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 + Von1

1.25 -0.25 + 0.75 > vicm > 0.25+0.75+0.25, unsymmetric!

p-n complementary input pairs

n-channel: vicm > VDSN5sat + VTN1 + VonN1

p-channel: vicm <VDD- VDSP5sat - VTP1 - VonP1

Non-constant input gm

N

constant input gm solutionLet Vb1 depends on Vicm so that Mb1 is turned on when MN1,2 are turned off, and Ip becomes 4 times.

Similarly when MP1,2 are off, In becomes 4 times.

When both pair on, In and Ip are bothe 1 times

Set VB1 = Vonn and VB2 = Vonp

Rail-to-rail constant gm input

As Vin+ and Vin- reduce, MN1,2 begins to turn off, MNC1,2 also begins to turn off. I7 reduces, so does I8. I9 = I12-I8 increases, so does I10, which is 3(I12-I8)=3(Ip-In), which becomes 3Ip when n-pair turns off.

When both on, I5=I1=I12=IBP=Ip; I11=I7=I6=IBN=In

Vi+ Vi-

Complementary input stage with rail-to-rail Vicmr and constant gm

Vi+ Vi-

3:

:3

Vi- Vi+

Ip

In

3(Ip-In)

Ip

In

InVbp

Vbn

Ip

3(In-Ip)

In

Ip

(Ip-In)

(In-Ip)

in+

in-

ip+

ip-

N1 N2P1 P2PC1,2 NC1,2

BN

BP

1 2 3 4

Vo1+ Vo1-

Folded cascode stage: summing current and convert to voltage

in+

in-

ip+

ip-

-in+

-ip-

io1-=ip- - in+

in+ =+gmn1*vid/2

in- = -gmn1*vid/2

ip+ =+gmp1*vid/2

ip- = -gmp1*vid/2

io1- =ip- - in+ = -(gmp1+gmn1)*vid/2

io1+=ip+ - in- = (gmp1+gmn1)*vid/2

Vo1- = io1- /go1

Vo1+ = io1+ /go1

Vo1d = (Vo1+ -Vo1+ ) = vid *(gmp1+gmn1)/go1

Vxx

Vyy

Vzz

Vbb

Folded cascode stage: feedback to reduce go1

Vxx

Vyy

Vzz

M1 M1

M2a M2a M2bM2b

Vbb

M3 M3

M4M4

i

gmn1vd/2 gdsn1

gds4

gds3

vcp

vcn

gds1

gds2agds2b

gm2avcn

+gmb2avcn

gm2bvcn

+gm2bvcp

+gmb2bvcn

vo1+

gm3vcp

Show that it is possible to make gain (vo1/vd) infinity by proper sizing.

Folded cascode stage: feedback to reduce go1, alternative

Vxx

Vyy

VzzM1a M1a

M2 M2

M1bM1b

Vbb

M3 M3

M4M4

i

gmn1vd/2 gdsn1

gds4

gds3

vcp

vcn

gds1

gds2a

gds2b

gm2avcn

+gmb2avcn

gm2bvcp

vo1+

gm3vcp

In either case, you can set vd=0, write KCL’s for the vn, vn and vo1 nodes, eliminate vn and vp, obtain expression in vo1 alone, set coefficient to zero, this gives conditions for go=0. From that, you can solve for gm for the feedback transistor and see how that can be realized.

For example, in the first choice, if you make gds of M1 and M3 4 times as large as the other transistors, it becomes relatively simpler to meet the conditions.

Small signal analysis for 2nd choice is easier, but quiescent voltage a concern. You can also feedback to PMOS transistors.

Feeding back to top or bottom transistors faces big challenges when supply voltage increases.

If the whole M2 (or M3 in the P version) is controlled by feedback, then the VgsQ of M2 is independent of supply.

M1

VG3

VG2

M1

M3

M2

M4

M3

M2

M4

Regulated Cascode for gain improvement

Vxx

Vzz

k

VD

VS

VS

VD

VG

VG

If you regulate, you have to regulate all four.

Second stage

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

Second stage push pull: Monticelli style

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

Requires: VDD-VSS > Vgs6+Vgs7+Vdssat_floating_CS

Vbp Vbn

D. M. Monticelli, “A quad CMOS single-supply Op Amp with rail-to-rail output swing,” IEEE J.Solid-State Circuits, no. 6, pp. 1026–34, Dec. 1986.

Don’t doVxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

Unpredictable current in second stage

Vzz

Vbn Vxx

Vbp

So, Vg6Q = VzzThis sets Id6.Q So, Vg7Q = Vxx

This sets Id7Q.

