TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3832 ~ 38
4
0
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5046
3832
Re
cei
v
ed
Jul
y
30, 201
3; Revi
sed
Jan
u
a
r
y 1, 20
14; Accepted
Jan
u
a
ry 1
4
, 2014
A Low-Voltage High PSRR and High Precision CMOS
Bandgap Reference
Zhou Qiann
e
ng*
1
, Xue Rong
1
, Li Hongjuan
2
, Lin Jinzhao
1
, Li Qi
1
, Pang Yu
1
, Li Guoquan
1
1
Colle
ge of Ele
c
tronic Eng
i
ne
erin
g, Chon
gq
i
ng Un
iversit
y
o
f
Posts and T
e
l
e
commu
nicati
o
n
s,
Cho
ngq
in
g 40
0
065, Ch
in
a;
2
Colle
ge of Co
mputer Scie
nc
e and T
e
chno
l
o
g
y
, Cho
n
g
q
in
g Univ
ersit
y
of Posts and T
e
le
communic
a
tio
n
s
,
Cho
ngq
in
g 40
0
065, Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhouq
n@cq
u
p
t.edu.cn
A
b
st
r
a
ct
By adopti
ng t
he techn
i
q
ue
of pre-reg
u
lat
o
r,
a high PS
RR an
d low
temper
ature co
efficient
piec
ew
ise-li
ne
ar ban
dga
p re
ference (BGR)
is design
ed for anal
og a
n
d
mixe
d-sig
nal
app
licati
on in t
h
is
pap
er. T
h
e
pi
e
c
ew
ise-lin
ear
BGR w
i
th pre-
regu
lator,
w
h
ic
h is
a
naly
z
e
d
and
si
mu
late
d
in
SMIC
0.18
μ
m
CMOS proc
es
s, has si
mpl
e
circuit arc
h
itect
u
re. Si
mu
lati
on
results s
how
that pi
ecew
ise-
line
a
r BGR
w
i
th
pre-re
gul
ator a
c
hiev
es pow
er
supp
ly rej
e
cti
on rati
o
(PSR
R) of -10
2
.488
dB an
d -99.
73
dB, -82.98
3dB
at
10H
z
,
10
0H
z
and 1k
H
z
res
p
ectively. Piec
e
w
ise-line
a
r
BGR w
i
th pre-reg
u
lator ac
hiev
e
s
the temper
ature
coefficie
n
t of 2.235 p
p
m/°C w
hen te
mp
eratu
r
e is in
the ra
n
ge fro
m
-50°C
to 115°C. W
h
en pow
er su
pp
ly
voltag
e V
DD
c
han
gin
g
fro
m
1.2V to
10V,
output v
o
lta
g
e
devi
a
tio
n
of
piec
ew
ise-li
ne
ar BGR w
i
th
pre-
regu
lator
is o
n
ly 0.
276
5
m
V, but
o
u
tput v
o
ltag
e of
piec
ew
ise-lin
ear
B
G
R w
i
thout pr
e-reg
u
lator
ha
s
a
devi
a
tion of
38.08
mV.
Ke
y
w
ords
:
piec
ew
ise-li
ne
ar co
mpe
n
sati
on, pre-r
egu
lat
o
r,
pow
er sup
p
ly rej
e
ctio
n ra
tio (PSRR), ba
ndg
a
p
referenc
e (BGR)
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
Bandga
p ref
e
ren
c
e
(BG
R
) is a very i
m
porta
nt
blo
ck in m
o
st a
nalog a
nd mi
xed-si
gnal
appli
c
ation
s
, su
ch a
s
digit
a
l-to-anal
og (D/A) and
a
n
a
log-to
-di
g
ital (A/D) conve
r
ters [1, 2].The
BGR voltage
sho
u
ld be i
n
depe
ndent of
fluctuation
s
of power
sup
p
ly voltage a
nd tempe
r
atu
r
e,
and al
so be
implemente
d
without m
odificatio
n
of fabrication
pro
c
e
ss.
In stand
ard CM
OS
techn
o
logy, the ba
sic id
ea
of BGR voltage is a
weigh
t
ed summ
atio
n of the forward
-
bia
s
emitt
e
r-
base voltage
V
EB
acro
ss para
s
itic ve
rtical PNP
bipolar
tran
sist
or an
d the therm
a
l voltag
e
V
t
.Traditional
BGR in
spi
r
ed by
Wid
l
ar [3] and
Brokaw [4
] is first-ord
e
r temp
erat
ure
comp
en
satio
n
.
