標題: PLL Bandwidth definition and calculation? [打印本頁] 作者: gavin114 時間: 2009-3-30 01:53 PM 標題: PLL Bandwidth definition and calculation? 1, 2 B9 w$ d3 b+ D3 [$ _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)?; V5 q+ O: s4 h# ^/ C
2, # U" O. i7 {9 M& Cand I know Wc means the frequency where gain=1. W-3db means the frequency where gain decrease 3db. what does natural frequency mean?2 ^: P9 g, C; \0 J0 O4 }
+ Q( K3 ? w' |# {3 m: G/ M3, If all the parameters are know, like Ich, Kvco, R,C1,C2. How to get Wc, Wn, ( v0 n; f- M4 r8 iW-3db, Phase Margin, Damping factor. can anyone give the formulars ? I found some thing for internet: 0 e& ?1 V2 J) R# V |3 Q8 N( k/ x( g+ z# o' U4 i: R
Natural Freq: Wn=sqrt[(Kvco*Icp)/(2*pi*Cbig*N)] # K& `. E' g1 y( j' ~( W1 s, MDamping Factor: zeta=(Rlpf/2)*sqrt[(Icp*Cbig*Kvco/2*pi*N)] * i' \; s# g6 h: XOpen loop bandwidh Freq: w0=(Icp*Kvco*Rlpf)/2*pi*N" _; P3 s6 u9 W2 }
3dB Bandwidth: w3dB=wn*sqrt(1+2*zeta^2+sqrt(2+4*zeta^2+4*zeta^4))5 n, _. s0 r1 |+ c G% N: N I; n a
: N2 N1 z. g$ R( u& I. O" I5 q3 QRegards,作者: renzhq 時間: 2009-3-31 11:33 AM
it is Wc, if we make an approximate，it equals W-3db作者: gavin114 時間: 2009-4-2 05:59 PM 標題: 回復 2# 的帖子 Hi, renzhq, $ x0 b- R( G4 l$ E9 ^, j L0 [4 L' z/ _. y( N- |/ c
I don't think Wc=W-3db?# X# Y) Z: t, f
Assume forward transfer is H(s), Closed loop transfer is Close(s), feedback divider ratio is N. ; r1 [! X w% n2 L0 C5 a9 O% m0 X$ \; _6 L$ l1 ?
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?6 W9 `1 A8 S! l9 r o