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ML12179-5P Arkusz danych(PDF) 6 Page - LANSDALE Semiconductor Inc.

Numer części ML12179-5P
Szczegółowy opis  500-2800 MHz Single Channel Frequency Synthesizer
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Producent  LANSDALE [LANSDALE Semiconductor Inc.]
Strona internetowa  http://www.lansdale.com
Logo LANSDALE - LANSDALE Semiconductor Inc.

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Issue A
LANSDALE Semiconductor, Inc.
ML12179
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
damping coefficient,
ζ ≈ 1. T(s) is the transfer function of the
loop filter.
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 6. Graphical Analysis of Optimum Bandwidth
–150
–140
–130
–120
–110
–100
–90
–80
–70
–60
Crystal Reference
15dB NF of the Noise
Contribution from Loop
20*log(256)
VCO
Optimum Bandwidth
10
100
1k
10k
100k
1M
Hz
Figure 7. Closed Loop Frequency Response for
ζ = 1
–60
–50
–40
–30
–20
–10
0
10
0.1
1k
Hz
1
10
100
Natural Frequency
3dB Bandwidth
Legacy Applications Information
T(s)
RoCos1
NCo
KpKv
s2
RoCos1
2
ωo
ζ
ζ
s1
1
ωo2 s
2
2
ωo s1
NCo
KpKv
1
o2
ω
o
ω
o=
KpKv
NCo
Co
KpKv
N
ωo2
RoCo=
=
==
+
+
++
++
→ ω
→ ζ =
=
2
ζ
oRoCo
2
Ro
2
ζ
oCo
Figure 8. Design Equations for the 2nd Order System
ω
( (
( (
( (
( (
( ( ( (
( (
( (
( (
( (
Let:
NCo
KpKv
1
o2
ω
ω
ω
ω
ωω
ω
ωω
ω
ω
=
=
==
=
==
==
=+
+
+
,R
==
oCo
2
ζ
o
Figure 9. Loop Parameter Relations
Let: Ca
aCo ,Cx
bCo , A
1
a , and B
1
a
b
Let: RoCo
1
3
,RxCx+
1
4
,Ro(Ca
Cx)
1
5
Let: K33
o ,K44
o ,K55
o


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