However, temperature coeffici
ent
(
T
C
)
o
f
firs
t-
or
de
r
te
mp
er
a
t
ur
e
co
mp
en
sate
d
referen
c
e
s
is limited betwe
en 10 and 1
0
0ppm/º
C over the whol
e tempea
ra
ure range [5], so the
first-o
r
de
r
te
mperature compen
sate
d BGR
cann
ot meet the requireme
nts
of high p
r
e
c
ision
cir
c
uit
s
.
To improve
temperatu
r
e perfroma
n
c
e of
BG
R, many tempera
u
re co
m
pen
sation
techni
que
s h
a
ve been
re
p
o
rted [6
-9]. These re
porte
d BGRs in [7
-9] have a
c
hi
eved very go
od
temperature
cha
r
a
c
teri
stic, but t
h
e
i
r
pow
e
r
s
u
pp
ly r
e
je
c
t
io
n ra
tio
(PSRR) at
10
Hz is le
ss th
an
-
80dB. Re
ce
n
t
ly, demands for low-volta
ge BGR
ci
rcuits have in
crea
sed
eno
rmously b
e
ca
use
they are
wid
e
ly use
d
in
portabl
e ele
c
tronic
ap
plications.
Unfo
rtunately, po
wer supply n
o
ise
become
s
on
e
of the bottlenecks un
der
low po
we
r
su
pply voltage, and the p
o
wer supply n
o
i
s
e
injecte
d
to the output of th
e BGR
circuit
is so
metime
s the mo
st si
gnifica
nt noise. So, for mixed-
sign
al and a
nalog inte
gra
t
ed circuits
u
nder lo
w po
wer
sup
p
ly voltage, in order to rej
e
ct
the
power supply
noise coupl
ed from t
he high-sp
eed d
i
gital circuit o
n
the chip, it is nece
s
sa
ry to
cho
o
se a BG
R structu
r
e t
o
achieve hi
gh PSRR
pe
rforma
nce ov
er a b
r
oa
d freque
ncy ran
ge.
Fortun
ately, many techniq
ues
have
be
en repo
rted t
o
imp
r
ove P
S
RR
of BG
R, su
ch
as su
pply
indep
ende
nt current so
urce tech
niq
ue [10], pr
e-regul
ator tech
niqu
e [11-14], su
btracto
r
techni
que [1
5], pseu
do floating voltag
e so
urce
te
chniqu
e [16], ca
scade te
ch
nique [17], self-
ca
scode
current mirro
r
te
chniqu
e [18], l
o
w
dro
pout
re
gulator te
chni
que [1
9], and
voltage follo
wer
techni
que
with PMOS as i
nput tran
si
sto
r
[
20]. These
repo
rted BG
R with en
han
ceme
nt PSRR
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Low-Volta
g
e
High PSRR and Hig
h
Pre
c
isi
on CM
OS Bandga
p Ref
e
ren
c
e
(Zho
u
Qianne
ng)
3833
techni
que
ha
ve achi
eved
some
improvement PS
RR perfo
rman
ce
, but they ge
nerally h
a
ve
a
relatively hig
h
temp
eratu
r
e coefficie
n
t. The
r
ef
o
r
e, BGR archite
c
ture
with
lo
w
tem
peratu
r
e
coeffici
ent an
d high PSRR performan
ce
must
still be
analyzed an
d
discusse
d u
nder lo
w po
wer
sup
p
ly voltage.
A high PSRR and l
o
w te
mperature
co
efficent
CM
O
S
BGR with
less than 1V
output
voltage is d
e
s
ign
ed by ad
opting pie
c
e
w
ise-lin
ear
te
mperature co
mpen
sation a
nd
pre-reg
u
la
tor
techni
que in t
h
is pa
per. E
m
ploying a pi
ece
w
i
s
e-li
nea
r temperature
compe
n
satio
n
techni
que, the
desi
gne
d BG
R ci
rcuit a
c
hi
eves ve
ry go
od temp
eratu
r
e
cha
r
a
c
teri
stic ove
r
a
wide temp
erat
ure
rang
e. And,
the p
r
e-reg
u
l
a
tor
archite
c
ture i
s
used
to improve P
S
RR of BG
R over a
bro
a
d
freque
cny ran
ge.
