PLL Bandwidth definition and calculation?

gavin114

1,
, v3 [1 Q7 N% \" S7 l) z6 HWhen 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,
! G) s" h, C0 b0 [0 fand 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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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:
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8 e$ o6 }9 D! ?* y, a  ~3 gNatural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
7 {1 C- e8 N& @) ~: Q4 Y# |* pDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
Open 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))
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* P3 {% I0 d; _' ^5 ~Are these equations are correct?
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- E$ @6 U' L* Y( MRegards,

renzhq

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

gavin114

Hi, renzhq,

8 D& D/ x6 o6 CI don't think Wc=W-3db?
2 ]& ~  D+ {( c6 D' q( Z6 tAssume 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?