MC12179 View Datasheet(PDF) - Motorola => Freescale
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MC12179 Datasheet PDF : 11 Pages
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Freescale SMeCm1i2c1o79nductor, Inc.
Figure 6. Graphical Analysis of Optimum Bandwidth
–60
Optimum Bandwidth
–70
–80
VCO
–90
–100
20*log(256)
–110
–120
–130
–140
–150
10
Crystal Reference
100
1k
15dB NF of the Noise
Contribution from Loop
10k
100k
1M
Hz
15kHz/2.5 or 6kHz (37.7krads) with a damping coefficient,
ζ ≈ 1. T(s) is the transfer function of the loop filter.
Figure 8. Design Equations for the 2nd Order System
+ ǒ Ǔ ) ) ) + ǒ Ǔ ǒ )Ǔ ǒ)Ǔ ) T(s)
RoCos 1
NCo s2
KpKv
RoCos
1
2z
wo
s
1
1
wo2
s2
2z
wo
s
1
ǒ Ǔ ǒ Ǔ Ǹ ǒ Ǔ + ³ + ³ [ NCo
KpKv
1
wo2
wo
KpKv
NCo
Co
KpKv
Nwo2
ǒ Ǔ ǒ Ǔ ǒ Ǔ + ³ + ³ + RoCo
2z
wo
z
woRoCo
2
2z
Ro woCo
Figure 7. Closed Loop Frequency Response for ζ = 1
Natural Frequency
10
3dB Bandwidth
0
–10
–20
–30
–40
In summary, follow the steps given below:
Step 1: Plot the phase noise of crystal reference and the
VCO on the same graph.
Step 2: Increase the phase noise of the crystal reference by
the noise contribution of the loop.
Step 3: Convert the divide–by–N to dB (20log 256 – 48 dB)
and increase the phase noise of the crystal
reference by that amount.
Step 4: The point at which the VCO phase noise crosses the
amplified phase noise of the Crystal Reference is the
point of the optimum loop bandwidth. This is
approximately 15 kHz in Figure 6.
–50
–60
0.1
1
10
100
1k
Hz
To simplify analysis further a damping factor of 1 will be
selected. The normalized closed loop response is illustrated
in Figure 7 where the loop bandwidth is 2.5 times the loop
natural frequency (the loop natural frequency is the
frequency at which the loop would oscillate if it were
unstable). Therefore the optimum loop bandwidth is
Step 5: Correlate this loop bandwidth to the loop natural
frequency and select components per Figure 8. In
this case the 3.0 dB bandwidth for a damping
coefficient of 1 is 2.5 times the loop’s natural
frequency. The relationship between the 3.0 dB loop
bandwidth and the loop’s “natural” frequency will
vary for different values of ζ. Making use of the
equations defined above in a math tool or spread
sheet is useful. To aid in the use of such a tool the
equations are summarized in Figures 9 through 11.
Figure 9. Loop Parameter Relations
+ + Let: NCo
KpKv
1
wo2
,
RoCo
2z
wo
+ + + ) + ) ) Let: Ca aCo , Cx bCo , A 1 a , and B 1 a b
+ + ) + Let: RoCo
1
w3
,
RxCx
1
w4
,
Ro(Ca
Cx)
1
w5
+ + + Let: K3w3 wo , K4w4 wo , K5w5 wo
6
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