWhen 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)?
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0 J5 g/ z# [6 ]& Z- Hand I know Wc means the frequency where gain=1. W-3db means the frequency where gain decrease 3db. what does natural frequency mean?
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: y5 M6 W' }$ n1 S( Y3 _, M( n3, If all the parameters are know, like Ich, Kvco, R,C1,C2. How to get Wc, Wn,
* {" Y6 i* v' cW-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)]
9 A1 N2 |9 |+ H  X* f( W; G9 n' nDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
Open loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
8 ]1 B- U( }$ K& |/ D3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))
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9 x$ r6 d* c  V1 v# F! s! v/ _3 fAre these equations are correct?


* e# }, W8 P! x4 R; c( Z9 cRegards,

renzhq

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

gavin114

Hi, renzhq,
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+ _# G$ z4 e! a$ qI don't think Wc=W-3db?
( @" O7 F: |" s3 z/ [0 hAssume forward transfer is H(s), Closed loop transfer is Close(s), feedback divider ratio is N.

1 z8 d3 Y+ `1 {& H: MSo 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?
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) B( t: a1 G7 w: \* @" b! a1 wThank you?