1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator...
31
Rafael J. Betancourt-Zamora, Shwetabh Verma and Thomas H. Lee Department of Electrical Engineering Stanford University http://www-smirc.stanford.edu/ 1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator Prescalers
Transcript of 1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator...
Raf
ael J
. Bet
anco
urt
-Zam
ora
, Sh
wet
abh
Ver
ma
and
Th
om
as H
. Lee
Dep
artm
ent o
f Ele
ctric
al E
ngin
eerin
gS
tanf
ord
Uni
vers
ityht
tp://
ww
w-s
mirc
.sta
nfor
d.ed
u/
1-G
Hz
and
2.8
-GH
z C
MO
S
Inje
ctio
n-l
ock
ed R
ing
O
scill
ato
r P
resc
aler
s
Ou
tlin
e
•In
tro
du
ctio
n•In
ject
ion
Lock
ing
The
ory
•C
ircui
t Im
plem
enta
tion
•M
easu
red
Res
ults
•C
oncl
usio
n
•U
nd
erst
and
th
e In
ject
ion
-lo
ckin
g
mec
han
ism
•G
rasp
th
e lim
itat
ion
s o
f In
ject
ion
-lo
cked
Fre
qu
ency
Div
ider
s
•D
esig
n In
ject
ion
-lo
cked
Fre
qu
ency
D
ivid
er u
sin
g a
Rin
g O
scill
ato
r
Go
als
Mo
tiva
tio
n:
Low
-pow
er F
req
uen
cy S
ynth
esis
•F
req
uen
cy s
ynth
esiz
ers
are
imp
lem
ente
d u
sin
g P
LL
s.
•M
ajo
r so
urc
es o
f p
ower
dis
sip
atio
n a
re t
he
VC
O a
nd
F
req
uen
cy D
ivid
er.
320
MH
z C
MO
S P
LL
[V.K
aen
el’9
6]90
0 M
Hz
CM
OS
RE
CE
IVE
R[D
arab
i’00]
÷8
QI
LN
A
VC
O
500µ
A
300µ
A40
0µA
300µ
A
100µ
A
150µ
A
Q I
÷2
÷N
PF
DC
P &
LF
UP
DN
VC
OF
RE
F
FO
UT
2µA
10µ A
240µ
A50
µ A
800µ
A
Fre
qu
ency
Div
ider
Pow
er T
rad
e-o
ff
•W
e pr
opos
e a
tech
niqu
e in
whi
ch p
ower
d
ecre
ases
with
div
isio
n ra
tio.
÷2
200µ
A10
0µA
100µ
A
÷2
÷2
900
MH
z45
0 M
Hz
225
MH
z11
2.5
MH
z
TOTA
L P
OW
ER
200µ
A30
0µA
400µ
A
PO
WE
R IN
CR
EA
SE
S W
ITH
DIV
ISIO
N R
AT
IO
[Dar
abi’0
0]
Ou
tlin
e
•In
trod
uctio
n
•In
ject
ion
Lo
ckin
g T
heo
ry•C
ircui
t Im
plem
enta
tion
•M
easu
red
Res
ults
•C
oncl
usio
n
Rin
g O
scill
ato
r M
od
el
V O
R L
CL
ωP
1R
LC
--------
-- L=
HS
j ω()
HO
1j ω
ωP
⁄+
--------
--------
--------
--=
•N
egle
ct fe
edfo
rwar
d ze
ro
I TAI
L
BA
RK
HA
US
EN
CR
ITE
RIA
•N
eces
sary
con
ditio
ns fo
r os
cilla
tion
Hj ω
O(
)1
≥
Hj ω
O(
)∠
180°
=
SM
AL
L-S
IGN
AL
MO
DE
L
PH
AS
E C
ON
DIT
ION
GA
IN C
ON
DIT
ION
Rin
g O
scill
ato
r M
od
el (
II)
ωP
ω0 π n---
ta
n
--------
---------
=
N-S
TAG
E M
OD
EL
Hj ω(
)H
On
1j
ω ωo
------
π n---
tan
+
n----
--------
--------
--------
--------
--------
=H
O1
π n---
tan
2+
≥
PH
AS
E C
ON
DIT
ION
GA
IN C
ON
DIT
ION
n2
>V O
•ω
0 is
free
-run
ning
osc
illat
or fr
eque
ncy.
