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Sam PalermoAnalog & Mixed-Signal Center

Texas A&M University

Lecture 13: Folded Cascode & Two Stage Miller OTA

ECEN474/704: (Analog) VLSI Circuit Design Spring 2018

Announcements

• Exam dates reminder• Exam 2 is on Apr. 10• Exam 3 is on May 3 (3PM-5PM)

• Project description is posted on website

2

Agenda

• Single-Stage Cascode OTA

• Folded Cascode OTA

• Two Stage Miller OTA

3

Simple OTA

4

M1 M2Vi+ Vi-

VDD

VSS

Rbias

Itail

M5 M6

M3 M4

CL

Vo

621 || oomoutmv rrgRGA Gain DC

• Gain is limited by single-transistor output resistance

Single-Stage Cascode OTA

• Gain is larger by a gmro factor• Output swing range is limited

due to large compliance voltage of cascode current source load

5

6864241 || oomoommoutmv rrgrrggRGA Gain DC

[Razavi]

Single-Stage Cascode OTA Unity Gain Feedback Voltage Range

6

!!! a than Less Range Input) (&Output

conditionsat M2 into plugging and As

saturation M2by set V Maximum

saturationM4by set V Minimum

244

24242

4

2

out

4

out

TH

THGSTH

THGSbTHGSbTHxout

xGSxb

THxout

THbout

VVVV

VVVVVVVVVVVVVVVV

VVV

• Cascode configuration constrains output & unity-gain swing

[Razavi]

Folded Cascode Circuits

7

• “Folding” about the cascode node will increase input and output swing range

PMOS Input & NMOS Cascode

NMOS Input & PMOS Cascode

[Razavi]

Folded Cascode OTA

8

[Razavi]

Folded Cascode OTA Unity Gain Feedback Voltage Range

9

• With proper (high-value) choice of Vb2, a decent output and input swing range can be achieved

1

2 ||

GSDSATIoutDSATNDSATNCout

THPbout

VVVVVV

VVVMP

Tail

OR saturation sourcecurrent tailor cascode NMOSoutput byset V Minimum

saturation byset V Maximum

out

out

MP

MNC

TAMU-ELEN-474 2009 Jose Silva-Martinez

- 10 -

Folded-Cascode OTA: gm, rout and poles?

VB1 and VB2 must keep M1

- M5 in saturation region

VB2 > Vsat,4 + VGS3

VB1 < VDD - Vsat,5 – VSG2

Notice that ID5 biases both M2 and M1

43351221 ; dsmdsdsdsmdsoutmm rgrrrgrrgG

(for M4 sat)

(for M5 sat)

TAMU-ELEN-474 2009 Jose Silva-Martinez

- 11 -

Example: Folded-Cascode OPAMP

Find the gain and the phase from input to output and from input to node 2.

The low frequency gain is 77 dB and the unity gain frequency is around 80 MHz.The behavior of the gain from the input to node 2 is interesting: above the dominant pole.

51

1

oo

m

ggg

2

1

m

m

gg

Loutoo

mz Crgg

g 1

51

22

TAMU-Elen-474 Jose Silva-Martinez-08

- 12 -

FOLDED-CASCODE OTAFrequency response:

Can be approximated as having 4 poles associated

with nodes Vout, VX/W, VZ, and VY

The poles at Vy and Vz are associated to

N-type transistors higher frequencies

mnc

Z

mn

Y

mp

PC

out

outoutmV

gsC

gsC

gsC

gsCRgsA

1

1

1

1

1

1

1

11

vin-

2ID1

M1

MP

vout

VB2

VB1vin+

2ID1

VB2iOUT1

2ID1

VDD

-VSSMN

VB3

MN

VB1

VWVX

VY

VZ


- 13 -

Output referred noiseM1 produces an output current given by

Each transistor M2 generates a differential output current

Similarly, for each transistor M5

At low and medium frequencies, noise contribution of the cascode transistors can be neglected (M3 and M4)

Vn4

ro5

i04

M405

4n4n

054m

4m04 r

vv

rg1g

i

For cascode transistors

1n1m01 vgi

2n2m02 vgi

5n5m05 vgi

vin-

2ID1

M1

M2

vout

VB2

VB1vin+

2ID1

VB2iOUT1

2ID1

VDD

-VSSMN

VB3

MN

VB1

VWVX

VY

VZM4

M5

M3

iout2 = 2(ieq1

2 + ieq22 + ieqn

2 )

meq kTgi382 Remember

mnmmout gggkTf

i

21

2

316


- 14 -

Noise level for the folded-cascode OTA

Let’s find the input rms noise

Low-noise is associated with large gm1 and relatively small gm2 and gm5

BW m

m

m

m

mnoise df

gg

gg

gkTv 2

1

52

1

2

1

13

16

1

5

1

2

1

18

m

m

m

m

mnoise g

gggBW

gkTv

Or for a dominant (single) pole system with NBW = (/2)BW

vin-

2ID1

M1

M2

vout

VB2

VB1vin+

2ID1

VB2iOUT1

2ID1

VDD

-VSSM5

VB3

M5

VB1

VWVX

VY

VZ

Noise of diff pair Noise Factor (due to other transistors)

