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)?
' g9 U" M1 z4 e" ^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?

. ?8 V2 M4 W& K. U0 e5 J$ x1 g3, 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:

  Q; X1 \; P( d. |( A( T0 FNatural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)]
Damping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)]
Open loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N
1 b: ?9 {" @* [. \. w/ M3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))

Are these equations are correct?


Regards,

renzhq

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

gavin114

Hi, renzhq,

$ \8 d3 y' m1 y) z% vI 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?

! a7 O6 a$ _6 Y% F) N) IThank you?