1 opamps part 2 dr. david w. graham west virginia university lane department of computer science and...
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OpampsPart 2
Dr. David W. Graham
West Virginia UniversityLane Department of Computer Science and Electrical Engineering
© 2009 David W. Graham
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High Gain
• Goal of opamp design – High gain• Previous opamps do not have very high gain• Example – 5T Opamp
– Gain = -gm1ro2||r04
– Subthreshold operation – |Gain| ≈ 650– Above threshold operation – |Gain| ≈ 50
• Need much higher gain– Cascode structures provide high gain– Cascade of multiple amplifiers
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Telescopic Opamps
MbVb
Vi1
Vo2
Vi2M1 M2
Vo1
Vb1
Vb2
Vb3
M5 M6
M7 M8
M3 M4
6684421 || oxooxomv rgrrgrgA
Approximately the square of the original gain
This is a high-speed opamp design
Major Drawback• Very limited allowable signal swing• Must ensure all transistors stay in saturation• Limited signal swing at both the input and
the output
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Telescopic Opamps – Single-Ended Output
MbVb
Vi1
Vout
Vi2M1 M2
Vb1
M5 M6
M7 M8
M3 M4
MbVb
Vi1
Vout
Vi2M1 M2
Vb1
M5 M6
M7 M8
M3 M4
Vb2
• Increased output signal swing• Requires an additional bias
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Unity-Gain Feedback Connection• Another major drawback to the telescopic opamp is the very limited
range for unity-feedback connections• Therefore, this opamp is rarely used as a unity-gain buffer• Often used in switched-capacitor circuits, where the output is fed
back to the input only for short durations of time
MbVb
Vi1
Vout
M1 M2
Vb1
M5 M6
M7 M8
M3 M4
Vx
For M2 and M4 to stay in saturation
24141
441
22412
for
for
TgsboutTb
Tbout
TgsbTxout
VVVVVV
MVVV
MVVVVVV
Voltage range for Vout
42
244minmax
ovT
TgsT
VV
VVVVV
Always less than a threshold voltage
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Folded Cascode Structure
Used in opamps to increase input/output voltage ranges
VoutVin
Vb
Iref1
Iref2MbVb
Vi1 Vi2M1 M2
M3 M4
Iref1
Vb
Vo2Vo1
Iref2
Iref3 Iref4
13 2 refb
ref II
I
• Iref1 is typically greater than Ib to improve response after slewing
• Burns more power than the telescopic version
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Folded Cascode Opamp
MbVb
Vi1 Vi2M1 M2 Vb2
M7 M8
M9 M10
M5 M6
M3 M4
Vb3
Vb1
Vb4
Vo2Vo1
Vout
M5 M6
M3 M4
Vout
M5 M6
M3 M4
Vb1
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Differential Gain of the Folded Cascode Opamp
MbVb
Vi1 Vi2M1 M2
M7 M8
M9 M10
Vb3
Vb4
Vout
M5 M6
M3 M4
Vb1
• Resistance looking into the source of M7 is much less than ro1||r09
• Virtually all current flowing out of M1 will flow into the source of M7
466210881 |||| oxoooxomv rgrrrgrgA
[Slightly] reduced gain from telescopic amplifier
ICMR
19,
11,9,,1
Tovdd
gssatsatddbsatgs
VVV
VVVVVV
to
Output range
satddsat VVV 22 to
Can use pFET inputs for operation to ground
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Folded Cascode Summary
Comparison to Telescopic Opamp• Larger input/output swings• Can be used in unity-gain configuration• One less voltage is required to be set
• Do not need to worry about the CM voltage• Decreased voltage gain• Increased power consumption (plus, I9 should
be ~1.2-1.5 times Ib)• Lower frequency of operation• More noise
Overall, the folded cascode opamp is a good, widely used opamp
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Two-Stage Opamp
• Cascade of two amplifier stages– First stage – Differential amplifier– Second stage – High-gain amplifier
V1 V2M1 M2
M3 M4
MbVb1
M5 M6
M7 M8
Vb2
Vb3
Vo2Vo1