This pa
per i
s
o
r
g
ani
zed
as foll
ows. I
n
sectio
n
2, analy
s
is of
piecewi
s
e
-
lin
ear BGR
without p
r
e
-
regulato
r
will
be di
scusse
d
.
Secti
on 3
will di
scuss t
he imp
r
oved
piecewi
s
e
-
li
near
BGR with pre-regulator. Simulation results will be
shown in Section 4. Fi
nally, conclusions
will
be given in Section 5.
2. Analy
s
is o
f
Piece
w
i
se
-l
inear BG
R
w
i
thout Pre
-
re
gulator
Figure 1 sho
w
s pi
ecewi
s
e
-
linea
r BG
R without
p
r
e-regulato
r
, whi
c
h con
s
ist
s
of MOS
trans
is
tors M
1
~M
11
, b
i
p
o
l
ar
tr
an
s
i
s
t
or
s
Q
1
~Q
2
,
re
sist
ors
R
1
~R
4
and amplifiers A
1
~A
2
. In t
h
is
pape
r, all M
O
S tran
sisto
r
s ad
opt the
long
cha
nnel
comp
one
nt so that the
cha
nnel
-len
gth
modulatio
n effect is negligi
b
ly small. For
convenie
n
ce
analysis, it is assu
med tha
t
I
j
is the drai
n
c
u
rrent of trans
is
tor M
j
, he
re j=1, 2
…
, 11.
M
1
M
2
A
1
A
2
M
3
M
4
M
5
M
6
M
7
M
8
M
9
M
10
M
11
Q
1
Q
2
R
1
R
2
R
3
R
4
A
B
C
V
RE
F
I
PTA
T
I
CT
A
T
I
PTA
T
I
CT
A
T
I
NL
V
DD
Figure 1. Piece
w
ise-lin
ear
BGR witho
u
t Pre-reg
u
lator
As
sho
w
n i
n
Figure 1,
bip
o
lar t
r
an
si
sto
r
Q
2
ha
s a
n
emitter a
r
ea
that is m time
s that
of
Q
1
. Amplifiers A
1
and A
2
are entirely the
same, a
nd th
eir d
c
gain A
d
has that A
d
>>1. Amplifier
A
1
force
s
voltag
e V
A
of n
ode
A and
voltag
e V
B
of n
ode
B be
equal,
a
nd am
plifier
A
2
force
s
voltage
V
B
of node B and voltage
V
C
of node C
be equ
al, i.e. V
A
=V
B
=V
C
=V
EB1
. Here, V
EB1
is the emitte
r–
base voltag
e
of bipol
ar tra
n
si
stor Q
1
. Trans
is
tors M
1
and M
2
ar
e
en
tir
e
ly th
e
same, so the drain
cur
r
e
n
t
I
PT
AT
of
M
2
can be
obtaine
d as:
1
1
ln
PTA
T
kT
Im
qR
(1)
Whe
r
e,
k is
Boltzman
n’s
con
s
tant, q i
s
ele
c
tr
onic
cha
r
ge, a
nd
T is a
b
solut
e
tempe
r
ature.
