TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 82
1
2
~ 821
6
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.65
24
8212
Re
cei
v
ed
Jun
e
18, 2014; Revi
sed Septe
m
ber
24, 201
4; Acce
pted
Octob
e
r 19, 2
014
A Design of Bang-Bang PLL in Low Jitter and Wide
Pull-in Range
Xihong Che
n
, Qiang Liu*, Denghu
a Hu
Air and Miss
ile
Defens
e Col
l
e
ge, Air F
o
rce Engi
neer
in
g Uni
v
ersit
y
,
No. 1 Cha
n
g
l
e
Roa
d
, Xi'
a
n, 71
005
1, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: dreaml
q
@1
6
3
.com
A
b
st
r
a
ct
As ba
ng-b
a
n
g
PLL (BBP
LL) c
oul
d res
u
me c
l
ock d
a
ta ra
pi
dl
y, its ap
plic
atio
n in
cl
ock d
a
ta
recover
y
has b
e
co
me i
n
creasi
ngly
abr
oad. Ai
min
g
at
the co
ntrary
d
e
man
d
of l
o
w
e
r jitter an
d w
i
d
e
r pu
ll-i
n
ra
nge
of
BBPLL, the
iss
ue p
u
ts forth a
meth
od to c
h
o
o
se the
most
a
ppro
p
riate
ga
in
of dig
i
tally c
o
n
t
rolle
d osci
llato
r
(DCO)
to
settl
e.
A
ju
dg
ed an
d mod
i
fie
d
mo
del has be
en add
ed
to
the 2
nd
order trad
itio
nal BB
PLL, w
h
ic
h
mo
difi
ed the g
a
in of DCO dy
na
mic
a
lly
by step forw
ard method. Mea
n
w
h
il
e
it propos
es p
u
ll-i
n
jitter funct
i
o
n
(PJF
) to ju
dg
e
the
mo
difie
d
r
e
sults. T
hen
it t
a
kes
a
grad
ua
l
co
mp
ariso
n
means
to s
earch
the
max PJF
.
It
coul
d be co
ncl
ude
d from the
simulati
ons tha
t
the algor
ith
m
of the issue co
uld g
e
t a comp
romise DCO g
a
i
n
in view of BBPLL’
s jitter and pull-in range.
Ke
y
w
ords
: ba
ng-b
ang P
LL, DCO, pull-i
n
ra
nge, jitter, pul
l-i
n
jitter function
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
High preci
s
ion
atomi
c
clock
has been widely
used in sa
tellites’
com
m
uni
cati
on, like
navigation, o
r
ientation a
nd
timing.
The cl
ocks’ perfo
rm
ances are
th
e
base of satel
lites’ services.
While the cl
ocks errors will wo
rsen the services
precisi
on,
even interrupt satellites normal
operation
s
. In order to ge
t ideal
satellites
se
rvic
e
s
, we sho
u
ld
e
s
tablish prope
r
PLL circuit
s
to
c
a
librate the
c
l
oc
k
errors
[1-3].
Bang-bang P
LL (BBPLL)
has
been
taken in hi
gh
speed
clock
data recovery area wi
del
y
for the adva
n
tage
s of ea
sy de
sign
an
d high
sp
e
e
d
pro
c
e
s
s. T
he main
disa
dvantage i
s
t
h
e
system’
s
jitter brou
ght by pha
se dete
c
tion, wh
ich co
uld be dep
re
ssed by redu
cing the gai
n
of
digitally co
ntrolled o
s
cillato
r (DCO),
but
also l
eadi
ng t
o
a n
a
rro
w
er
pull-in
ra
nge.
Some
schola
r
s
have made
re
sea
r
che
s
abo
ut this probl
e
m
[4-6].
In 2005,
Dalt
desi
gned a
nonlinear
dynamics
digital BBPLL
and studied
the effects of
loop delays
of the first- and
second-order BBPLL.
