MC12179D View Datasheet(PDF) - LANSDALE Semiconductor Inc.
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MC12179D Datasheet PDF : 11 Pages
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ML12179
Legacy Applications Information
LANSDALE Semiconductor, Inc.
Figure 10. Transfer Function for the Crystal Noise in the Frequency Plane
T(jω) = N •
1+j
(2ζ
ω
ωo
)
( ( 1
+
K3K4
ω4
ωo4
–
B
ω2
ωo2
+j
2ζ
ω
ωo
–
(AK4
+
K5)
ω3
ωo3
Figure 11. Transfer Function for the VCO Noise in the Frequency Plane
T(jω) =
( ( K3K4
ω4
ωo4
–
B
ω2
ωo2
–j
(AK4
+
K5)
ω3
ωo3
( ( 1 +
K3K4
ω4
ωo4
–
B
ω2
ωo2
+j
2ζ
ω
ωo
–
(AK4 +
K5)
ω3
ωo3
Appendix: Derivation of Loop Filter Transfer Function
The purpose of the loop filter is to convert the current from the
phase detector to a tuning voltage for the VCO. The total transfer
function is derived in two steps. Step 1 is to find the voltage gen-
erated by the impedance of the loop filter. Step 2 is to find the
transfer function from the input of the loop filter to its output.
The “voltage” times the “transfer function” is the overall transfer
function of the loop filter. To use these equations in determining
the overall transfer function of a PLL multiply the filter's imped-
ance by the gain constant of the phase detector then multiply that
by the filter's transfer function (which is unity in the 2nd and 3rd
order cases below).
Figure 12. Overall Transfer Function of the PLL
For the 2nd Order PLL: Vp
Ro
Co
For the 3rd Order PLL: Vp
Ro
Co
For the 4th Order PLL: Vp
Ro
Co
Vt
ZLF(s) =
RoCos + 1
Cos
Vt(s)
TLF(s) = Vp(s) = 1 , Vp(s) = Kp(s)ZLF(s)
Vt
Ca
ZLF(s) =
RoCos + 1
CoRoCas2 + (Co +
Ca)s
Vt(s)
TLF(s) = Vp(s) = 1 , Vp(s) = Kp(s)ZLF(s)
Ca Rx
Vt
Cx
(RoCos + 1) (RxCxs + 1)
ZLF(s) = CoRoCaRxCxs3 + [ (Co + Ca)RxCx + CoRo(Cx + Ca) ] s2 + (Co + Ca + Cx)s
TLF(s) =
Vt(s)
Vp(s)
=
1
(RxCxs
+
1)
,
Vp(s) = Kp(s)ZLF(s)
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