EEL 6713 - Analog Integrated Circuit Design 1
n IV.1 Introduction
n IV.2 Performance parameters
n IV.3 OTA (single-stage op amp)
n IV.4 Cascode and folded-cascode amplifiers
n IV.5 Cascade amplifiers
n IV.6 Fully-differential amplifiers and common-modefeedback
Chap. IV –CMOS Operational Amplifiers
EEL 6713 - Analog Integrated Circuit Design 2
IV.1 IntroductionThe ideal op amp
+
vi
-
+
-
+Avi-
RS
+vo-
A→∞RS=0
+
vi
-
+
-
Gmvi GS +vo-
Gm=AGS
EEL 6713 - Analog Integrated Circuit Design 3
IV.1 Introduction
2 2
1 12
1
11 1
11 1
o
i
v R Rv R RR
A R
= + ≅ + + +
Applications of op amps - 1
+vi-
-
+
R2
R1 +vo-
Inverting amplifier
2 2
1 12
1
11
1 1
o
i
v R Rv R RR
A R
= − ≅ −
+ +
-
+
R2
R1
+vi-
+vo-
Noninverting amplifier
EEL 6713 - Analog Integrated Circuit Design 4
IV.1 IntroductionApplications of op amps - 2
Transimpedance amplifier
2 2 2
11
1ov A
R R Ri A A
= − ≅ − − ≅ − +
-
+
R2
i +vo-
- Continuous-time filters- SC filters- D/A & A/D converters- Sensor signal conditioning- Voltage & current references- Comparators- Nonlinear analog functions,- .......
EEL 6713 - Analog Integrated Circuit Design 5
IV.1 Introduction
P. Allen and D. Holberg – CMOS Analog CircuitDesign, 2nd. Ed., Oxford, New York, 2002.
Op amp design:•Choice of architecture;•Bias currents &Transistors dimensions;•Compensation;•Simulation;•Layout;•Post-layout simulation
Op amp requirements:•Technology;•Supply voltage;•Gain, GBW, output swing,noise, offset voltage, PSRR, ICMR, ....
EEL 6713 - Analog Integrated Circuit Design 6
IV.2 Performance parameters - 1
W.-C. S. Wu et al., Digital-Compatible High-Performance Operational Amplifier with Rail-to-Rail Input and Output Ranges, IEEE JSSC, vol. 29, no. 1, pp. 63-66, Jan. 1994.
Gate channel capacitances are used for compensation capacitors.
EEL 6713 - Analog Integrated Circuit Design 7
IV.2 Performance parameters - 2
L. Moldovan and H. H. Li, A Rail-to-Rail, Constant Gain, Buffered Op-Amp for Real Time Video Applications, IEEE JSSC, vol. 32, no. 2, pp. 169-176, Feb. 1997
Op Amp fabricated by MOSIS service in 2-µm, n-well CMOS, DPDM
EEL 6713 - Analog Integrated Circuit Design 8
IV.2 Performance parameters - 3
J. F. Duque-Carrillo et al., 1-V Rail-to-Rail Operational Amplifiers in Standard CMOS Technology, IEEE JSSC, vol. 35, no. 1, pp. 33-44, Jan. 1990
EEL 6713 - Analog Integrated Circuit Design 9
IV.2 Performance parameters - 4
Vid(mV)
Vod(V)
VOS
Offset voltage
Systematic offset – results from circuit design and is present even when all supposedly identical devices are matched (usually can be set to a low value).
Random offset – results from mismatches in supposedly identical pairs ofdevices (depends on area and bias).
P. R. Gray and R. G. Meyer, MOS Operational Amplifier Design – A Tutorial Overview, IEEE JSSC, vo. 17, n0. 6, pp. 969-982, Dec. 1982.
EEL 6713 - Analog Integrated Circuit Design 10
IV.2 Performance parameters - 5
P. R. Gray and R. G. Meyer, MOS Operational Amplifier Design – A Tutorial Overview, IEEE JSSC, vo. 17, n0. 6, pp. 969-982, Dec. 1982.
Differential voltage gain
d dBA
Extrapolated unity-gain frequency
1p−0 dB
EEL 6713 - Analog Integrated Circuit Design 11
IV.2 Performance parameters - 6
P. Allen and D. Holberg – CMOS Analog Circuit Design, 2nd. Ed., Oxford, New York, 2002.
Settling time
EEL 6713 - Analog Integrated Circuit Design 12
IV.2 Performance parameters - 7
CMRR, PSRR, Slew rate, Noise, Common-Mode Input Range, Output Swing, Power, Silicon Real State, ....
