Philips Semiconductors
Product specification
Phase-locked-loop with VCO
74HC/HCT4046A
PLL design example
The VCO gain is:
and the damping value ζ is defined as
follows:
˙
2fL × 2 × π
The frequency synthesizer, used in
the design example shown in Fig.32,
has the following parameters:
Kv
=
=
----------------------------------------------
1 + Kp × Kv × Kn × τ2
1
0.9 – (VCC – 0.9)
ζ =
×
---------- -----------------------------------------------------
2ωn (τ1 + τ2)
Output frequency: 2 MHz to 3 MHz
frequency steps : 100 kHz
1 MHz
-----------------
3.2
In Fig.33 the output frequency response to
a step of input frequency is shown.
=
× 2 π ≈ 2 × 106 r/s/V
settling time
overshoot
:
:
1 ms
< 20%
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 ωnt = 5. The required settling
time is 1 ms.
The gain of the phase
comparator is:
The open-loop gain is
H (s) x G (s) = Kp × Kf × Ko × Kn.
VCC
Kp
=
= 0.4 V/r.
------------
4 × π
Where:
The transfer gain of the filter is
given by:
Kp = phase comparator gain
Kf = low-pass filter transfer gain
Ko = Kv/s VCO gain
This results in:
1 + τ2s
Kf =
.
------------------------------------
5
--
t
5
1 + (τ1 + τ2) s
Kn = 1/n divider ratio
ω n
=
=
= 5 × 103 r/s.
--------------
0.001
The programmable counter ratio
Kn can be found as follows:
Where:
Rewriting the equation for natural
frequency results in:
τ 1 = R3C2 and τ2 = R4C2.
fout
2 MHz
---------------------
100 kHz
Nmin.
=
=
= 20
----------
fstep
Kp × Kv × Kn
The characteristics equation is:
1 + H (s) × G (s) = 0.
(τ1 + τ2) =
.
-------------------------------
ω2n
This results in:
fout
3 MHz
---------------------
100 kHz
The maximum overshoot occurs at Nmax.:
Nmax.
=
=
= 30
----------
fstep
1 + Kp × Kv × Kn × τ
s2 +
2s+
0.4 × 2 × 106
50002 × 30
-----------------------------------------------------
(τ1 + τ2)
(τ 1 + τ 2 ) =
= 0.0011 s.
---------------------------------
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 fo = 2.5 MHz and fL = 500 kHz
this gives the following values
(VCC = 5.0 V):
Kp × Kv × Kn
When C2 = 470 nF, then
(τ1 + τ2) × 2 × ωn × ζ – 1
= 0.
-------------------------------
(τ1 + τ2)
R4 =
= 315 Ω
----------------------------------------------------------------
Kp × Kv × Kn × C2
The natural frequency ωn is
defined as follows:
now R3 can be calculated:
Kp × Kv × Kn
τ1
ωn
=
------------------------------- .
R1 = 10 kΩ
R2 = 10 kΩ
R3 =
– R4 = 2 kΩ.
-------
(τ1 + τ2)
C2
C1 = 500 pF
1997 Nov 25
31