Equation
(1
) sh
ows th
at
I
PT
AT
i
s
pro
p
o
rtional
to a
b
sol
u
te temp
eratu
r
e
T. Similarly, the
d
r
ain
cur
r
e
n
t
I
CT
AT
of
M
3
can also be obtain
e
d
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3832 – 38
40
3834
1
2
E
B
CTA
T
V
I
R
(2)
In Equation
(2), V
EB1
has
a neg
ative te
mperature
co
efficient, so
I
CT
AT
i
s
a
current with
negative tem
peratu
r
e
coef
ficient. M
3
and M
9
are enti
r
ely the sa
m
e
, so drain current I
9
of M
9
is
equal to
drai
n current I
3
of M
3
, i.e. I
9
=I
3
=I
CT
A
T
. M
2
an
d M
6
a
r
e al
so entirely the
sam
e
, an
d it is
con
c
lu
ded th
at I
6
=I
2
=I
PT
AT
. M
7
and M
8
form cu
rre
nt mirror
pair, a
nd t
he chan
nel
width-len
g
th ratio
of M
8
is
α
ti
mes that of
M
7
. For the
drain
current
I
8
of M
8
, it i
s
con
c
lu
ded
that I
8
=
α
×I
PT
A
T
. By
optimizin
g the param
eter
α
, it is concl
u
ded that I
8
=
α
×I
PT
A
T
=I
9
=I
CT
A
T
und
er the room tempe
r
a
t
ure
T
r
. Therefo
r
e,
the following
expre
ssi
on can be obtai
ne
d as:
1
89
12
1
89
12
1
89
12
ln
,
ln
,
ln
,
EB
r
EB
r
EB
r
V
kT
Im
I
w
h
e
n
T
T
Rq
R
V
kT
Im
I
w
h
e
n
T
T
Rq
R
V
kT
Im
I
w
h
e
n
T
T
Rq
R
(3)
Acco
rdi
ng to
the ci
rcuit sh
own
in Fi
gure 1, d
r
ain
cu
rrents of M
8
, M
9
and
M
10
h
a
ve that
I
10
=I
8
-I
9
. M
10
and
M
11
are e
n
tirely the sa
me, so the drain cu
rrent I
NL
of M
11
can be obtaine
d as:
1
13
0,
1
ln
,
NL
r
EB
NL
r
Iw
h
e
n
T
T
V
kT
Im
w
h
e
n
T
T
qR
R
(4)
M
3
and M
4
, M
5
and M
2
are,
respe
c
tively, entirely the
same, so the
o
u
tput voltage
V
REF
of
BGR can be
written a
s
:
1
34
4
12
1
()
(
l
n
)
EB
R
E
F
NL
PT
AT
C
T
AT
N
L
V
kT
VR
R
m
R
I
V
V
V
qR
R
(5)
Whe
r
e,
34
1
1
()
l
n
PT
AT
kT
VR
R
m
qR
(6)
1
34
2
()
E
B
CT
A
T
V
VR
R
R
(7)
4
NL
NL
VR
I
(8)
Acco
rdi
ng to the above analysi
s
, V
PTAT
and V
CT
A
T
are a voltage with po
sitive- and
negative- tem
peratu
r
e
co
efficient respe
c
tively, and V
NL
is a volta
g
e
with pi
ecewi
s
e tem
peratu
r
e
cha
r
a
c
teri
stic. So, by choo
sing
ap
pro
p
ri
ate value
s
of R
1
~R
4
and
m,
the
tem
p
e
r
ature coeffici
ent
of bandg
ap voltage V
REF
will become
negligibly sm
all in theory. Figure 2 sho
w
s the relatio
n
of
V
REF
, V
PT
AT
, V
CT
AT
and
V
NL
. However, t
he op
eration
su
pply volta
ge of pi
ecewise-li
nea
r BG
R
without pre-regulato
r
is p
o
we
r su
pply voltage V
DD
,
whi
c
h cann
ot achieve hi
g
h
PSRR ove
r
a
broa
d fre
que
ncy rang
e. To imp
r
ove
PSRR of
th
e BGR
sh
o
w
n in
Figu
re
1, an im
proved
piecewi
s
e
-
lin
ear BG
R is a
nalyze
d
and
desi
gne
d by
adoptin
g a pre-regul
ator in
the next sect
ion.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Low-Volta
g
e
High PSRR and Hig
h
Pre
c
isi
on CM
OS Bandga
p Ref
e
ren
c
e
(Zho
u
Qianne
ng)
3835
Te
m
p
e
r
a
t
u
r
e
Volt
ag
e
T
r
V
PT
A
T
V
CTA
T
V
RE
F
V
NL
Figure 2. Rel
a
tion of V
PT
AT
, V
CT
AT
and V
NL
3. Analy
s
is a
nd Design o
f
Impro
v
ed Piece
w
i
s
e
-line
a
r BG
R
w
i
th
Pre-reg
u
lato
r
To improve t
he PSRR pe
rforman
c
e of BGR
sh
own in Figure 1, a
high PSRR pi
ece
w
i
s
e-
linear B
G
R i
s
de
sig
ned
by adoptin
g pre
-re
gulat
o
r
techni
que,
as
sho
w
n in
Figure 3. T
h
e
improve
d
BG
R with
pre
-
regulato
r
con
s
ist
s
of
a
start-u
p
ci
rcuit, pre
-re
gulato
r
and B
G
R
co
re
circuit. The B
G
R core circuit is simila
r as that
re
port
ed in Sectio
n
2, but the operatin
g su
p
p
ly
voltage of BGR core
circuit is the output voltage V
REG
of pre-re
gulator in
stea
d of powe
r
supply
voltage V
DD
. There are two possi
ble equ
ilibri
um poi
nts in the B
G
R
co
re
circuit, so a
start-up
cir
c
uit
is ne
ce
ss
ary
.