Dynamic Range (DR)
,max
,min
20log in
in
vDR
v
=
Noise (distinguish between signal and noise)
Distortion (within acceptable level: application-dependent).
EEL 6713 - Analog Integrated Circuit Design 13
IV.3 OTA (single-stage op amp) - 1Or current-mirror op amp (Johns & Martin) /symmetric OTA (Laker & Sansen)
VSS
IT
+vG1-
M1 M2
I1 I2
+vG2-
1:B CM 1:B CM
1:1 CM
CL
BI1 BI2
BI1
Io= B(I2-I1)
EEL 6713 - Analog Integrated Circuit Design 14
IV.3 OTA (single-stage op amp) - 2
K. Laker and W. Sansen: Design ofAnalog Integrated Circuits and Systems, McGraw-Hill, 1994
Fig. AP6-1
Bias circuitry Cascode outputLow-gain diff. amp.
EEL 6713 - Analog Integrated Circuit Design 15
IV.3 OTA (single-stage op amp) - 3
D. Johns and K. Martin, Analog Integrated Circuit Design, Wiley, 1997.
EEL 6713 - Analog Integrated Circuit Design 16
IV.3 OTA (single-stage op amp) - 4Input common-mode range: see diff. amp.
( )T
L P
BISR
C C=
+
1 2id g gv v v= −
CL+CP1m idBg v−oR
+vo
-
( ) ( )1
1m o
do L P
Bg RA s
sR C C=
+ +
( )11
( )2
m
L P
BgGBW Hz
C Cπ=
+
Io= B(I2-I1)
VSS
IT
+vG1-
M1 M2
I1 I2
+vG2-
1:B CM 1:B CM
1:1 CM
BI1 BI2
BI1CL
CM delays were neglected
asymmetry
EEL 6713 - Analog Integrated Circuit Design 17
IV.4 Cascode & folded-cascode amplifiers - 1
Telescopic diff. amp. with self-biased cascode CM
Telescopic diff. amp. with high-swing cascode CM
- Reduced output swing;
-Doublet !
- Not applicable to low supply voltage.
EEL 6713 - Analog Integrated Circuit Design 18
IV.4 Cascode & folded-cascode amplifiers - 2
D. Johns and K. Martin, Analog Integrated Circuit Design, Wiley, 1997.
Low-gain diff. amp. High-gain diff. amp.
EEL 6713 - Analog Integrated Circuit Design 19
IV.4 Cascode & folded-cascode amplifiers - 3
P.R. Gray, P.J. Hurst, S.H. Lewis, andR.G. Meyer, Analysis and Design ofAnalog Integrated Circuits, 4th. Ed.,Wiley, 2001.
EEL 6713 - Analog Integrated Circuit Design 20
IV.4 Cascode & folded-cascode amplifiers - 4
IT
IT/2
IT
IT/2
IT/2IT/2
IT∆i ∆i∆i
∆i
∆i2∆i
P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th. Ed., Wiley, 2001.
Can be changed toincrease positive output swing
Folded-cascode amplifier - 1
EEL 6713 - Analog Integrated Circuit Design 21
IV.4 Cascode & folded-cascode amplifiers - 5
0
01d
dL
AA
sC R≅
+
P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th. Ed., Wiley, 2001.
Folded-cascode amplifier - 2ICMR : Exercise
Output swing : ExerciseNote: The output swing can be around
-VSS+2VDSsatp to VDD-2VSDsatp for high-
swing current mirror and optimized bias.Ro
T
L
ISR
C± = ±
0d m oA G R=
& doublet
1m mG g=
( )
44
4
212 2
2
1 ds Ao ds
o ms A
ds Ads ds
ms A
gG g
R g
gg g
g
= =
+ +High-swing current mirror
EEL 6713 - Analog Integrated Circuit Design 22
IV.4 Cascode & folded-cascode amplifiers - 6
K. Bult & G.J.G.M. Geelen, A fast-settling CMOS opamp for SC circuits with 90-dB DC gain, IEEE JSSC, no.6, pp. 1379-1384, Dec. 1990.
The gain-boost technique - 1
Stacked devices reduce output swing.Cascade amplifiers: stability?