And he
sum
m
ari
z
ed the
desi
gn m
e
thod of
su
ch PLL a
n
d
gave optim
al paramete
r
s in lo
w jitte
r [7]. Aiming
at negle
c
ting
the effect of the
BBPLL dynamics
on the
effective jitter in the tradi
tional calculati
on of bina
ry pha
se dete
c
t
o
r
(
BPD
)
,
in
20
06
, D
a
lt
p
u
t
for
t
h
a me
th
od
to
mo
d
e
l BB
PLL dyna
mics by
Markov
chai
n, which
got
more
a
c
curate p
r
e
c
isio
n [
8
]. While
con
v
erting th
e p
hase e
r
ror int
o
digital
valu
e by Ba
ng-b
ang
Phase Detector
(BBPD) will
bro
ught
seri
ous nonli
nearity into the loop, whi
c
h will limit
the
traditional li
n
ear
analysi
s
.
In 2008,
Dalt analyz
ed
the defici
e
n
c
e of the lin
e
a
rized lo
op
and
applie
d it to jitter tran
sfe
r
an
d the jitter g
ene
ratio
n
in comp
utation [9]. It wa
s validate
d
by
analysi
s
of actual circuits.
Beside
s,
Cha
n
et al
de
sign
ed a
ne
w PL
L by
dynami
c
ally scale
s
its gain,
whi
c
h
achi
eved
fast lock times an
d grea
t jitter performance
in lo
ck [10]. Ch
u
n
and Kenn
edy studie
d
the
stationa
ry sta
t
e pro
bability
based o
n
a
d
e
layed
M
a
rko
v
chain
mod
e
l and a
state
flow dia
g
ra
m,
whi
c
h imp
r
ov
ed ca
pture
ra
nge an
d lock
time [11].
Based
o
n
the
idea
of
dyna
mically
scale
s
PL
L’s gai
n
brou
ght
by Chun [1
1], aimi
ng at
the
contrary of jitter and p
u
ll-in
rang
e for DCO’s gai
n,
in this issue, we use a fun
c
tion
to evaluate the
comp
oun
ded
cha
r
a
c
teri
sti
c
s of jitter a
n
d
pull
-
in
rang
e, and
get a
com
p
ro
mise
re
sult bet
we
en
them. In secti
on 2 and 3, traditional and improved
BBPLL model
s
will be presen
ted. In section 4,
we
will validate our improved model
by examples
. At last, the conclusion will be arrived in
se
ction 5.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Desig
n
of Bang-B
ang PL
L in Low
Jitter and
Wide P
u
ll-in Rang
e (Xihong Chen
)
8213
2. Traditiona
l BBPLL
A 2
nd
order
BBPLL is
composed
of a BBPD,
a DCO and
a
frequency divider, whi
c
h
coul
d be illust
rated in Figure 1 [9, 12].
Figure 1. Ske
t
ch diag
ram o
f
2
nd
order BBPLL
In the Digital Loop Filte
r
(DLF) mo
dule, we could g
e
t:
1
sgn(
)
kk
k
kk
k
kk
D
k
D
tr
td
w
(1)
Whe
r
e
k
,
k
tr
,
k
td
and
k
w
are denoted for output
of
BBPD, referred cl
ock,
feedback
clo
ck a
nd DL
F's outp
u
t se
parately.
sg
n(
)
is sign fun
c
tion,
D
,
and
are th
e filter latency,
integral
and proportional gains
re
specti
vely. Based on (1), we
will
get the transfer function
F
in
z
domai
n as:
1
(z)
(z)
(z)
1
D
w
F
z
z
(2)
Subs
titute
re
f
jT
ze
into (2), we will
get:
()
1
re
f
re
f
j
TD
jT
Fe
e
(3)
From thum
b rules, we co
ul
d get
the pull-in rang
e of the BBPLL as:
=2
R
e
(
j
)
0
2
p
T
p
K
F
Fj
N
(4)
Whe
r
e
T
K
is the gain of DCO,
N
is the divider
coeffici
ent.
Mean
while
we coul
d get the PLL’s jitter
as [13]:
0
2
1+
8
3
tv
tT
T
D
NK
K
(5)
w
v
d
r
T
K
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8212 – 82
16
8214
3. Impro
v
ed
Design o
f
BBPLL
Aiming at th
e
co
nflict of
jitter
and
pull
-
in
ra
nge, i
n
o
r
d
e
r to
comp
ro
mise
them,
we ad
d a
judge
d and m
odified mod
u
l
e
in DCO part
,
which
coul
d be interp
rete
d in Figure 2.
Figure 2. Improved sket
ch
diagram of 2
nd
order BBPLL with modified DCO’s
gain.
