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ML12179 View Datasheet(PDF) - LANSDALE Semiconductor Inc.

Part Name
Description
Manufacturer
ML12179
LANSDALE
LANSDALE Semiconductor Inc. LANSDALE
ML12179 Datasheet PDF : 11 Pages
1 2 3 4 5 6 7 8 9 10
ML12179
Legacy Applications Information
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
Figure 7. Closed Loop Frequency Response for ζ = 1
Natural Frequency
10
3dB Bandwidth
0
–10
–20
–30
–40
–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 opti-
mum loop bandwidth is15kHz/2.5 or 6kHz (37.7krads) with a
LANSDALE Semiconductor, Inc.
damping coefficient, ζ 1. T(s) is the transfer function of the
loop filter.
Figure 8. Design Equations for the 2nd Order System
( ( ( ( T(s) =
RoCos + 1
=
NCo
KpKv
s2
+
RoCos
+1
2ζ s + 1
ωo
1
ωo2
s2
+
2ζ
ωo
s
+
1
( ( ( NCo
KpKv
=
1
ωo2
→ ωo =
KpKv Co
NCo
KpKv
Nωo2
( ( ( 2ζ
RoCo = ωo → ζ =
oRoCo
2
Ro =
2ζ
ωoCo
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.
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 spreadsheet 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
ωo2
,
RoCo =
2ζ
ωo
Let: Ca = aCo , Cx = bCo , A = 1 + a , and B = 1 + a + b
Let:
RoCo =
1
ω3
,
RxCx =
1
ω4
,
Ro(Ca
+ Cx) =
1
ω5
Let: K3ω3 = ωo , K4ω4 = ωo , K5ω5 = ωo
Page 6 of 11
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