AN178 Philips, AN178 Datasheet - Page 5

• Manufacturer Part Number: AN178
• Description: Modeling the PLL
• Manufacturer: Philips

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DataSheet
Philips Semiconductors
The procedure to follow for obtaining K
1. Establish the desired external bias and gain conditions for the
2. With the Function Generator turned off, set the free-running
3. Turn on the Function Generator and check to make sure the
4. Adjust the input frequency for lock. Lock is discernable on a
5. Set the input frequency to the free-running frequency and note
6. Adjust f
7. Making a plot of V
8. A plot of f
1988 Dec
4
U
Modeling the PLL
PLL under test.
frequency of the loop via the timing capacitor and timing resistor
if appropriate. Monitor f
amplitude of the input signal is appropriate for the particular loop
under test.
dual-trace scope when the input and VCO waveforms are
synchronized and stationary with respect to each other. One
should be especially careful to check that locking has not
occurred between the VCO and some harmonic frequency.
Carefully inspect both waveshapes, making sure each has the
same period. (If a second Frequency Counter is available, an
alternate scheme can be used to confirm frequency locking.
One frequency counter is used to monitor the input signal
frequency, and the second counter is used for the VCO
frequency. When the two counters display the same frequency,
the PLL is locked.)
the Gain-Phase Meter display. It should be approximately 90
voltage, V
V
measurement data and the system’s linearity. The slope of this
plot ( V
180/ gives the desired K
check the VCO linearity. The slope of this plot is K
particular free-running frequency. The units of slope taken
directly from the graph are Hz/V. Multiplying this slope figure by
2 gives the desired K
10 nominally. Record the phase error,
.com
D
for each f
l
D
for frequencies above and below f
/
l
D
= f
, and the input frequency, f
GENERATOR
e
FUNCTION
l
O
, as appropriate.
) is K
versus V
D
d
versus
in units of V/ . Multiplying this slope by
o
O
D
in units of radians/ volt-sec.
’ with the Frequency Counter.
d
while the loop remains locked will
f
in volts/radian.
I
e
is useful for checking the
KHRON–NITE
GAIN–PHASE
FILTER #1
d
Figure 5. Measurement Scheme for K
METER
and K
l
.
e
O
o
, the VCO control
’ and record
is as follows:
FREQUENCY SET
FREE–RUNNING
o
at the
DataSheet4U.com
e
and
KHRON–NITE
FILTER #2
f
UNDER
TEST
VCO
OUT
PLL
5
K
related to the input signal amplitude. K
level but does vary linearily with f
a normalized K
The K
estimated as
AThe loop gain for the PLL system is
(Often when the gain A is due to an amplifier internal to the IC, A will
be included in either K
on the 565 PLL.)
MODELING THE PLL SYSTEM WITH VARIOUS
LOW-PASS FILTERS
The open-loop transfer function for the PLL is
Using linear feedback analysis techniques, and assuming that the
VCO is in the forward path, the closed-loop transfer characteristics
H(s) can be related to the open-loop performance as
and the roots of the characteristic system polynomial can be readily
determined by root-locus techniques.
From these equations, it is apparent that the transient performance
and frequency response of the loop is heavily dependent upon the
choice of filter and its corresponding transfer characteristic, F(s).
d
is generally constant over wide frequency ranges, but is linearily
d
K
K
K
T(s)
H(s)
LOW PASS
FILTER
and K
o
O(norm)
O
v
value at any desired free-running frequency then can be
(@ any%f
OSCILLOSCOPE
K
o
1
BIAS
d
K
Determinations
1
K
V
o
o
F(s)
s
T(s)
as
A
K
f
DataSheet4U.com
O
O
T(s)
O
rad
)
V
d
or K
K
DVM
o(norm)
o
V
. This is further illustrated in the article
CC
BIAS AND
GAIN SET
O
FREQUENCY
f
’. Often it is convenient to specify
O
V
COUNTER
D
f
I
o
f
o
is constant with input signal
Application note
AN178
SL01015
(15)
(16)
(17)
(18)
(19)