As the incre
a
se of DCO’
s gain
T
K
will
better the pull-in range but worsen the jitter
perfo
rman
ce,
we brin
g ou
t a track of DCO’s out
pu
t to a judgment and mod
i
fication mod
u
le
(JM
M
), and
modulate
T
K
based o
n
the re
sult of judgm
ent. Detailed
step
s are a
s
f
o
llows.
Before we
start the pro
c
e
ss of JMM, we s
houl
d wait
the whole PLL to locked the input
sign
al, which
is
call
ed bi
g
feedb
ack l
o
op. When
th
e big
loop
be
come
s l
o
cke
d
an
d
stable,
the
jitter or the p
u
ll-in rang
e o
f
the PLL is n
o
t ideal at th
e mome
nt, even though t
he loop i
s
lo
cked.
As a
re
sult, it need
s the
small fe
edba
ck l
oop
JM
M
to modify th
e DCO’
s gai
n to imp
r
ove
the
perfo
rman
ce of
BBPLL.
Step 1: Initialization
Initialize DCO
’s ori
g
inal
gai
n
0
T
K
and other
parameters of BBPLL based on the
referred
clo
ck,
in
cludi
ng
,
,
D
and
N
etc.
Step 2: Particles traini
ng
After the BBPLL ha
s lo
cked, we
calculate
the p
u
ll-i
n
ra
nge
and
jitter in a
ce
rtain
Ti
K
.
The process
is call
ed a tra
i
ning an
d the
Ti
K
a particle. I
n
the Step 3, we will adj
ust the DCO’
s
gain
T
K
gradual
ly. When we
get a new p
a
r
ticle, i.e.
Ti
K
, we will get the correspondi
ng pull-i
n
rang
e and jitter.
Step 3: Judg
ment and Mo
dification
Pull-in ran
ge and
jitter
are the
fun
c
tion
s of
T
K
. In order to get a
n
id
eal
pull-i
n
rang
e
and
jitter, we
b
r
in
g a
pull
-
in jitt
e
r fu
nctio
n
(PJF) to j
udg
e t
he m
odified
result
s a
n
d
ta
ke
step
forwa
r
d
method to se
arch the be
st particl
e. PJF i
s
define
d
as:
p
t
PJF
(6)
Whe
n
the
i
th particl
e
an
d PJF
a
r
e
Ti
K
and
i
PJF
, we in
crease a po
sitive step length to
Ti
K
, then
we
wi
ll get
(1
)
Ti
K
an
d
1
i
PJ
F
. If
1
ii
PJ
F
P
J
F
, we
will
co
ntinue
in
crea
se
(1
)
Ti
K
positively a
n
d
re
peat th
e p
r
oce
s
s a
bove.
If
1
ii
PJ
F
P
J
F
, we
will increase
a ne
gative step length
to
Ti
K
and conti
nue ma
ke co
mpari
s
o
n
s. If
1
ii
PJ
F
P
J
F
, we will make
(1
)
Ti
K
fixed. During the
compari
s
ons,
we will get the maximum
of
P
JF
, and the correspon
ding
best parti
cle
T
K
, whic
h
is the comp
ro
mise g
a
in for jitter and pull
-
in range. After we get the
best pa
rticl
e
, we will
se
nd
it
to DCO a
nd
modify its gain to the particle we get.
As the input of PLL is dynami
c
, so the pro
c
e
s
s
is not stable.
When the in
put chan
ge
s, the big
loop will wo
rk to lock the input
frequen
cy. After
the pro
c
e
ss,
the small loo
p
start
s
to work, in o
r
de
r to get a comp
romi
se pull
-
in
range a
nd jitter
perfo
rman
ce
s again
s
t the input sig
nal.
w
v
d
r
T
K
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Desig
n
of Bang-B
ang PL
L in Low
Jitter and
Wide P
u
ll-in Rang
e (Xihong Chen
)
8215
4. Examples Calcula
t
ions
and Analy
ses
The initial
pa
rameters
are
set as follo
ws:
10
N
,
0
=1p
s
tv
,
0.5
,
16
,
15
0
10
s
T
K
,
10
M
H
z
ref
f
and
step l
e
ngth
14
10
s
ste
p
l
. When
2
D
,
we will
get curves of
BBPLL’s pull-i
n
rang
e and jitter agai
nst
T
K
in
Figure 3.
a) Pull-in
ran
ge agai
nst DCO’
s gain
T
K
, (b) Jitter again
s
t DCO’s g
a
i
n
T
K
Figure 3. BBPLL’s pa
rtial
para
m
et
ers curves
with DCO’
s gain
T
K
From Figu
re
3, we coul
d get that the pull-in ran
ge is
prop
ortio
nal to
T
K
approxima
t
ely,
while
jitter
experie
nces de
cre
a
si
ng f
o
rmer
and
in
creasi
ng l
a
ter.
