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,
and 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,
6 d: Z# I, l9 s$ b' N5 BW-3db, Phase Margin, Damping factor. can anyone give the formulars ? I found some thing for internet:
4 U5 ~1 g5 t; r% X  c( p
Natural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
) W% o" _- ~, S" F8 @0 d- ~' LDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
Open loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
6 Z" S1 Q, m. l! L8 h1 n3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))

" W. z' z2 Y2 q3 Q; u9 u* _- f4 k6 KAre these equations are correct?

" u% ]# O2 N, i: |8 F
: I. ]4 a/ r9 H) yRegards,

renzhq

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

gavin114

Hi, renzhq,

+ t0 z: J* b3 Y  W3 v6 bI 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?

2 v$ S9 c( M4 }! T! z+ k8 S. @Thank you?