mc12179 Freescale Semiconductor, Inc, mc12179 Datasheet - Page 6

• Manufacturer Part Number: mc12179
• Description: 500 - 2800 Mhz Single Channel Frequency Synthesizer
• Manufacturer: Freescale Semiconductor, Inc

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
6
Figure 6. Graphical Analysis of Optimum Bandwidth
Figure 7. Closed Loop Frequency Response for = 1
To simplify analysis further a damping factor of 1 will be
–100
–110
–120
–130
–140
–150
–60
–70
–80
–90
–10
–20
–30
–40
–50
–60
10
0
10
0.1
Crystal Reference
Natural Frequency
100
1
1k
3dB Bandwidth
Hz
10
Hz
Let:
Let: C a
Let: R o C o
Let: K 3
Freescale Semiconductor, Inc.
20*log(256)
10k
For More Information On This Product,
K p K v
NC o
Optimum Bandwidth
15dB NF of the Noise
Contribution from Loop
w
+
3
100
Figure 9. Loop Parameter Relations
+
+
aC o , C x
+
100k
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w
w
w
1
1
o 2
o , K 4
3
VCO
, R x C x
, R o C o
+
w
MC12179
1M
1k
4
bC o , A
+
+
+
w
w
1
w
o , K 5
2
4
z
o
15kHz/2.5 or 6kHz (37.7krads) with a damping coefficient,
In summary, follow the steps given below:
Step 1: Plot the phase noise of crystal reference and the
Step 2: Increase the phase noise of the crystal reference by
Step 3: Convert the divide–by–N to dB (20log 256 – 48 dB)
Step 4: The point at which the VCO phase noise crosses the
Step 5: Correlate this loop bandwidth to the loop natural
, R o (C a
Figure 8. Design Equations for the 2nd Order System
+
K p K v
NC o
T(s)
R o C o
1. T(s) is the transfer function of the loop filter.
1
w
)
5
+
VCO on the same graph.
the noise contribution of the loop.
and increase the phase noise of the crystal
reference by that amount.
amplified phase noise of the Crystal Reference is the
point of the optimum loop bandwidth. This is
approximately 15 kHz in Figure 6.
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 . 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.
+
a , and B
+
+
)
K p K v
w
NC o
C x )
o
w
w
2
1
o 2
z
o
s 2
R o C o s
+
³
)
³
+
w
1
z
R o C o s
5
w
+
1
)
o
MOTOROLA RF/IF DEVICE DATA
)
+
1
w
a
o R o C o
)
)
2
K p K v
NC o
1
b
+
³
w
³
1
o 2
s 2
C o
R o
w
2
z
o
)
[
+
s
)
w
2
z
o
N
K p K v
w
1
s
w
o C o
2
)
o 2
z
1