A model of the GS9035A PLL is shown below. The main
components are the phase detector, the VCO, and the
external loop filter components.
0
PHASE
DETECTOR
Ø
+
i
VCO
Ι
K
CP
PD
2πK
f
-
Ø
o
Ns
R
LF
LOOP
FILTER
C
LF2
C
LF1
W
W
W
W
P2
Z
P1
BW
FREQUENCY
Fig. 16 Bode Plot for PLL Transfer Function
Fig. 15 PLL Model
The transfer function of the PLL is defined as Øo/Øi and can
be approximated as
The 3dB bandwidth of the transfer function is approximately
wBW wBW
--------------------------------------------------------------------- -----------
w3dB
=
≈
0.78
2
sCLF1RLF + 1
Øo
1
wBW
-----------
wP2
(wBW ⁄ wP2
+ ---------------------------------
wBW
-----------
)
------------------------------------------------------------------------------------------------------------------------
------ =
Øi
1 – 2
L
L
s2CLF2L + s
+ 1
s CLF1
R
LF – ---------- + 1
---------
RLF
RLF
1 – 2
wP2
Equation 1
Transfer Function Peaking
where
There are two causes of peaking in the PLL transfer function
given by Equation 1.
N
L = -------------------
DICPKƒ
The first is the quadratic
N is the divider modulus
L
RLF
s2CLF2L + s
+ 1
---------
D is the data density (=0.5 for NRZ data)
ΙCP is the charge pump current in Amps
Kƒ is the VCO gain in Hz/V
which has
1
CLF2
Q = RLF ------------
L
wO = --------------------
CLF2
L
This response has 1 zero (wZ) and three poles (wP1, wBW
,
and
wP2) where
This response is critically damped for Q = 0.5.
Thus, to avoid peaking:
1
wZ = ----------------------
CLF1RLF
CLF2
RLF ------------ <
L
1
2
--
1
wP1 = --------------------------------------
L
C
LF1RLF – ---------
RLF
or
1
L
RLF
wBW = ---------
L
-------------------------------
> 4
RLFCLF2RLF
1
Therefore,
wP2 = ----------------------
CLF2RLF
wP2 > 4 wBW
The bode plot for this transfer function is plotted in Figure
16.
However, it is desirable to keep wP2 as low as possible to
reduce the high frequency content on the loop filter.
10
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