M
s1
~M
s6
form the start-u
p
circuit,
as sho
w
n in
Figure 3(c).
V
DD
M
1
M
2
A
1
A
2
M
3
M
4
M
5
M
6
M
7
M
8
M
9
M
10
M
11
M
12
M
15
M
13
M
14
M
16
M
17
M
18
M
19
Q
1
Q
2
R
1
R
2
R
3
R
4
3
1
A
B
C
(a
)
(b
)
(c
)
VR
E
G
V
RE
F
I
PT
A
T
I
CT
A
T
I
PT
AT
I
CT
AT
I
NL
4
V
RE
G
M
s1
M
s2
M
s3
M
s6
M
s4
M
s5
Figure 3. Improved BG
R (a
) BGR core ci
rcui
t; (b
) pre-regulato
r
; (c)st
a
rt-u
p circuit
As sho
w
n
i
n
Figure
3
(
b
)
, pre
-re
gulato
r
is
ma
de up o
f
tran
sisto
r
s M
12
~M
19,
and
wh
ose
function will
provide a reg
u
lated su
pply
voltage V
REG
which i
s
the operatio
n su
pply voltage of
BGR core
c
i
rc
uit. V
REG
is
adju
s
ted by a negative fe
edba
ck l
oop
so that the variation of po
we
r
sup
p
ly voltage V
DD
is rejected at node VREG. Assum
ed an in
cre
m
ental voltage
variation v
reg
at
node
VREG,
nod
e 1
an
d no
de B
will a
c
hieve
increm
ental
voltage va
riation v
1
an
d v
b
respe
c
tively. And, node
3
achi
eves a
n
am
plified in
cremental volta
ge variatio
n v
3
, which fe
ed
s a
curre
n
t into the output of p
r
e-regul
ator a
nd forc
e
s
the
voltage at no
de VREG to t
he rig
h
t voltage.
So, the PSRR of piecewi
s
e-linear B
G
R
with pre-
regul
a
tor
will be i
m
proved and be quantitatively
analyzed a
s
follows.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3832 – 38
40
3836
For
conveni
e
n
ce, it is a
ssumed that g
mj
and i
j
are,
resp
ectively, the tran
scon
d
u
ctan
ce
and
small
-
si
g
nal d
r
ain
cu
rrent of M
j
, he
re j=1, 2, 3…,
19. Assum
e
d that the
r
e i
s
a
n
in
creme
n
tal
voltage variat
ion v
reg
at node VREG, th
ere a
r
e in
cre
m
ental voltag
e variation v
a
and v
b
at nod
e
A
and no
de B resp
ectively.Then, v
a
and v
b
can be obtai
ned a
s
:
11
(-
)
r
am
r
e
g
a
vg
v
v
(9)
21
(v
-
)
r
bm
r
e
g
b
vg
v
(10)
Whe
r
e, r
a
an
d r
b
are
the
resi
stan
ce
se
en from n
ode
A an
d n
ode
B to groun
d
resp
ectively.
MOS
trans
is
tors
M
1
, M
2
, M
5
, M
6
and M
12
are
entirely the same, so it is
con
c
lu
ded th
at g
m1
=g
m2
=g
m5
=
g
m6
=g
m12
. Amplifier A
1
and A
2
are entirely the sa
me, and thei
r dc gai
n A
d
has that A
d
>>
1.