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Two-Stage Opamp (Single-Ended Output)
• Cascade of two amplifier stages– First stage – Differential amplifier– Second stage – High-gain amplifier (CS Amp)
VoutV1 V2M1 M2
M3 M4
Mb
Vb
M5
M6
4211 || oomv rrgA
6552 || oomv rrgA
655421 |||| oomoomv rrgrrgA
• Large output swing (Vsat,6 to Vdd – Vsat,5)• ICMR same as 5T opamp• Unity-gain configuration sets a minimum
voltage to Vgs1-Vsat,b
• Can include cascodes, as well• Adding an amplifier stage adds a pole• Typically requires compensation to
remain stable
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Feedback Systems
H(s)
F(s)
+-
Vin(s) Vout(s)
If F(s)=1, then unity gain feedback
VinVout
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Opamp Poles
• Several poles in an opamp• Typically, one pole dominates
– Dominant pole is closest to the origin (Re-Im Plot)– Dominant pole has the largest time constant
• Dominant pole is often associated with the output node in an unbuffered opamp
– Large Rout and load capacitance
|H(j)|dB
log()
Av,dc
-3dB GB
Gain Bandwidth, GB
out
m
outoutoutm
dBdcv
C
G
CRRG
AGB
1
3,
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Multiple Poles
• For multi-pole systems, other poles may be close enough to the dominant pole to affect stability
• Typically two poles are of primary concern• Typically, for a two-stage, unbuffered opamp
– Pole at output of stage 1– Pole at output of stage 2– Dominant pole is usually associated with a large load
capacitance (i.e. output node)
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Multiple Poles
Gm1Vin Rout1 Cout1
Vin
Vx
Gm2Vx Rout2 Cout2
Vout
222
111
1
1
CRp
CRp
p2 typically dominates because of the load capacitance
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Multiple Poles
Unity Gain
Phase of -180°
|H(j)|dB
log()
Av,dc
2 1
log()
arg(H(j))
-90o
-180o
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Negative Feedback
In negative feedback configuration, if
Then, combined with subtraction (-180°) at the input
• Results in -360° phase shift
• This is addition (positive feedback)
• Since the gain is > 1 at this frequency, the output will grow without bound
• Therefore, this system is unstable at this frequency
• For stability, must ensure that
1801 jHjH and
1801 jHjH where for
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Phase Margin
• Typically, we like to design to provide a margin of error– These conditions (magnitude and phase) can deviate
from their designed values due to processes like noise and temperature drift
• Phase margin– A measure of how far away from a complete 360°
phase shift– Phase margin = 180° - arg(H(jω))– Measure at ω where |H(jω)| = 1
• Typical designs call for Phase margins of greater than 45°– Often higher, e.g. 60° - 90°
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Miller Compensation
• Need to spread the poles apart
• Add a capacitor from input to output of stage 2
VoutV1 V2M1 M2
M3 M4
Mb
Vb
M5
M6
Cc
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Miller Compensation
Gm1Vin Rout1 Cout1
Vin
Vx
Gm2Vx Rout2 Cout2
Vout
Cc
1
1
21222112121212
222121
cmcccc
mmm
in
out
CRRGCCRCCRsCCCCCCRRs
GsCRRGG
sV
sV
2
2
1221
22
2121
1
C
G
CCCCCC
CGp
CRRGp
m
cc
cm
cm
If C2 >> C1 and Cc > C1
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Miller Compensation|H(j)|dB
log()
Av,dc
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log()
arg(H(j))
-90o
-180o
Phase Margin
c
m
C
GGB 1
ω2 should be ≥ GB
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Opamp Comparison
GainOutput Swing
SpeedPower
DissipationNoise
Telescopic Medium Medium Highest Low Low
Folded-Cascode
Medium Medium High Medium Medium
Two-Stage High Highest Low Medium Low