•E
ach
stag
e co
ntrib
utes
π/ n
to th
e ph
ase.
Rin
g O
scill
ato
r M
od
el (
III)
EX
AM
PL
E
nH
0ω
p
32.
000.
58 ω
0
41.
41ω
0
51.
241.
38 ω
0
Hjω(
)H
On
1j
ω ωo
------
π n---
tan
+
n----
--------
--------
--------
--------
--------
= •D
C g
ain
Η0
decr
ease
s w
ith n
umbe
r of
sta
ges.
•P
oles
ωp
coin
cide
with
ω0
only
for
n=4.
V O
Inje
ctio
n-l
ock
ed R
ing
Osc
illat
or
R L
CL
ωR
F
VB
IAS
EX
AM
PL
E:
3-st
age,
Div
ide
by 4
ωω
RF
4--------
=
ω RF
•A
n os
cilla
tor c
an b
e in
ject
ion-
lock
ed to
a h
arm
onic
of
the
free
-run
ning
osc
illat
ion
freq
uenc
y.
Reg
ener
ativ
e D
ivid
er [
Mill
er 1
939]
•C
omm
only
use
d w
here
the
freq
uenc
y of
ope
ratio
n is
ver
y hi
gh,
beyo
nd w
hat c
an b
e ac
hiev
ed w
ith fl
ip-f
lop
base
d ci
rcui
ts.
•Fr
eque
ncy
mul
tiplie
r ca
n re
pres
ent n
on-li
near
ities
pre
sent
in
the
circ
uit.
•U
sed
a m
odel
sim
ilar
to M
iller
’s, s
ince
the
lock
ing
mec
hani
sms
are
iden
tical
.
ω RF
H(j
ω)
3
ωR
F3 4-----
ωR
F±
ωω
RF
4--------
=
FR
EQ
. MU
LT.
EX
AM
PL
E:
Div
ide
by 4
Mo
del
for
Inje
ctio
n-l
ock
ed F
req
uen
cy D
ivid
er
n-s
tag
e L
PF
H(j
ω)
LO
Po
rtω
= ω R
F/M
RF
Po
rt
Dif
fere
nti
al P
air’
sN
on
-lin
eari
ty
Mix
er
-1
LO
+L
O-
I TA
ILω R
F
DC
+ ω R
F| ω
RF
- (M
+1)ω
|| ω
RF
- (M
-1)ω
|
ω
MIX
ER
•D
iffer
entia
l-pai
r si
ngle
-bal
ance
d m
ixer
•In
ject
ed ω
RF in
to th
e ta
il de
vice
FIL
TE
R•
Sup
pres
s pr
oduc
ts >
ω•
VO
is s
inus
oida
l (sm
all n
) .
ω , 3
ω , 5
ω ...
Mo
del
for
Inje
ctio
n-l
ock
ed F
req
uen
cy D
ivid
er (
II)
3-st
age
LP
F
H(j
ω)
LO
Po
rtω
= ω
RF/ 4
RF
Po
rt
Dif
fere
nti
al P
air’
sN
on
-lin
eari
ty
Mix
er
-1
LO
+L
O-
I TAIL
ω RF
DC +
ωR
F| ω
RF -
5ω|
| ωRF
- 3ω
|
ω
•W
ith n
o in
ject
ion,
ω =
ω0.
ω , 3
ω , 5
ω ...
