W3000 Datasheet, PDF (20/28 Pages) Agere Systems – W3000 PLL Dual-Band Frequency Synthesizer

W3000 PLL Dual-Band Frequency Synthesizer
Advance Data Sheet
December 1999
Application Information (continued)
General rules for the values of these components have been derived many times¹, and are quoted here merely
for reference. If:
T1 = ^{sec φ − tan φ}
ω_p
T2
=
ω^2c
1
* (T1+
T3)
T3 = ^{10attn / 20 − 1}
(2π * FREF)²
where
φ = Phase margin required, normally 45° for a critically damped response.
ω_p = Loop bandwidth.
ω_c = Loop bandwidth modified for extra pole of R3 and C3, as described by:
ω_c
=
tan φ * (T1+ T3)

*^
(T1+ T3)² + (T1* T3) ^
1+
(T1+ T3)² + (T1* T3)
[tan φ * (T1+ T3)]²
−

1^

fREF = Reference frequency.
atten = Attenuation provided by the third pole at the reference frequency.
The loop filter values can then be derived as:
C1 =
T1
*
KPD
*
Kvco
*


(1 + ω_c2 * T2² )
^{1/ 2}

T2 _ωc ² _{* N (1 + ωc} ² _{* T1}² _{)(1+ ωc} ² _{* T3}² _{) }
C2 = C1*  ^T2 − 1
 ^T1 
R1 = ^T2
C2
The final pole, consisting of R2 and C3, should be chosen such that the following guidelines are followed:
C3 ≤ ^C1 and R2 ≥ 2 * R1
10
1. Rohde, Ulrich L., Digital PLL Frequency Synthesizers Theory and Design, Prentice-Hall, 1983.
20
Lucent Technologies Inc.