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參數(shù)資料
| 型號： | MC12179 |
| 廠商： | Motorola, Inc. |
| 英文描述： | 500 - 2800 MHz Single Channel Frequency Synthesizer |
| 中文描述： | 500 - 2800兆赫頻率合成器的單頻道 |
| 文件頁數(shù)： | 6/11頁 |
| 文件大?。?/td> | 353K |
| 代理商： | MC12179 |
6
MOTOROLA RF/IF DEVICE DATA
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
d
Figure 7. Closed Loop Frequency Response for
ζ
= 1
Natural Frequency
–60
–50
–40
–30
–20
–10
0
10
0.1
1k
Hz
d
1
10
100
3dB Bandwidth
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
15kHz/2.5 or 6kHz (37.7krads) with a damping coefficient,
ζ
≈
1. T(s) is the transfer function of the loop filter.
T(s)
RoCos
1
NCo
KpKv
s2
RoCos
1
2
o
s
1
1
o2
s2
2
o
s
1
NCo
KpKv
1
o2
o
KpKv
NCo
Co
KpKv
N o2
RoCo
2
o
oRoCo
2
Ro
2
oCo
Figure 8. Design Equations for the 2nd Order System
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 spread
sheet is useful. To aid in the use of such a tool the
equations are summarized in Figures 9 through 11.
Let:
NCo
KpKv
1
o2
, RoCo
2
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: K3 3
o, K4 4
o, K5 5
o
A
A
F
Freescale Semiconductor, Inc.
For More Information On This Product,
Go to: www.freescale.com
n
.
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