Acco
rdi
ng to
the ci
rcuit sh
own i
n
Fig
u
re
3, the voltag
e variatio
n v
1
at node
1 h
a
s that v
1
=A
d
×(
v
b
-
v
a
). So, v
1
can be written a
s
:
1r
e
g
1
1
1+
dm
dm
A
gv
v
Ag
(11)
Whe
r
e,
ba
rr
(12)
So, the following expre
s
sio
n
can b
e
obta
i
ned a
s
:
1
1
1
()
1+
1
~
2,
5
~
6,1
2
mj
mj
r
e
g
m
j
r
e
g
dm
ig
v
v
g
v
Ag
j
(13)
Acco
rdi
ng to
Equation
(1
3) and
the
circu
i
t sh
o
w
n
in Fi
gure
3, the
d
r
ain
curre
n
t va
riation
i
15
of M
15
can be obtain
ed a
s
:
2
15
1
5
1
(1
)
1+
mb
mm
r
e
g
dm
gr
ig
v
Ag
(14)
M
13
and M
14
are e
n
tirely
the sam
e
, so it is co
ncl
uded that i
14
=i
13
=i
12
. So, the drain
curre
n
t variation i
16
of M
16
c
an be obtai
ne
d as:
2
16
16
3
1
5
1
6
3
12
11
1
(1
)
1+
1+
mb
mm
m
r
e
g
m
m
r
e
g
dm
dm
gr
i
g
rg
v
g
rg
v
Ag
A
g
(15)
Whe
r
e, r
3
is the resi
stan
ce
of no
de
3. v
4
ha
s al
so
that
v
4
=A
d
×(v
c
-v
b
), and v
c
=g
m3
×(
v
reg
-v
4
). So, the
voltage variat
ion v
4
at node 4 can be o
b
tained a
s
:
42
1
4
reg
42
1
4
2
(1
)
(
1
+
)
(
1
)
dm
r
e
g
dm
b
dm
d
m
dm
Ag
R
v
Ag
r
vv
Ag
R
A
g
A
g
R
(16)
M
3
, M
4
and
M
9
are
entire
l
y the same,
so
it is con
c
lud
ed th
at g
m3
=g
m4
=g
m9
.Then, the
followin
g
expression
can b
e
obtaine
d as:
11
re
g
14
2
1+
(1
+
)
(1
)
3,
4
,
9
dm
dm
b
mj
mj
dm
dm
Ag
A
g
r
ig
v
Ag
A
g
R
j
(17)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Low-Volta
g
e
High PSRR and Hig
h
Pre
c
isi
on CM
OS Bandga
p Ref
e
ren
c
e
(Zho
u
Qianne
ng)
3837
Tran
si
st
or
s M
10
and M
11
are entirely the
same, a
nd th
e aspe
ct ratio
of M
8
is
α
times
that
of M
7
. So, it is co
ncl
ude
d that i
10
=i
11
=i
8
-i
9
=
α
×i
6
-i
9
.
Tra
n
si
st
or
s M
13
and M
19
are
entirely the same,
and it is co
ncl
uded that g
m19
=g
m13
.
Acco
rdi
ng to
the Kirchhoff
curre
n
t law
(KCL)
at nod
e
VREG, the f
o
llowin
g
e
q
u
a
tion can
be obtain
ed a
s
:
19
17
12
1
2
5
6
3
4
9
1
0
11
12
15
1
6
1
7
13
18
dd
r
e
g
mm
om
m
vv
gg
i
i
i
i
i
i
i
i
ii
iii
rg
g
(18)
Whe
r
e, v
dd
is the increm
e
n
tal voltage v
a
riation
of po
wer supply v
o
ltage V
DD
, r
o17
is the sou
r
ce-
drain resi
stan
ce of M
17
. It is assum
ed that A
d
β
>>r
b
, A
d
g
m15
β
>>1 a
nd A
d
g
m1
β
>>1. Acco
rding
to
Equation (9)~Equation (18), the followi
ng
expressio
n
can be obtai
ne
d as:
1
6
31
5
1
51
7
1
7
2
1
1(
+
)
re
g
b
dd
mm
m
o
o
d
v
r
v
g
rg
g
r
r
AR
(19)
In the similar ways, the re
lation of v
reg
and output voltage variati
on v
ref
of
BGR ca
n be
written a
s
:
43
3
reg
2
(1
)
ref
b
dd
v
rR
R
R
vA
R
A
(20)
So, PSRR of piecewi
s
e
-
lin
ear BG
R with
pre-reg
u
lato
r can be exp
r
e
s
sed a
s
:
2
0
lg
2
0
lg
2
0
lg
re
f
r
e
f
re
g
dB
dd
re
g
d
d
vv
v
PS
R
R
vv
v
(21)
Acco
rdi
ng to
Equation (1
9)~E
quatio
n (21
)
, it
is co
nclu
ded that
piecewi
s
e
-
lin
ear BG
R
with pre
-
regul
ator achieve
s
an impr
ove
d
PSRR by ado
pting pre
-
reg
u
lator.
