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Improving Op Amp performance
• Improving gain
– cascoding
– cascading
– feedback
– feed forward
– push pull
– complementary input
– decreasing current
– using “analog friendly” CMOS processes
– using bipolar
• Improving speed
– Increasing UGF,  increase transient speed
• Settling may not improve, which depends on PM and
secondary poles
• Cannot simply increase W/L ratio  optimal sizing for a
given CL
• Two stage optimal design: can potentially achieve higher
UGF than single stage
– Increasing PM at UGF,  reduce ringing
• Once PM large enough, no effect
– Taking care of secondary poles and zeros,  reduce
settling time to 1/A0 level
• Pole zero cancellation be accurate and at sufficiently high
frequency
• Cascode or mirror poles sufficiently high frequency
• Reduce parasitic capacitances
– Increasing current
– Using better processes
• Other specifications to improve
– reduced power consumption
– low voltage operation
– low output impedance (to drive resistive load,
or deliver sufficient real power)
– large output swing (large signal to noise ratio)
– large input common mode range
– large CMRR
– large PSRR
– small offset voltage
– improved linearity
– low noise operation
– common mode stability
Two-Stage Cascode Architecture
• Why Cascode Op Amps?
– Control the frequency behavior
– Increase PSRR
– Simplifies design
• Where is the Cascode Technique Applied?
– First stage • Good noise performance
• May require level translation to second stage
• Requires Miller compensation
– Second stage • Increases the efficiency of the Miller compensation
• Increases PSRR
– Folded cascode op amp
• Reduce # transistors stacked between Vdd and Vss
VDD
Differential
Telescopic
Cascoding
Amplifier
VDD
Vyy
M7
M5
Vxx
M1
Needs CMFB
On either Vyy
Or VG9
M6
Vbb
M3
CL
M8
M4
CL
M2
Vin+
VinM9
Single-ended telescopic cascoding
Analysis very similar to
non-cascoded version:
think of the cascode pair
as a composite transistor.
M2-MC2 has gm=gm2
go=gds2*gdsC2/gmC2
Ao=gm/go
p1=-go/Co
Right half plane zero: gm/Cgd2
Output swing is much less
Vo1 max: VDD – Vsg3-I1*R + |VTP|
Vo1 min: Vicm – Vgs1 – Vbias – VTN
> Vss + Vdssat5 – Vbias – VTN
Several additional pole-zero pairs
At node D2-SC2:
Pole: g=gmC2+gmbC2+gds2+gdsC2
C=CgsC2+cgd2+cdb2
p=-g/C ≈-gmC2/(CgsC2+cgd2+cdb2)
Zero: z≈-gmC2/CgsC2
Pole-zero cancellation at -2pfT of MC2
Two stage
M4
M3
M2
Vi1
bias3
bias2
bias1
M1
M4
M3
M2
M1
Mb
Vi2
CMFB
Depends on supply and first stage biasing, may
need level shifting
Analysis very similar, except very small go1, more p/z
Cascoding the second stage
Very similar analysis, very small go
Not suitable for low voltage design
A balanced version
Mirror gain M:
gm6:gm4 =
gm8:gm3 *
gm11:gm10
SR=I6/CL
GB=gm1M/CL
Ao = gm1/go * M
Should have small current in these
But parasitic poles should be high enough
Layout of cascode transistors
With double poly:
In a single poly process:
Folded cascode
Balanced has better output swing and better
gain than telescopic cascode
Both single stage
Neither require compensation
But balanced limits input common mode
range due to diode connection
folding
VDDVDD
3
folded cascode amp
Same GBW as telescopic
Iss determines slew rate
4
6
Vin+
1
2
Iss
Vin-
Vbb
5
10
11
8
9
Differential amp requires CMFB
CL
• I1=I2=Iss/2, I3=I4=Iss*1.2~1.5
• Ao=gm1/go; go=gds9*gds11/gm11 +
(gds1+gds3)*gds5/gm5;
• p1=-go/CL; GB = gm1/CL
• Slew rate: Iss/CL
• Vomin = Vg11–VTN, Vomax=Vg5+|VTP|
• Vicmmin = vs+Vgs1,
vicmmax=Vg3+VTN+|VTP|
• Power = (Vdd-Vss)*(I3+I4) + biasing
power
Appropriate Rz moves zero to cancel p2
VDDVDD
VDD
Triode
transistor
Vb
Vb
3 4
15
Vx
Vin+
1
2
5
vo1-
Vin-
Vy
Iss
Vb
Cc
CMFB
11
9
vo+
Rz
CL
13
The left side cascode and second stage not shown
VDDVDD
Vb
3
NMOS11b
serves as Rz
4
Vb
vx
Vin+
1
2
Iss
Vb
VDD
vo1-
Vin-
Triode
5 transistor
Cc
15
vo+
11a
Vy
CMFB
11b
9
CL
13
VDD
VDD
4
Vb
Vbx
2
Iss
Vb
5
vo1-
Vin-
Cc
15
vo+
11a
Vby
CMFB
11b
9
CL
13
High speed low voltage design
• Assume VDD-VSS<VTN-VTP, assume a given
Itot
• Use minimum length for high speed operation
• Use appropriate Von13,15 to achieve balance
between high fT and high swing
• Select Von4,5,9,11 so that vo1 has + – 10%
(VDD-VSS) swing
• Set desired vocm at (VDD+VSS+Vdssat13Vsdsat15)/2
• Size transistors so that Vgs13 = mid range of
vo1 swing
• Show that the compensation scheme has very
similar pole splitting effect as in 7 transistor op
amp before
• Show that appropriate sizing of M11b can cause
the zero to move over p2
• If CMFB is applied at G3,4, compensation can
be connected to channel of M9
• Show that with an appropriate attenuator, the go
at vo1 can be made zero by positive feedback
from opposite side vo1+ to G5
• Show that with an appropriate gm5, the go at
vo1 can be made zero by positive feedback from
opposite side vD12 to G5
PUSH-PULL Output Stage
v
v
At low frequency, vg7 and vg8 nearly constant as vo swings
PUSH-PULL Output Stage
• Let AI be the current gain from M1 to M7
• Icc=sCcVg6, (Iss-Icc)/2–>I3, DI7=AI*Icc/2
• KCL at D6: -Icc + Vg6*gm6 +DI7=0, 
Can choose AI so that z cancels p2 for high speed
PUSH-PULL Output Stage
VDD
True push pull
VDD
3
VDD
4
5
Vin+
1
2
Iss
Vin-
CL
6
Problem: bias current in second stage unknown
VDD
VDD
3
If VDD-VSS is sufficient
VDD
4
Vbn
Vbp
Vin+
1
5
2
Iss
CL
Vin1st
But gain of
stage reduced!
6
VDD
VDD
3
VDD
To recover gain:
VDD
4
5
Vbp
Vin+
1
2
Iss
Vbn
CL
Vin-
6
VDD
VDD
3
VDD
VDD
4
5
Vbp
Vin+
1
2
Iss
Vbn
CL
Vin-
6
Figure 7.11 in book: process variations can cause
large change in M21/22 current, and mismatch in
M21 vs M22 bias results in offset voltage
Figure 7.1-2
Same comment applies to this one
Both can have very small quiescent current when vin≈0
But provide large charging or discharging current
power efficiency
Dynamically Biased (Switched) Amplifiers
• Switched amplifiers lead to smaller parasitic
capacitors and therefore higher frequency
response.
– Switched amplifiers require a non-overlapping clock
– Switched amplifiers only work during a portion of a
clock period
– Bias conditions are setup on one clock phase and
then maintained by capacitance on the active phase
– Switched amplifiers use switches and capacitors
resulting in feed-through problems
– Simplified circuits on the active phase minimize the
parasitics
Dynamically Biased Amplifiers
• Two phase non-overlapping clocks
Dynamically Biased Inverter
In f2 offset and bias
are sampled
In f1, COS provides
offset cancellation plus
bias for M1; CB
provides the bias for
M2.
Dynamic, Push-pull, Cascode Op
Amp
VDD - VB2 - vIN
vIN - VSS - VB1
A Dynamic Op Amp which
Operates on Both Clock Phases
True push-pull
Single stage
Differential-in
Single-ended out
No tail current
Off-set cancelled
For large swing:
Remove cascodes
S. Masuda, et. al.,
1984
LOW VOLTAGE OP AMPS
• We will cover:
– Low voltage input stages
– Low voltage bias circuits
– Low voltage op amps
– Examples
• Methodology:
– Modify standard circuit blocks for reduced
power supply voltage
– Explore new circuits suitable for low voltage
design
ITRS Projection – near term
ITRS Projection – longer term
Low-Voltage, Strong-Inversion Operation
• Reduced power supply means decreased dynamic range
• Nonlinearity will increase because the transistor is
working close to VDS(sat)
• Large values of λ because the transistor is working close
to VDS(sat)
• Increased drain-bulk and source-bulk capacitances
because they are less reverse biased.
• Large values of currents and W/L ratios to get high
transconductance
• Small values of currents and large values of W/L will give
smallVDS(sat)
• Severely reduced input common mode range
• Switches will require charge pumps
Input common mode range drop
VDD – VDS3sat + VT1 > vicm > VDS5sat + VT1 + VEB1
1.25 -0.25 + 0.75 > vicm > 0.25+0.75+0.25
p-n complementary input pairs
n-channel: vicm > VDSN5sat + VTN1 + VEBN1
p-channel: vicm <VDD- VDSP5sat - VTP1 - VEBP1
Non-constant input gm
constant input gm solution
Set VB1 = Vonn and VB2 = Vonp
Rail-to-rail constant gm input
Rail-to-rail constant gm input
Coban and Allen, 1995
The composite transistor
Bulk-Driven MOSFET
Bulk-Driven, n-channel Differential Amplifier
I1=I2=I5/2
As Vic varies,
Vd5 changes
and gmb varies