These circuits can come from the same biasing circuit for the main amplifier.So, no extra current, power consumption, noise, and offset introduced.

gds4

gds3

gds1

gds2a

gm2avcn

+gmb2avcn

vo1+

gm3vcp

Floating CS do not change ro1 or DC gain

gdsn gdsp

gmnvo1+

-gmpv’o1+

V’o1+

The impedance looking down from Vo1+ is Rn

To find impedance looking up from Vo1+, inject a test current i up.

V’o1+ = i*Rp

i_gdsn/p = (i-gmnvo1++gmpv’o1+)

Vo1+=V’o1+ + i_gdsn/p /(gdsn + gdsp)

Vo1+=i*Rp+(i-gmnvo1++gmpi*Rp) /(gdsn+gdsp)

Vo1+(1+gmn /(gdsn+gdsp))=i*{Rp[1+gmp/(gdsn+gdsp)] +1/(gdsn+gdsp)}

Vo1+/I =Rp gmp/gmn

Rn

Rp

So, size them so that gmp ≈ gmn

Note: gmn and gmp include possible body effects.

To the two gate terminals of M6 and M7, the two floating CS appears as a voltage source providing a voltage offset between the gates.

The impedance seen by the two gate terminals can be calculated by:

Rs = (Vgp – Vgn)/(current through the floating CS) = (Vgp – Vgn)/(gmp*Vgp – gmn*Vgn + (Vgp – Vgn)*(gdsn+gdsp)) ≈ 1/(gmp + gdsn+gdsp) ≈ 1/gmp

The above assumed that the NMOS and PMOS are sized to have the same gm.

Also, the calculation is only valid when both NMOS and PMOS are fully on and both in saturation.

When Vo is experiencing large swings, these conditions are not met. And the voltage difference between the two gate terminals no longer remain constant.

Differential signal path compensation

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

In order for M6 and M7 to have well defined quiescent current, we have to bias the circuit so that at Q, Vd2 = Vzz.

This is naturally provided by the usual bias generator:

Vzz

Vbb

Problem:Vd2 is a high impedance

node, small current mismatch in M1 and M4 leads to significant voltage change at vd2, which in turn changes the biasing current in the output stage.

Solution:use feedback to stabilize

common mode of Vd2.

VzzVd2L Vd2R

Feedback toM4 or part of it

Since Vd2L and Vd2R are normally nearly constant. We do not need to worry about the input range accommodation for this circuit.

Size the circuit so that, when vid =0, Id6 remain near desired level over all process variations in M1 and M4.

Current sensors

Quiescent biasing

IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 33, NO. 10, OCTOBER 1998

Vo+ and Vo- also need common mode stabilization

M6M6

M7 M7

Vocmd

M7t M7t

M7t’s are in triode

Choose R to a couple times bigger than RoChoose C to be near or a couple times larger than Cgs of CMFB circuit.

R R

C C

M6M6

M7 M7Vocmd

M7t M7t

M7t’s are in triode

R R

C C

Insert these

Why RC in common mode detector

V1

V2

R

R

Cgs

V

KCL at V:

(V1 – V)/R + (V2 – V)/R = V * sCgs

(V1 + V2)/R = V(sCgs + 2/R)

V = (V1 + V2)/2 * 1/(1 + sRCgs/2)

When |s| =|jw| << 2/RCgs,

V ≈ (V1 + V2)/2

Otherwise V is not close to common mode

To have CM detector work up to GB,

R << 2/(2GB*Cgs)

Why RC in common mode detector

V1

V2

R

R

Cgs

V

KCL at V:

(V1 – V)(1/R +sC) + (V2 – V) (1/R +sC) = V * sCgs

(V1 + V2) (1/R +sC) = V(sCgs + 2/R +2sC)

V = (V1 + V2)/2 * (1 + sRC)/(1 + sRC + sRCgs/2)

As long as Cgs/2 < C, at all freq:

V ≈ (V1 + V2)/2

C

C

Hence, the RC network acts as a better CM detector

Why CMBF to M7t instead of first stage:

Vo1+

Vo1-Vo+

For CM behavior, assume DM=0.Vo1+=Vo1-, and Vo+=Vo-=Vocm.

Without CMFB effect, at Q, Vo+ will be equal to Vg, which may be far below desired Vocm level.

With CMFB connected, the feedback effect will drive Vo1 so as to move Vo+ up to the desired Vocm level.

Since Vo1+ and Vo1- have a competing action on Vo+, it may take quite bit Vo1 movement to achieve the desired Vo+ movement, causing the biasing current in the second stage to be much larger than what is intended.

Vg

Compensation for diff signal path closed-loop stability

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

CCCC

At relatively low frequency:

• Because of gain from Vo1 to Vo, small signal Vo1 is much smaller than small signal Vo.