Whe
n
2
D
, we will get
PJF
again
s
t
T
K
in Figure 4. Me
an
while
PJF
in other latenci
e
s, like
0,
1
D
are also prese
n
ted.
Figure 4. PJF
again
s
t DCO
’
s gain
T
K
in different laten
c
y
D
From
Figu
re
4, we
will
ge
t that
P
JF
in
cr
ea
se
s f
o
rme
r
a
nd d
e
c
r
ea
se
s lat
e
r
wit
h
t
he
incr
ea
se of
T
K
. We
will achi
eve the best
parti
cle
when the
P
JF
r
e
ac
he
s
ma
ximu
m. W
h
en
latency
D
incr
e
a
se
s,
t
he
P
JF
de
cre
a
ses, in
di
cating th
at the pull-i
n
ra
ng
e and jitter
compou
nd
perfo
rman
ce
s deterio
rate.
10
-1
5
10
-14
10
-13
10
-1
2
0
1
2
3
x 1
0
-6
de
l
t
a
w
K
T
,s
(a
)
10
-1
5
10
-14
10
-13
10
-1
2
0
1
2
3
x 1
0
-1
0
J
i
tte
r
,
s
K
T
,s
(
b
)
10
-1
5
10
-14
10
-1
3
10
-1
2
0
2
4
6
8
10
12
x 1
0
4
JP
F
K
T
,s
D=
0
D=
1
D=
2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8212 – 82
16
8216
5. Conclusio
n
Aiming at th
e
co
ntra
ry de
mand
s of
DCO's gai
n
whil
e con
s
ide
r
ing
jitter a
nd
pull
-
in
ran
ge
in BBPLL, we have ad
de
d a judg
ed a
nd modifie
d
module i
n
DCO pa
rt ba
sed on tra
d
itional
BBPLL. In o
r
de
r to g
e
t
a compromi
se DCO'
s
gai
n, we
put fo
rth the
pull-i
n
jitter fun
c
ti
on
.
Besides, We
have made comparis
ons of BBPLL’s pull-in range &
jitter characteri
stics and PJF
cha
r
a
c
teri
stics in
differen
t
latenci
e
s.
From
examp
l
es
cal
c
ul
atio
ns
and
an
al
ysis,
we
co
uld
conclude that
with the help of PJF,
we
will get
a compromi
se
DCO gain whil
e
consi
d
ering
jitter
and pull
-
in ra
nge. And with
the incre
a
se of la
tency, PJF experie
nce
s
wo
rse pe
rfo
r
man
c
e
s
.
Referen
ces
[1]
W
ang Y,
Z
hou
JH, Ye
K. R
e
searc
h
on E
ndtoEn
d
Del
a
y Performa
nce
Based
o
n
GP
S Sche
du
lin
g
Sy
s
t
e
m
.
T
E
LK
OMNIKA Indon
esia
n Journ
a
l o
f
Electrical Eng
i
ne
erin
g.
201
4; 12(6): 440
0-4
404.
[2]
F
an Z
.
Res
ear
ch o
n
PVT
Sol
u
tion
Meth
ods
for Nav
i
gati
o
n
Messag
e
of GPS Rec
e
iver.
TEL
K
OMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
ng.
2014; 1
2
(2): 9
29-9
39.
[3]
Huque ASA. Achieving P
u
llin Avoiding Cy
c
l
e Slip
Us
ing Secondorder PLLs.
Internatio
n
a
l Jour
nal
of
Electrical and Co
mp
uter
Engi
neer
ing.
2
014; 4(2):
243-
25
6.
[4]
Che
n
Y, W
ang
Z
,
Z
hang L. Lo
w
-
jitter PL
L b
a
s
ed
on s
y
mm
etric phas
e-fre
que
nc
y detect
o
r techni
qu
e.
Anal
og Integr
ated Circ
u
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