EX
AM
PL
E:
3-st
age,
Div
ide
by 4
Mix
er
∆ V
∆ II B
IAS
VSA
T
-IB
IAS
-VSA
T
2IR
F
•T
he d
iffer
entia
l-pai
r is
non
-line
ar w
ith o
dd s
ymm
etry
. •
Non
-line
arity
pro
duce
s od
d ha
rmon
ics
at 3
ω, 5
ω, e
tc.
•I T
AIL
is m
odul
ated
by
ω a
nd it
s ha
rmon
ics.
LO
Po
rt
RF
Po
rt
Mix
er
LO
+L
O-
I TA
ILω R
F
ω, 3
ω, 5
ω ...
I TA
IL =
I RF
cos(
ω RFt
+ α
) + I B
IAS
VS
AT
WL⁄
() T
AIL
WL⁄
() D
IFF
--------
--------
--------
--------
VO
DT
⋅=
V0
cos(
ωt)
I TAI
L
Mix
er (
II)
LO
Po
rt
Mix
er ω , 3
ω , 5
ω ...
Ck
1 k π------
1– ()
k1
–(
)2 ⁄
⋅
0 =
odd
k
othe
rwis
e
Fo
uri
er C
oef
fici
ents
of
Πt ()
I TA
IL⋅
ρ s =
V0/
VSA
T >
> 1
(Sq
uar
e W
ave)
DE
FIN
E S
WIN
G R
AT
IO
Mix
ing
Fu
nct
ion
Π(t
)
V0
cos(
ωt)
I TA
IL
Lin
eari
ze P
has
e o
f H
(jω
)
ω
Hjω(
)∠
ω Ο
−π
d φ/d
ω H
j ω()
∠–π
≅n
2π n------
sin 2
--------
--------
-------
∆ω ω0
--------
⋅+
∆ω
ωω
O–
=
Filt
er
Hj ω(
)H
On
1j
ω ωo
------
π n---
tan
+
n----
--------
--------
--------
--------
--------
=
n-s
tag
e L
PF
H(j
ω)
-1| ω
RF
- 5ω
|| ω
RF
- 3ω
|
ω
Use
Rin
g O
scill
ato
r M
od
el
Des
crib
ing
Fu
nct
ion
An
alys
is
•If
VO
is la
rge,
then
the
inje
ctio
n lo
ckin
g dy
nam
ics
are
dete
rmin
ed b
y th
e ph
ase
rela
tions
hip
arou
nd th
e lo
op (
phas
e-lim
ited)
and
ther
efor
e w
e ca
n ig
nore
the
ampl
itude
exp
ress
ion.
η iC
M1
–C
M1
+–
()
αsi
n
C1
η iC
M1
–C
M1
++
()
αco
s+
--------
--------
--------
--------
--------
--------
--------
--------
--------
--------
--
at
anH
j ω∠–
π–=
η iI R
F
2I B
IAS
--------
--------
=
INJE
CT
ION
WR
ITE
PH
AS
E E
XP
RE
SS
ION
AR
OU
ND
TH
E L
OO
P
MIX
ER
FIL
TE
R
FIN
D S
OL
UT
ION
FO
R α
∈ (
- π, π
].
EF
FIC
IEN
CY
LR
4
n2
π n------
sin
--------
--------
-------
k 0
1k 1
2–
--------
--------
-----
atan
≅
k 0η i
CM
1–
CM
1+
– C1
--------
--------
--------
--------
----=
k 1η i
CM
1–
CM
1+
+ C1
--------
--------
--------
--------
-----
=
•F
unct
ion
of in
ject
ion
effic
ienc
y η i
, and
the
mag
nitu
de o
f the
F
ourie
r co
effic
ient
s C
M-1
and
CM
+1.
•F
or s
mal
l val
ues
of in
ject
ed s
igna
l the
lock
ing
rang
e in
crea
ses
linea
rly w
ith th
e in
ject
ed s
igna
l str
engt
h.