Varied gain,
slew rate, gain
bandwidth;
nonlinearity;
and difficulty in
compensation
Bulk-driven current mirrors
Increased vin range and vout range
Traditional techniques for wide
input and output voltage swings
Ib
Iin
1
Von
1
–
+
VT+Von
Ib
VT+2Von 1/4
VT+Von
Io =
Iin+Ib
1
>2Von
Von
1
Traditional techniques for wide
input and output voltage swings
Iin
Ib
Ib
+
VT+2Von
Veb
–
Von
1
Io =
Iin
1/4
VT+Von
Io
>2Von
1
Von
1
A 1-Volt, Two-Stage Op Amp
Uses a bulk-driven differential input pair,
wide swing current mirror load, and emitter
follower level shifter
Low voltage VBE and PTAT reference
Low voltage band-gap reference
Needs a low
voltage op amp
Vref=I3*R3=
VGo
To
A2 VBE  VG 0
1 k
m 1
R3 [
(
ln( ) 
) T 
kT  ln( )]
R1
R0 q
A1
To
R1q
T
One example implementation
Threshold Voltage Tuning for low
power supply voltages operation
standard
transistors
virtual
transistors
+
-
V tn
V tn'  Vtn  V dcn
V tp
V tp'  Vtp  V dcp
+
-
V dcn
V dcp
Implementation of the voltage
sources
Bias Voltage
V
-+
f
IN
dc
f2
f2
C1
1
f
1
OUT
C2
Bias Voltage V
dc
+ -
IN
f
f2
1
C1
C2
f2
f
1
OUT
A low voltage Op Amp core
Op Amp Implementation
VDD
VDD
R
M3
C
-
+
M2
IN
M4
OUT
OUT
M1
M5
VSS
Clock booster
Bias voltage generator
Clock booster (doubler)
CB1 >> CBL
Experimental Results
Power supply
Slew Rate
GB
DC gain
Input offset voltage
Input common mode range
Output swing for linear operation
PSRR at DC
CMRR at DC
Total power consumption
750mV
3.1V/uS
3.2MHz
62dB
2.2mV
0.1V-0.58V
0.31V-0.58V
82dB
56dB
38.3uW
Regulated Cascode
Vb7
Vi+
Q1
Vi-
Q2
Q11
A3
Q3
Vb5
A1
Q1