4. Simulation Resul
t
s
To verify the
archite
c
ture
of the
de
si
gned
pie
c
e
w
i
s
e-li
nea
r BG
R in
this pa
per, it i
s
desi
gne
d a
n
d
sim
u
lated
by
Ca
den
ce
Sp
ectre
tool
s i
n
SMIC
0.18
μ
m CM
OS te
chnolo
g
y with
a
1.35-V po
we
r supply voltag
e.
Figure 4 sh
o
w
s the
simul
a
ted output v
o
ltage V
REF
of piece
w
ise-li
near BG
R
with- and
without-
pre
-
regulato
r
a
s
a func
tion
of temperatu
r
e
.
Simulation results
sho
w
that the outpu
t
voltage temp
eratu
r
e coefficient of pie
c
e
w
ise-lin
ear B
G
R with
out p
r
e-reg
u
lato
r is 3.313
ppm/
°
C
whe
n
tempe
r
ature rangin
g
from -50°
C
to 115°
C. And, the outp
u
t voltage V
REF
temperature
coeffici
ent of the improve
d
piecewi
s
e
-
lin
ear
BG
R with
pre-reg
u
lato
r is only 2.235
ppm/°C.
Figure 5
give
s the
PSRR
simulatio
n
re
sults of
pi
ece
w
ise-lin
ear B
G
R
with- an
d
witho
u
t-
pre
-re
gulato
r
.
Piecewi
s
e
-
li
near BG
R without
pre
-re
gulator a
c
hi
e
v
es PSRR o
f
-75.354dB,
-
75.308
dB, -72.2dB, -55.
181dB, -35.
23dB at
10Hz, 100
Hz, 1kHz, 10kHz an
d 10
0kHz
respe
c
tively, and
pie
c
e
w
ise-line
a
r BGR with
pre
-
reg
u
lator
achiev
es PS
RR of
-10
2
.488
dB, -
99.73dB, -8
2
.
983dB, -63.
036dB a
nd -42.962
dB at
10Hz, 100
Hz, 1kHz, 10kHz a
nd 1
0
0
k
Hz
respe
c
tively. Simulation
re
sults sho
w
th
at the PSRR is i
n
crea
se
d
by ab
out 36
% at 10
Hz b
y
adoptin
g the tech
niqu
e of pre-reg
u
lato
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3832 – 38
40
3838
Figure 4. Simulated Outp
ut Voltage of
Piece
w
ise-lin
ear BG
R with
- and with
out- pre-
regul
ator a
s
a
Function of T
e
mpe
r
ature
Figure 5. Simulated PSRR of Piece
w
ise-
Linea
r BGR
with- an
d with
out- pre-reg
u
l
a
tor
Figure 6. Simulated Lin
e
Regulatio
n of Piece
w
i
s
e-li
ne
ar
BGR with- and
with
out- pre
-re
gulato
r
Simulated lin
e reg
u
lation
s of piece
w
i
s
e
-
linea
r BG
R with- a
nd wit
hout- p
r
e
-re
g
u
lator i
s
sho
w
n in Fi
g
u
re 6. When
power
sup
p
ly voltage V
DD
cha
nge
s fro
m
1.2V to 10V, output voltag
e
variation of pi
ece
w
i
s
e-li
nea
r BGR with
ou
t pre-r
egul
ato
r
is 38.08mV,
but output voltage variati
on
of piece
w
i
s
e-linear BG
R
with pre-regu
lator is
o
n
ly 0.2765mV. S
i
mulation results sh
ows t
hat
piecewi
s
e
-
lin
ear B
G
R with
pre
-
regul
ator achiev
e
s
we
ll
line reg
u
lati
on
p
e
rfo
r
man
c
e by
ad
optin
g
the techni
que
of pre-regul
a
t
or.
Finally, perfo
rman
ce
s of piecewi
s
e
-
lin
ear
BG
R wit
h
- and
witho
u
t- pre
-
regul
ator are
summ
ari
z
ed
i
n
Tabl
e 1.