WH
ER
E
Lo
ckin
g R
ang
e o
f In
ject
ion
-lo
cked
Rin
g O
scill
ato
r
Lim
ited
Inje
ctio
n E
ffic
ien
cy a
nd
Par
asit
ics
•Li
mite
d in
ject
ion
effic
ienc
y du
e to
sho
rt-c
hann
el e
ffect
s an
d ta
il de
vice
non
-line
arity
.
VR
F
VB
IAS
CPA
R
•S
hunt
pat
h fo
r I R
F r
educ
ing
the
inje
ctio
n ef
ficie
ncy
at h
igh
freq
uenc
ies.
TAIL
PA
RA
SIT
ICS
INJE
CTO
R N
ON
-ID
EA
LIT
IES
VR
F
VB
IAS
I DS
KV
RF
VO
DT
+(
)γ⋅
=
η iV
RF
2V
OD
T----
--------
----γ⋅
=
γ =
1 -
2
SH
OR
T-C
HA
NN
EL
–0.3
–0.2
–0.10
0.1
0.2
Sw
ing
Ra
tio, ρ
s=V
o/V
sat
24
68
10
Normalized Coefficients
C3/C/C
1
C5/C/C
1
Lim
ited
Mix
er G
ain
•T
he a
ssum
ptio
n th
at th
e m
ixer
’s s
witc
hing
func
tion
is a
squ
are
wav
e is
ver
y ac
cura
te if
the
swin
g ra
tio ρ
s >
> 1
.
•A
s ρ s
get
s sm
alle
r, th
e no
rmal
ized
coe
ffici
ents
Ck/
C1
are
sign
ifica
ntly
sm
alle
r, th
us d
egra
ding
the
lock
ing
rang
e.
00.
51
1.5
22.
53
3.5
4024681012141618
VR
F/V
OD
Locking Range (%)
ab
c
Exa
mp
le:
5-st
age,
Mo
du
lo-8
Rin
g O
scill
ato
r
(a)I
deal
(ph
ase-
limite
d) c
ase
(b)C
ompr
essi
on d
ue to
Inje
ctor
non
-line
arity
(sq
uare
-law
dev
ice)
(c)E
ffect
s of
Inje
ctor
non
-line
arity
and
tail
para
sitic
s (5
0% lo
ss)
Ou
tlin
e
•In
trod
uctio
n
•In
ject
ion
Lock
ing
The
ory
•C
ircu
it Im
ple
men
tati
on
•M
easu
red
Res
ults
•C
oncl
usio
n
5-st
age
Inje
ctio
n-l
ock
ed R
ing
Osc
illat
or
Fre
qu
ency
Div
ider
•U
sed
mod
ified
cro
ss-c
oupl
ed
sym
met
ric lo
ad b
uffe
rs.
•R
F s
igna
l inj
ecte
d at
the
tail
of
the
first
buf
fer (
sing
le-b
alan
ced
mix
er).
•T
he b
uffe
r st
ages
beh
ave
as
the
H(jω
) fil
ter.
+_
BR
OPA
MP
VB
IAS
VC
TL
Vdd
ωB
1
VR
F
B4
B3
B2
RE
PLI
CA
BIA
SIN
JEC
TIO
N-L
OC
KE
D R
ING O
SC
ILLA
TORB
5B
O
OU
T B
UF
FE
R
RB
IAS
VR
F
VB
IAS
VC
TL
Die
Mic
rog
rap
h:
5-st
age
Rin
g O
scill
ato
r D
ivid
er
RIN
GO
SC
ILLA
TOR
BIA
S
VR
F
OUTBUF
VO
UT
VO
UT
•Fa
bric
ated
3 a
nd 5
-sta
ge
ring
osci
llato
rs.
•0.
24-µ
m C
MO
S
•0.
012
mm
2 of
are
a
Ou
tlin
e
•In
trod
uctio
n
•In
ject
ion
Lock
ing
The
ory
•C
ircui
t Im
plem
enta
tion
•M
easu
red
Res
ult
s•C
oncl
usio
n
Res
ult
s
Inje
cted
Fre
quen
cyFr
ee-r
unni
ng F
requ
ency
Pha
se N
oise
@10
0KH
z
5-st
age
ILF
D1.
