Datasheet

1997 Nov 25 31
Philips Semiconductors Product specification
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) = K
p
× K
f
× K
o
× K
n
.
Where:
K
p
= phase comparator gain
K
f
= low-pass filter transfer gain
K
o
=K
v
/s VCO gain
K
n
= 1/n divider ratio
The programmable counter ratio
K
n
can be found as follows:
The VCO is set by the values of R1,
R2 and C1, R2 = 10 kΩ (adjustable).
The values can be determined using
the information in the section
“DESIGN CONSIDERATIONS”.
With f
o
= 2.5 MHz and f
L
= 500 kHz
this gives the following values
(V
CC
= 5.0 V):
R1 = 10 kΩ
R2 = 10 kΩ
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 210
6
×≈× r/s/V=
K
p
V
CC
4 π×
------------
0.4 V/r.==
K
f
1τ
2
s+
1τ
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
ω
n
. 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
n
t = 5. The required settling
time is 1 ms.
This results in:
Rewriting the equation for natural
frequency results in:
The maximum overshoot occurs at N
max
.:
When C2 = 470 nF, then
now R3 can be calculated:
ζ
1
2ω
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
+()2ω
n
ζ1–×××
K
p
K
v
K
n
C2×××
-----------------------------------------------------------------
315 Ω==
R3
τ
1
C2
--------
R4 = 2 kΩ.–=