1 22
2 2
2 1 2 1
1 1ds ds
mg ddmg dd mg
ods ds ds ds
g gg n A
g A gR
g g g g
++ +
= ≅
EEL 6713 - Analog Integrated Circuit Design 23
IV.4 Cascode & folded-cascode amplifiers - 7The gain-boost technique - 2
P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th. Ed., Wiley, 2001.
EEL 6713 - Analog Integrated Circuit Design 24
IV.4 Cascode & folded-cascode amplifiers - 8The gain-boost technique - 3
P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th. Ed., Wiley, 2001.
EEL 6713 - Analog Integrated Circuit Design 25
IV.5 Cascade amplifiersTwo-stage amplifiers - 1
ICMR: see diff. amp.VDD
Output swing:
4 5DD DSsat o SS DSsatV V V V V− > > +
Low-voltage gain:
1 6
2 2 6 7
o m mdo
i ds ds ds dsLF
v g gA
v g g g g= = −
+ +
CL
VSS
M4M3
M1 M2
M8 M5
M7
M6
IT vi
+
-
CC
vo
1:1 1:B
1:1 1:2B
inv noninv
For systematic offset → 0. “Early” effect at the output
1:2B
EEL 6713 - Analog Integrated Circuit Design 26
IV.5 Cascade amplifiers
( )1
2 12 1
o x o o To C C
C
o o o oo o L
L
d v v dv dv II C C
dt dt dt C
dv dv I II I C
dt dt C
−= ≅ → =
−= + → =
Two-stage amplifiers - 2CC
CL
voGmI -AdII
Io1
Io2
vi
+
-
vx
T
C
ISR
C± = ±
6max ( 1) Bext
L
I B ISR SR
C+ +− +
≅ >
( 1) Text
L
B ISR
C− −
= −The output node can be the SR limiting node*
*For a discussion, see Laker & Sansen, pp. 510-512
EEL 6713 - Analog Integrated Circuit Design 27
IV.5 Cascade amplifiers
0 0max
; sin ; o oo
dv dvSR v A t A SR
dt dtω ω≤ = = ≤
Two-stage amplifiers - 3Amplitude x frequency limitation due to SR
J. Dostál, Operational Amplifiers, 2nd. Ed., Butterworth-Heinemann, Boston, 1993.
Amplitude limitation
SR-limited slope
EEL 6713 - Analog Integrated Circuit Design 28
IV.5 Cascade amplifiersTwo-stage amplifiers - 4
( ) ( )( ) ( )1
=+
o
in
A sVs
V A s F s
Determines the poles ofthe closed-loop system
Allen & Holberg, 1st ed.
EEL 6713 - Analog Integrated Circuit Design 29
IV.5 Cascade amplifiersTwo-stage amplifiers - 5
x x x x1
I IR C−
1
II IIR C− 1p2p
jω
σ
s-plane
The op amp design must take into account both load and feedback loop
φM
Allen & Holberg, 1st ed.
EEL 6713 - Analog Integrated Circuit Design 30
IV.5 Cascade amplifiersTwo-stage amplifiers - 6
Response of second order system with various phase margins
Allen & Holberg, 1st ed.
EEL 6713 - Analog Integrated Circuit Design 31
IV.5 Cascade amplifiersTwo-stage amplifiers - 7
Equivalent differential circuit
+
vin
-
RIgmIvinCI
+
vI
-
gmIIvIRII CII
+
vo
-
CC
1mI mg g=
( ) 12 4
2 4 6 6
I ds ds
I db db gb gs
R g g
C C C C C
−= +
= + + +
6mII mg g=
( ) 16 7
6 7
II ds ds
II db db L
R g g
C C C C
−= +
= + +
If CC→0, then
( ) ( ) ( )1 1o mI mII I II
in I I II II
V g g R Rs
V sR C sR C≅ −
+ +
Poles relatively close → phase margin can be low or even negative !!!