0 G
Hz
125
MH
z-1
10 d
Bc/
Hz
3-st
age
ILF
D2.
8 G
Hz
700
MH
z-1
06 d
Bc/
Hz
Inp
ut L
ock
ing
Ran
ge
M
odul
o-2
M
odul
o-4
M
odul
o-6
M
odul
o-8
12.7
MH
z (-
3dB
m)
32 M
Hz
(-3d
Bm
)17
MH
z (-
3dB
m)
20 M
Hz
(-3d
Bm
)
125
MH
z (-
3dB
m)
56
MH
z (-
5dB
m)
no-lo
ckno
-lock
Pow
er d
issi
pat
ion
Vdd
Ico
re I
bias
Cor
e po
wer
Pow
er e
ffici
ency
1.5
V23
3 µA
108
µA35
0 µW
2.86
GH
z/m
W
3.0
V33
1 µA
661
µA99
3 µW
2.82
GH
z/m
W
0.5
11.
52
2.5
33.
54
0
0.51
1.52
2.53
[ 0] d
iv8
[ 0] d
iv4
[ 3] d
iv8
[11]
div
8
[13]
div
128
[ 9] d
iv2
[15]
div
8 [13]
div
128
[14]
div
8
Fre
quen
cy, G
Hz
Power Efficiency, GHz/mW
•[0
] 5-s
tage
(di
v-8)
= 2
.86
GH
z/m
W @
1GH
z
•[0
] 3-s
tage
(di
v-4)
= 2
.82
GH
z/m
W @
2.8G
Hz
Pow
er E
ffic
ien
cy o
f In
ject
ion
-lo
cked
Rin
g O
scill
ato
r
•S
mal
l sw
ing
ratio
(ρs
≈ 3−
4) c
ause
d re
duct
ion
in m
ixer
gai
n.
Nee
d to
incr
ease
out
put s
win
g an
d re
duce
VS
AT.
Wh
at W
e L
earn
ed
•La
rge
tail
devi
ce (
W/L
=10
.2/1
) ca
used
loss
of I
RF.
Nee
d to
lo
wer
tail
node
par
asiti
cs to
incr
ease
the
inje
ctio
n ef
ficie
ncy.
•R
eson
atin
g ta
il w
ith a
n in
duct
or [ W
u, IS
SC
C’0
1]
is n
ot p
ract
ical
at s
ub-G
Hz
freq
uenc
ies.
LO
CK
ING
RA
NG
E C
OM
PAR
ISO
N
5-st
age
(div
-8)
@ 1
GH
z3-
stag
e (d
iv-4
) @
2.8
GH
z
TH
EO
RY
9%34
%
SIM
ULA
TIO
N5%
17%
TE
ST
2%2%
Ou
tlin
e
•In
trod
uctio
n
•In
ject
ion
Lock
ing
The
ory
•C
ircui
t Im
plem
enta
tion
•M
easu
red
Res
ults
•C
on
clu
sio
n
Co
ncl
usi
on
•D
escr
ibed
the
inje
ctio
n lo
ckin
g m
echa
nism
and
ho
w it
app
lies
to C
MO
S r
ing
osci
llato
rs.
•S
how
ed th
e de
sign
of f
requ
ency
div
ider
s th
at c
an
oper
ate
up to
2.8
-GH
z by
exp
loiti
ng in
ject
ion
lock
ing
in d
iffer
entia
l CM
OS
rin
g os
cilla
tors
.
•S
how
ed m
easu
red
resu
lts fo
r 1-
GH
z an
d 2.
8-G
Hz
inje
ctio
n-lo
cked
freq
uenc
y di
vide
rs fa
bric
ated
in a
0.
24-µ
m C
MO
S te
chno
logy
.
Ack
now
led
gm
ents
Nat
ion
al S
emic
on
du
cto
r
