Lecture 290 – Low Power and Low Noise Op Amps (3/28/10)
Page 2901
CMOS Analog Circuit Design
© P.E. Allen  2010
LECTURE 290 – LOW POWER AND LOW NOISE OP AMPS
LECTURE ORGANIZATION
Outline
• Review of subthreshold operation
• Low power op amps
• Review of MOSFET noise modeling and analysis
• Low noise op amps
• Summary
CMOS Analog Circuit Design,
2
nd
Edition Reference
Pages 393414
Lecture 290 – Low Power and Low Noise Op Amps (3/28/10)
Page 2902
CMOS Analog Circuit Design
© P.E. Allen  2010
REVIEW OF SUBTHRESHOLD OPERATION
Subthreshold Operation
Most micropower op amps use transistors in the subthreshold region.
Subthreshold characteristics:
The model that has
been developed for
the large signal sub
threshold operation
is:
i
D
=
I
t
W
L
exp
±
²
²
³
´
µ
µ
¶
v
GS

V
T
nV
t
±
²
²
³
´
µ
µ
¶
1 +
v
DS
V
A
where
v
DS
> 0
and
V
DS
(sat) =
V
ON
=
V
GS

V
T
= 2
nV
t
Smallsignal model:
g
m
=
di
D
dv
GS

Q
=
I
t
W
L
I
t
nV
t
exp
±
²
²
³
´
µ
µ
¶
v
GS

V
T
nV
t
±
²
²
³
´
µ
µ
¶
1 +
v
DS
V
A
=
I
D
nV
t
=
qI
D
nkT
=
I
D
V
t
C
ox
C
ox
+
C
js
g
ds
=
di
D
dv
DS

Q
·
I
D
V
A
100nA
1
μ
A
Weak Inversion
Transition
Strong Inversion
Square Law
Exponential
i
D
v
GS
i
D
v
DS
V
T
100nA
v
GS
=
V
T
v
GS
≤
V
T
Fig. 7.40A
1V
2V
0
0
0
0
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Lecture 290 – Low Power and Low Noise Op Amps (3/28/10)
Page 2903
CMOS Analog Circuit Design
© P.E. Allen  2010
Boundary Between Subthreshold and Strong Inversion
It is useful to develop a means of estimating when a MOSFET is making the transition
between subthreshold and strong inversion to know when to use the proper model.
The relationship developed is based on the following concept:
We will solve for the value of
v
GS
(actually
v
GS

V
T
) and find the drain
current where these two values are
equal [
v
GS
(tran.) 
V
T
)].
The large signal expressions for each
region are:
Subthreshold
i
D
±
I
t
W
L
exp
±
²
²
³
´
µ
µ
¶
v
GS

V
T
nV
t
·
v
GS

V
T
=
nV
t
ln
±
²
²
³
´
µ
µ
¶
i
D
I
t
(
W/L
)
±
nV
t
±
²
²
³
´
µ
µ
¶
1 
I
t
(
W/L
)
i
D
if
0.5 <
i
D
/(
I
t
W/L
).
Strong inversion
i
D
=
K'W
2
L
±
³
´
¶
v
GS

V
T
2
·
v
GS

V
T
=
2
i
D
K'
(
W/L
)
i
D
v
GS
V
T
i
D
=
(
v
GS

V
T
)
2
K‘W
2
L
i
D
=
nV
t
v
GS

V
T
I
t
W
L
exp
(
)
i
D
(tran.)
v
GS
(tran.)
07050701
Lecture 290 – Low Power and Low Noise Op Amps (3/28/10)
Page 2904
CMOS Analog Circuit Design
© P.E. Allen  2010
Boundary Between Subthreshold and Strong Inversion  Continued
Equating the two large signal expressions gives,
nV
t
±
²
²
³
´
µ
µ
¶
1 
I
t
(
W/L
)
i
D
=
2
i
D
K'
(
W/L
)
·
n
2
V
t
2
±
²
²
³
´
µ
µ
¶
1 
I
t
(
W/L
)
i
D
2
=
2
i
D
K'
(
W/L
)
Expanding gives,
n
2
V
t
2
±
²
²
³
´
µ
µ
¶
I
t
2
(
W/L
)
2
i
D
2

2
I
t
(
W/L
)
i
D
+ 1
±
n
2
V
t
2
=
2
i
D
K'
(
W/L
)
if
(
I
t
W/L
)/
i
D
< 0.5
Therefore we get,
i
D
(tran.) =
K'W
2
L
n
2
V
t
2
For example, if
K’
= 120
μ
A/V
2
,
W/L
= 100, and
n
= 2, then at room temperature the
value of drain current at the transition between subthreshold and strong inversion is
i
D
(tran.) =
120
μ
A/V
2
100
2
4·(0.026)
2
= 16.22
μ
A
One will find for UDSM technology, that weak inversion or subthreshold operation can
occur at large currents for large values of
W/L
.