Exercise: Derive the transfer function Ad(s) of the compensated operational amplifier
EEL 6713 - Analog Integrated Circuit Design 32
IV.5 Cascade amplifiersTwo-stage amplifiers - 8
( ) ( ) ( )( )( )
0
1 2
11 / 1 /
dod
in
A s zVA s s
V s p s p−
= = −− −
Compensated operational amplifier
0d mI mII I IIA g g R R=
( ) ( )1
1 1
I I C II II C mII I II c mII I II c
pR C C R C C g R R C g R R C
≅ − ≅ −+ + + +
( )2mII c
I II
mII
I I IC II
g Cp
C C C C CgC
−≅ − ≅+ +
mII
c
gz
C=
x x x x
s plane
pole splitting
mII
c
gz
C=1
I IR C−
1
II IIR C− 1p2p
jω
σ
Note: 0 12 /d mI CGBW A p g Cπ = =
/T CSR I C=( ) ( )/ 1 1
2 T mI t f
SRI g n i
GBWφ
π= = + +
EEL 6713 - Analog Integrated Circuit Design 33
IV.5 Cascade amplifiersTwo-stage amplifiers - 9
x x
s-plane
mII
c
gz
C=
1p
2p
jω
σ
To avoid low phase margin,choose 2 , 2π>p z GBW
12π ≅ m
C
gGBW
C
1 1
2
2 2tan tan
2π π π
φ − − ≅ − − − M
GBW GBWp z
1 1
6 6
( / )
+ +
m I II C I II m
m C m
g C C C C C gg C g
EEL 6713 - Analog Integrated Circuit Design 34
IV.5 Cascade amplifiersTwo-stage amplifiers - 10
Laker & Sansen’s book
Simplified model for noise analysis(input-referred noise current source not accounted for)
2 22
2 22
oI nId
oII nIIvII
v eA
f f
v eA
f f
=∆ ∆
=∆ ∆
Ad is the op amp voltage gain
AvII is the voltage gain relative to the second noise source. For the calculation, account for the output impedance of the first stage and compensation network)
2nIe
compensation
2nIIe
ov
EEL 6713 - Analog Integrated Circuit Design 35
IV.5 Cascade amplifiersTwo-stage amplifiers - 11
NOTE: white noise onlyK. Laker and W. Sansen: Design ofAnalog Integrated Circuits and Systems, McGraw-Hill, 1994
Open-loop output noise of a Miller OTA
1st stage
2nd stageAvII
Ad
EEL 6713 - Analog Integrated Circuit Design 36
IV.5 Cascade amplifiersTwo-stage amplifiers - 12
Two-stage CMOS op amp with a cascode current mirror load in the input stage
P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 4th. Ed., Wiley, 2001.
This connection reduces the feedforward current through Cwhen comparing to connectingC to node Y
EEL 6713 - Analog Integrated Circuit Design 37
IV.5 Cascade amplifiersTwo-stage amplifiers - 13
P. Allen and D. Holberg – CMOSAnalog Circuit Design, 2nd. Ed., Oxford, New York, 2002.
CMOS two-stage op amp using nulling resistor compensation
EEL 6713 - Analog Integrated Circuit Design 38
IV.5 Cascade amplifiersTwo-stage amplifiers - 14
CMOS two-stage op amp using nulling resistor compensation
P. Allen and D. Holberg – CMOSAnalog Circuit Design, 2nd. Ed., Oxford, New York, 2002.
1
1
mII I II c
pg R R C
≅ −
( )2mII c
I II
mII
I I IC II
g Cp
C C C C CgC
−≅ − ≅+ + ( )6
11/c z m
zC R g
= −−
3
1
z I
pR C
= −
Placing z on top of p2:6 6
11 c IIz
m c
c L
m c
CC
CR
g CC
gC +
= ≅
+
High-frequency pole
Determined by source/drain and gate voltages, and W/L
EEL 6713 - Analog Integrated Circuit Design 39
IV.5 Cascade amplifiersTwo-stage amplifier: design equations - 1
0 1 2
11
2 4
62
6 7
d d d
md
ds ds
md
ds ds
A A A
gA
g g
gA
g g
=
=+
=+
( )2mII c
I II
mII
I I IC II
g Cp
C C C C CgC
−≅ − ≅+ +
mII
c
gz
C=
0 12 /d mI CGBW A p g Cπ = =
/T CSR I C=
CL
VSS
M4M3
M1 M2
M8 M5
M7
M6
IT vi
+
-
CC
vo
1:1 1:B
1:1 1:2B
inv noninv
VDD
EEL 6713 - Analog Integrated Circuit Design 40
IV.5 Cascade amplifiersTwo-stage amplifier: design equations - 2
7 7SS DSsat o DD DSsatV V V V V− + < < −
max
min
ICM
ICM
V
V
=
=See diff. amp.
CMRR, noise (white & 1/f), PSRR±, (random) offset voltage,
CL
VSS
M4M3
M1 M2
M8 M5
M7
M6
IT vi
+
-
CC
vo
1:1 1:B
1:1 1:2B
inv noninv
VDD
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