MC12179 View Datasheet(PDF) - Motorola => Freescale
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MC12179 Datasheet PDF : 11 Pages
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Freescale SMeCm1i2c1o79nductor, Inc.
Figure 10. Transfer Function for the Crystal Noise in the Frequency Plane
+ @ ǒ ) * )Ǔ )ǒ ǒ Ǔ * ) Ǔ T(jw) N
1
j
2z
w
wo
1
K3K4
w4
wo4
B
w2
wo2
z j
2
w
wo
(AK4
K5)
w3
wo3
Figure 11. Transfer Function for the VCO Noise in the Frequency Plane
+ ǒ )ǒ ** Ǔ )Ǔ *ǒ ǒ *) ) Ǔ Ǔ T(jw)
K3K4
w4
wo4
B
w2
wo2
j (AK4
K5)
w3
wo3
1
K3K4
w4
wo4
B
w2
wo2
z j
2
w
wo
(AK4
K5)
w3
wo3
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 generated 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 impedance 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
Vt
+ ) ZLF(s)
RoCos 1
Cos
+ + + Vt(s)
TLF(s) Vp(s) 1 , Vp(s) Kp(s)ZLF(s)
For the 3rd Order PLL: Vp
Ro
Co
Vt
Ca
+ ) ) ) ZLF(s)
RoCos 1
CoRoCas2 (Co Ca)s
+ + + Vt(s)
TLF(s) Vp(s) 1 , Vp(s) Kp(s)ZLF(s)
For the 4th Order PLL: Vp
Ro
Co
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)
MOTOROLA RF/IF DEVICE DATA For More Information On This Product,
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