1210
IEEE
TRANSACTIONS
ON
COMMUNICATIONS,
VOL.
COM-25,
NO.
10,
OCTOBER
1977
ACKNOWLEDGMENT
The authors would like to express their gratitude to the UK
Science Research Council, Consiglio Nazionale delle Ricerche,
and NATO for support in this work.
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“A
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ings ACM Symposium
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and
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D. Cain, “MININET: a packet-switching
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1975:
Despres, R. “RCP, the experimental packet-switched data trans-
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“Proposed USA standard, data communication control procedures
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1969.
“General information-Binary synchronous communications”, IBM
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SRLGA27-3004.
Donnan, R.
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and
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R. Keisey, “Synchronous data link control:
a peispective”,ZBMSystems Journal, pp.
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Cain,
G.
D.,
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C.
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Morling and
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M.
Stevens, “Comparisons of
fixed and variable packet size for data communications”, PCL
Technical Memorandum MN-2,, November
1974.
Tymes, L. R., “TYMNET-
a
terminal oriented communication net-
Holt,
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Commoner, “Events and conditions”, Project
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work”, AFZPS-SJCC
38,
Pp.
211-216,1971.
Hangup in
Phase-Lock
Loops
FLOYD
M.
GARDNER,
SENIOR
MEMBER, IEEE
Abstruct-A phase-lock loop occasionally will take
a
long time to
settle to equilibrium. Phase dwells at a large error for
a
prolonged in-
terval. This phenomenon has been dubbed “hangup.”
The periodic nature of phase detectors is responsible for hangup,
which
OCCUIS
near the reverse-slope, unstable null. Restoring force is
small
in
the vicinity of the reverse null, and noise causes the loop to
equivocate about the
null.
Hangup is very troublesome when fast acquistion is needed
with high reliability. One example is synchronization of digital
communications.
Hangups can be avoided if a large restoring force is applied for
large phase errors and if equivocation is prevented.
An implementation
of
an antihangup circuit is proposed.
INTRODUCTION
Phase locked loops (PLL’s) occasionally exhibit unduly pro-
longed phase transients during initial acquisition of lock. The
.loop appears to stick, temporarily, at a large value of phase
Paper approved by the Editor for Data Communication Systems of
the IEEE Communications Society for publication after presentation, at
the URSI/USNC Conference, Stanford, CA, June
24, 1977.
Manuscript
received April
26, 1977.
This work was performed for the European
Space Agency, Noordwijk, The Netherlands.
The author
is
with the Gardner Research Company, Palo Alto, CA
94301.
error before settling
to
its normal tracking condition of small
error. This phenomenon has been dubbed the “hangup”
effect.
Hangup is associated with the reverse-slope null of the
phase detector (PD). The problem is caused by the small out-
put voltage that occurs in the vicinity of the reverse null and
by equivocation back and forth across the null.
Dwell time at the hangup point is finite (the loop cannot re-
main indefinitely at the unstable null), but even a short dwell
time may be excessive for some applications. An example
arises in burst-mode digital communications where rapid ac-
quistion
is demanded for efficient usage
of
channel time,
Failure of a PLL
to
settle within an allotted synchronization
preamble prevents correct detection of an identification pre-
amble and causes loss of the entire burst.
Hangup has been obscure because most PLL users
do
not
require fast phase acquisition (frequency acquisition is typi-
cally very much slower), because the loop always settles
eventually, and because hangup is an event of low probability.
It
simply has not been noticed by most users. Its existence
came as an unwelcome surprise to builders of TDMA (Time
Division Multiple Access) modems.
Recent practice
[
1-61 in TDMA synchronizers has been to
substitute narrow-band, tuned filters for a PLL in order to
avoid the hangup effect. The resulting equipment tends to be
overly complex and suffers from other unwanted characteris-
tics. A hangup-free; phase-locked synchronizer would be pre-
ferable, if one could be devised.
In this concise paper we examine the causes of hangup and
then formulate a pair of conditions that are necessary for pre-
vention of hangup. It is thought that the two conditions
together are sufficient, but experimental confirmation remains
to be obtained.
Methods are given for-implementing the conditions and a
particular implementation is proposed.
ATTRIBUTES
OF
HANGUP
Almost all phase detectors have a periodic characteristic of
output voltage vs. phase error; examples are shown in Fig.
1.
Because of the periodicity, the characteristic must have two
nulls per cycle. One null has a slope that provides negative
feedback for the loop and is the stable null for equilibrium
tracking. The other null has a reverse slope that provides un-
stable, positive feedback
so
stable tracking about this null is
not possible.
Experiments have revealed that if the initial phase error
in
a
PLL is very close to the reverse null, then the loop can dwell
in the vicinity of the null for a prolonged time; this is the
hangup effect. It is exemplified by the curves of Fig.
2
which
show typical phase transients
in a first-order PLL with sinusoi-
dal phase detector. The phase trajectories originating near
180’ remain in that vicinity for a long time before decaying
towards equilibrium at
0’.
(The first-order loop is not unique;
it
was chosen for an example only because its phase transient
is easily obtained by integrating the nonlinear differential
equation of the loop
[
71
.)
The loop cannot dwell at the reverse null forever; it must
eventually move away and converge towards the normal
equilibrium null (assuming that no conditions exist that
prevent eventual locking). But, if fast phase acquisition is
needed, the hangup interval can be excessively long and can
severely degrade the performance of fast TDMA systems.
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