Q5


VG2
VG3
Q8


Q7


A4
Q6
A2
Q4
Q2
Regulated Cascode: one
realization
VD
k
VS
Common mode feedback for low voltage
1.5v op amp for 13bit 60 MHz
ADC
Output Stage and CMFB
Folded cascode with AB output
Lotfi 2002
Simulated performance
•
•
•
•
•
•
•
•
0.25 um process
1.5 V power supply
82 dB DC gain
2 V p-p diff output swing
170 MHz UGF @ 10 pF load
o
77 PM with b = 1/5
0.02% 1V step settling time: 8.5 ns
Full output swing Op Amp power: 25 mW
Differential difference input AB output
Alzaher 2002
Nested Miller Cap Amplifier
Not much successes
Low voltage amp
Low voltage amp
LOW POWER OP AMPS
• Op Amp Power = (VDD-VSS)*Ibias
– Reduce supply voltage: effect is small
• Many challenges in low voltage design same as
before
– Reduce bias: factor of hundred reduction
• Weak inversion operation
• Nano-amp to small micro-amp currents
• Needs small current biasing circuits and small
current reference generators
• Needs output stage to drive the load
– Design it so that it consume tiny quiescent power
– But generate sufficient current for large signals
– Tradeoff speed for reduced power
Sub-threshold Operation
Most micro-power op amps use transistors in the
sub-threshold region.
np~1.5; nn~2.5
Two-Stage, Miller Op Amp in Weak Inversion
At VDD-VSS=3V, ID5=0.2uA, ID7=0.5uA, got
A=92dB, GB=50KHz, P=2.1uW
Push-Pull Output in Weak Inversion
First stage gain
Total gain
S=W/L
What is VON?
Increasing gain
L5=L12, W12=W5/2
S13<<S4
go
Gain=gm/go
Increasing Iout with positive feedback
When vi1>vi2
i2>i1
i26=i2-i1>0
i27=0
i28=A*i26
itail=i5+i28
=i1+i2
i2/i1=e(vi1-vi2)/nvt
=evin/nvt
i2=i1evin/nvt
i1=I5 /{A+1-(A-1)evin/nvt)}
A=0 is normal case
A > 0 can greatly
enhance available
output current
for load driving
i1
i1+i2 much faster than i2-i1
as vin 
New i1+i2
i1=i2
I5
i1+i2=I5
i2=i1evin/nvt
A=3
A=2
A=1
A=0
I5
i2