2

1212

22 13

161

mmnmm

m

outin

ggggkT

Gfi

fv

Considering thermal noise only

Multi-Stage Amplifiers

15

• Single-stage amplifiers typically have to trade-off gain and swing range

• Multi-stage amplifiers allow for higher gain without sacrificing swing range

• The major challenge with multi-stage amplifiers is achieving adequate phase margin to insure stability in a feedback configuration

Two Stage Miller OTA

16

42

2818

78

7842

82

78

8

42

221

1

oo

mmvmm

ooout

outmVDC

oooo

mm

oo

m

oo

mvvVDC

ggggAgG

ggR

RGAgggg

gggg

ggg

gAAA

Gain DC

Two-Stage Miller OTA – Frequency Response

17

• Stage 1 is a differential amplifier with an active load

• Stage 2 is a common-source amplifier with a large miller capacitor

• Using a Thevenin equivalent for Stage 1, we can use the common-source equations from Lecture 8

Two-Stage Miller OTA – Frequency Response

18

• The amplifier should be designed to yield one dominant pole, so we use the dominant pole approximation equations

872421

8

21

22812

28122811

and where

1

11

1esCapacitancTransistorNeglecting

OOoutOOout

L

m

LCoutout

LCoutCoutmoutp

CoutmoutLCoutCoutmoutp

rrRrrRCg

CCRRCCRCRgR

CRgRCCRCRgR

Jose Silva-Martinez -19- Texas A&M University

ELEN-474

VSS

M1 M1

01i 01i

-vd

01iM2 M2

02iM3

012i

vd

R1 C1RL CL

-v0

VDD

2

1

1

1

21

2

1

11

3

1

1

tantan180arg_

,min*

p

u

p

u

ppVDC

L

Lp

p

L

mmVDC

inmPhase

AGBWCgCg

gg

ggA

valid?) system, poledominant (if

(LHP)

(LHP)

Main equations

p1 p2 GBW

AVDCPhase Margin < 45 degrees

Phase

u

21

11pp

VDC

ssAsA

Frequency Response – No Compensation


- 20 -

VSS

M1 M1

01i 01i

-vd

01iM2 M2

02iM3

012i

vd

R1 C1 CMRL CL

-v0

VDD

Phase compensation Pole splitting techniques!!

p1 p2

GBW

AVDC

After compensation Phase Margin > 45 degrees Bandwidth is reduced!!!

p1’

p2’u

2

1

1

1

11

1

32

31

11

3

1

1

tantan180arg_

*

pp

M

mpVDC

L

mp

ML

mp

L

mmVDC

WGBWGBinmPhase

CgAWGB

CCg

CggC

ggg

ggA

(LHP)

(LHP)

Frequency Response – Miller Compensation (Ignoring z)


- 21 -

ZEROpp

M

mpVDC

L

mp

ML

mp

L

mmVDC

WGBWGBWGBinmPhase

CgAWGB

CCg

CggC

ggg

ggA

1

2

1

1

1

11

1

32

31

11

3

1

1

tantantan180arg_

*

(LHP)

(LHP)

VSS

M1 M1

01i 01i

-vd

01iM2 M2

02iM3

012i

vd

R1 C1 CMRL CL

-v0

VDD

Parasitic (bad) RHP zero!!

p1 p2

GBW

AVDC

After compensation Phase Margin > 45 degrees Bandwidth is reduced!!!

p1’

GBW’ZER

O

(RHP) M

mZERO C

g 3

p2’

21

11

1

pp

zVDC

ss

sAsA

Frequency Response – Miller Compensation (Considering z)


- 22 -

VSS

M1 M1

01i 01i

-vd

01iM2 M2

02iM3

012i

vd

R1 C1 CMRL CL

-v0

VDD

ZERO

u1

2p

u1

1p

u1 tan'

tan'

tan180inargm_Phase

Parasitic (bad) RHP zero!! Can be catastrophic if close or below wu!

p1 p2

GBW

AVDC After compensation Phase Margin > 45 degrees Bandwidth is reduced!!!

p1’

GBW’ZER

O

M

3mZERO C

g

p2’

p1 p2

GBW

AVDC

After compensation Phase Margin << 45 degrees Phase is equivalent to having 3 poles below unity gain frequency Unstable!

p1’

uZERO

p2’

z Impact on Frequency Response


- 23 -

VSS

M1 M1

01i 01i

-vd

01iM2 M2

02iM3

012i

vd

R1 C1 CMRL CL

-v0

VDD

M4VBIB1

IB2

Adding a series resistance

RZ

321

111

1

ppp

zVDC

sss

sAsA

13

1CRZ

p

MZm

z

CRg

3

11

(Generally high frequency & can be ignored)

p2

Z

Z

cancel can

LFP to RHP from zero pushes

infinity to zero RHP the pushes

)(initially frequencyhigher a to RHP push will R zero-Nonmargin phase improve to R design Can

Mm

MLZ

mZ

mZ

CgCCCR

gR

gR

3

1

3

3

1

1

Two Stage Miller OTA Noise

24

2

42

82

784

22

22

2

42

84

2

42

8278

2

22381

PSD Voltage Noise Referred-Input

223

8

PSDCurrent NoiseReferred-Output

oo

mm

mmm

mm

oi

oo

mm

oo

mmmm

o

gggg

ggggkT

Gfi

fv

gggg

ggggggkT

fi

Next Time

• OpAmp Feedback & Stability• Common-Mode Feedback Techniques

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