CXA3106Q
The loop filter F (S) is described below.
The loop filter smoothes the output pulse from the phase comparator and inputs it as the DC component to the
VCO. In addition to this, however, the loop filter also plays an important element in determining the PLL
response characteristics.
Typical examples of loop filters include lag filters, lag-lead filters, active filters, etc. However, the CXA3106Q's
LPF is a current input type active filter as shown below, so the following calculations show an actual example
of deriving the PLL closed loop transmittance when using this type of filter and then using this transmittance to
create a formula for setting the filter constants.
Current input type active filter
C
R
ii
Vo
–A
–1
–Vo
The filter transmittance is as follows.
The Bode diagram for formula (2) is as follows.
VO
A
1
SC
+ VO = (R +
)
1
τ
1 + SRC
A
1 + A
F (S) =
=
·
SC
log w
1 + Sτ
SC
A
·
1 + A
log w
τ = RC
0
Here, assuming A > 1, then:
–45deg
1 + Sτ
SC
...........................
F (S) =
(2)
–90
Next, substituting (2) into (1) and obtaining the overall closed loop transmittance for the PLL:
KPD · KVCO · τ
KPD · KVCO
NC
· S +
NC
θo/N
θr
...
=
=
(3)
KPD · KVCO · τ
KPD · KVCO
S2 +
· S +
NC
NC
2ζωnS + ωn2
S2 + 2ζωnS + ωn2
............................................
(4)
(5)
(6)
KPD · KVCO
......................................................
ωn =
√
NC
1
2
.................................................................
– 27 –
ζ =
ωnτ
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