From this table
,
co
mp
ari
ng
with the
tem
peratu
r
e
dep
ende
nci
e
s
of the
BGRs, whi
c
h
have be
en re
ported i
n
[8]
and [20], it ca
n be fou
nd th
at they are i
n
comm
en
sura
te
level. But, by adopting th
e
techni
que of
pre
-re
gulato
r
in this
pap
er, the imp
r
o
v
ed piecewi
s
e-
linear BGR with pre
-
regul
a
t
or a
c
hieve
s
better
PSRR
and lin
e
regu
lation pe
rformance tha
n
t
hat
repo
rted in [8
] and [20].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Low-Volta
g
e
High PSRR and Hig
h
Pre
c
isi
on CM
OS Bandga
p Ref
e
ren
c
e
(Zho
u
Qianne
ng)
3839
Table 1. Perf
orma
nce Summary of BGR
Ref. [8]
Ref. [20]
BGR w
i
thout
pre-
regulator
BG
R w
i
th
pre-r
egulator
Process 0.18
μ
m
CMOS
0.09
μ
m
CMOS
0.18
μ
m
CMOS
0.18
μ
m CMOS
Suppl
y
voltage (
V
)
1.8
2.7
1.35
1.35
Output voltage
(
m
V)
646.4
213.982
680.25
681.29
Temper
ature coe
fficient (ppm/°C)
1.7
6.071
3.313
2.235
Temper
ature
ran
ge
(°C
)
-40~125
-20~120
-50~115
-50~115
PSRR
@25ºC (dB
)
10Hz -75
-82.7
-75.354
-102.488
100Hz -
-
-75.308
-99.73
1kHz -
-
-72.2
-82.983
10kHz -
-
-55.181
-63.036
100kHz -
-
-35.23
-42.962
5. Conclusio
n
A pie
c
e
w
ise
-
linear CMOS
BGR with
p
r
e-reg
u
lato
r,
who
s
e
a
r
chit
ecture i
s
si
mple, i
s
desi
gne
d an
d analyzed in this pap
er.
By adopting
the techniq
u
e
of pre-reg
u
lator, piecewi
s
e-
linear BG
R
with pre-re
gula
t
or achieve
s
highe
r PSRR perfo
rman
ce
than pie
c
e
w
i
s
e-li
nea
r BG
R
without p
r
e
-
regulato
r
. Simulation
results sho
w
th
at piecewi
s
e
-
linear B
G
R
with pre-reg
u
l
ator
achi
eves a
n
output voltage with exce
llent stab
ility, a low-tem
p
eratu
r
e coefficient, and hi
gh
PSRR pe
rformance. It is well suit
ed for
high preci
s
io
n circuits.
Ackn
o
w
l
e
dg
ements
Proje
c
t supp
orted
by Natural S
c
ie
nce
Foun
dation
Proje
c
t
of CQ
CST
C
(G
rant
No.
cst
cjjA400
11
),
Scientific and Technol
ogical Re
se
arch P
r
og
ra
m of
Cho
n
gqing
Muni
ci
pal
Educatio
n
Commissio
n (Grant
No. K
J
12
050
3, KJ1205
07, an
d
KJ12
053
3),
Nation
al Sci
ence
Found
ation
of Chi
na
(G
rant
No.
611
020
7
5
, and
61
301
124), S
p
e
c
ial
Proje
c
t of Int
e
rnet
of Thi
n
gs
from Minist
ry of Industry and Inform
ation Technol
o
g
y
，
2013 Progra
m
for Innovation Tea
m
Building
at Institutions of
High
er Ed
uca
t
ion
in Cho
n
g
q
ing,
an
d Ch
ongqi
ng Dev
e
lopme
n
t
Pla
n
of
Innovative Young Tale
nts (Grant
No. cstc20
13
kjrc-qnrc01
26).
Referen
ces
[1]
Su SJ, Z
han
g
HL. T
he Stud
y
and
Achi
evi
ng of
Hig
h-pr
e
c
ision
Data-
a
c
quisiti
on
Base
d on
∆Σ
ADC.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(8): 4
453-
446
0.
[2]
Yu F
,
Yang
HJ
, Li G. A Hig
h
Performanc
e S
i
gma-d
e
lta A
D
C for Aud
i
o
De
coder
Chi
p
.
TELKOMNIKA
Indon
esi
an Jou
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