參數(shù)資料
型號： 74HC4046AD/T3
廠商： NXP SEMICONDUCTORS
元件分類： PLL合成/DDS/VCOs
英文描述： PLL FREQUENCY SYNTHESIZER, PDSO16
封裝： SOT-109, SOP-16
文件頁數(shù)： 25/34頁
文件大?。?/td> 442K
代理商： 74HC4046AD/T3
1997 Nov 25
31
Philips Semiconductors
Product specication
Phase-locked-loop with VCO
74HC/HCT4046A
PLL design example
The frequency synthesizer, used in
the design example shown in Fig.32,
has the following parameters:
Output frequency: 2 MHz to 3 MHz
frequency steps : 100 kHz
settling time
:
1 ms
overshoot
:
< 20%
The open-loop gain is
H (s) x G (s) = Kp × Kf × Ko × Kn.
Where:
Kp = phase comparator gain
Kf = low-pass filter transfer gain
Ko =Kv/s VCO gain
Kn = 1/n divider ratio
The programmable counter ratio
Kn can be found as follows:
The VCO is set by the values of R1,
R2 and C1, R2 = 10 k
(adjustable).
The values can be determined using
the information in the section
“DESIGN CONSIDERATIONS”.
With fo = 2.5 MHz and fL = 500 kHz
this gives the following values
(VCC = 5.0 V):
R1 = 10 k
R2 = 10 k
C1 = 500 pF
N
min.
f
out
f
step
-----------
2MHz
100 kHz
----------------------
20
==
=
N
max.
f
out
f
step
-----------
3MHz
100 kHz
----------------------
30
==
=
The VCO gain is:
The gain of the phase
comparator is:
The transfer gain of the filter is
given by:
Where:
The characteristics equation is:
1+H(s)
× G (s) = 0.
This results in:
The natural frequency
ω
n is
defined as follows:
K
v
2f
L
2
π
×
0.9
V
CC
0.9
–
()
–
-----------------------------------------------
˙
=
1MHz
3.2
-----------------
2
π 2106
×
≈
×
r/s/V
=
K
p
V
CC
4
π
×
------------
0.4 V/r.
==
K
f
1
τ
2 s
+
1
τ
1
τ
2
+
() s
+
------------------------------------- .
=
τ
1
R3C2 and
τ
2
R4C2.
=
s
2
1K
p
K
v
K
n
τ
2
×
+
τ
1
τ
2
+
()
----------------------------------------------------- s+
+
K
p
K
v
K
n
×
τ
1
τ
2
+
()
--------------------------------
0.
=
ω
n
K
p
K
v
K
n
×
τ
1
τ
2
+
()
-------------------------------- .
=
and the damping value
ζ is defined as
follows:
In Fig.33 the output frequency response to
a step of input frequency is shown.
The overshoot and settling time
percentages are now used to determine
ωn. From Fig.33 it can be seen that the
damping ratio
ζ = 0.45 will produce an
overshoot of less than 20% and settle to
within 5% at
ω
nt = 5. The required settling
time is 1 ms.
This results in:
Rewriting the equation for natural
frequency results in:
The maximum overshoot occurs at Nmax.:
When C2 = 470 nF, then
now R3 can be calculated:
ζ
1
2
ω
n
----------
1K
p
K
v
K
n
τ
2
×
+
τ
1
τ
2
+
()
-----------------------------------------------------
×
=
ω
n
5
t
---
5
0.001
---------------
510
3
×
r/s.
==
=
τ
1
τ
2
+
()
K
p
K
v
K
n
×
ω
n
2
-------------------------------- .
=
τ
1
τ
2
+
()
0.4210
6
×
5000
2
30
×
---------------------------------
0.0011 s.
==
R4
τ
1
τ
2
+
() 2 ω
n
ζ 1
–
×
K
p
K
v
K
n
C2
×
-----------------------------------------------------------------
315
==
R3
τ
1
C2
--------
R4 = 2 k
.
–
=
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