• Small signal current in compensation network is approximately Vo/(1/gmz+1/sCc).

• This current is injected to the Vo1 node.

Alternatively, a similar current can be injected:

• Impedance looking into a cascode node is about 1/gm

• Connecting Cc to a cascode node generates a current of the form Vo/(1/gm +1/sCc)

• Because the base transistor is a current source, this small signal current goes to the Vo1 node

• Even at high frequency, the current form is still valid.

Alternative compensation

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

CCCC

In the Cc+Mz connection,

• Bias voltage of Mz can be matched to track bias voltage of M6 robustness to process and temperature variations

• Size of Mz can be parameter scanned so as to place zero to cancel the secondary pole of the amplifier

In the Cc to cascode connection,

• Bias voltage can still be derived using current mirrors from a single current source, still have process and temperature tracking

• But size of cascode transistor is determined based on folded cascode stage design

• Cannot arbitrarily choose its size without considerations for output impedance at Vo1, gain of op amp, and so on.

Alternative compensation

Vxx

Vyy

VzzM1 M1

M2 M2

M6M6

Vbb

M3 M3

M4M4M7 M7

CCCC

VicmVicm

Vo+, Vo-

Use open loop Vicm sweep to find a “sweet spot” for your Vicm

VicmVin

Vo+

With Vicm at “sweet spot”, sweep Vin near Vicm with very fine steps (uV)

Vin

Vo-

d(Vo+-Vo-)dVin

Vo+-Vo- Vin

Vb2

VCMFB

Vb1

CC

Vo+

Vo-

Vo+

Vo-

Folded cascode stage: summing current and convert to voltage

Vi-

3:1

Summing circuit to add n-signal and p-signal together

Rail-to-rail constant gm input

Coban and Allen, 1995

The composite transistor

Bulk-Driven MOSFET

Bulk-Driven, n-channel Differential Amplifier

I1=I2=I5/2As Vic varies, Vd5 changes

and gmb varies

Varied gain, slew rate,

gain bandwidth;

nonlinearity; and difficulty

in compensatio

n

Bulk-driven current mirrors

Increased vin range and vout range

Traditional techniques for wide input and output voltage swings

1

Io =Iin+Ib

Iin

Ib Ib

1 1

1

1/4

VT+Von

VT+2Von

VonVon

>2Von

+

–VT+Von

Traditional techniques for wide input and output voltage swings

1

Io

Iin Ib Ib

1

1

1/4

VT+Von

VT+2Von

VonVon

>2Von

+

–Veb

Io =Iin

A 1-Volt, Two-Stage Op Amp

Uses a bulk-driven differential input pair, wide swing current mirror load, and emitter follower level shifter

Op AmpPerformance

Frequency Response

Low voltage VBE and PTAT reference

Threshold Voltage Tuning for low power supply voltages operation

+-

+ -

dcntntn VVV '

dcptptp VVV '

dcnV tnV

dcpV tpV

virtualtransistors

standardtransistors

Implementation of the voltage sources+-

+ -

1 12

21 1

2

Bias Voltage

21

C

2C

IN OUT

dcV

Bias Voltagedc

V

IN OUT1C

2C

A low voltage Op Amp core

Op Amp Implementation

Clock booster Bias voltage generator

VDD

OUT

VSS

RVDD

IN

OUTM1

M2

M3

M4

M5

C -+

Clock booster (doubler)

CB1 >> CBL

Experimental Results

Power supply 750mV

Slew Rate 3.1V/uS

GB 3.2MHz

DC gain 62dB

Input offset voltage 2.2mV

Input common mode range 0.1V-0.58V

Output swing for linear operation 0.31V-0.58V

PSRR at DC 82dB

CMRR at DC 56dB

Total power consumption 38.3uW

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

• 77o PM with = 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 OperationMost 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 InversionFirst stage gain

Total gain

S=W/L

Increasing gain

go

Gain=gm/go

What is VON?

L5=L12, W12=W5/2S13<<S4

Increasing Iout with positive feedbackWhen vi1>vi2

i2>i1

i26=i2-i1>0i27=0

i28=A*i26

itail=I5+i28

=i1+i2

i2/i1=e(vi1-vi2)/nvt

=evin/nvti2=i1evin/nvt

I5+ A*(evin/nvt-1)i1= (evin/nvt+1)i1

i1=I5 /{A+1-(A-1)evin/nvt)}

A=0 is normal case

A > 0 can greatly enhance available

output current for load driving

A=0

A=1

A=2

A=3

i1

i2

i1=i2

i2=i1evin/nvt

as vin

I5

I5

i1+i2=I5

New i1+i2

i1+i2 much faster than i2-i1

DC Offset (Self-mixing)

AD

ADc 0

c

)(, tx RFoffset