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

Sam PalermoAnalog & Mixed-Signal Center

Texas A&M University

Lecture 15: Fully Differential Amplifiers & CMFB

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

Announcements

• Project Report Due May 1• Email it to me by 5PM

• Exam 3 is on May 3• 3PM-5PM

2

Agenda

• Fully differential circuits

• Common-mode feedback circuits

• Multi-OTA stages CMFB

• OTA-C filter w/ CMFB example

3

TAMU-Elen-474 Jose Silva-Martinez-08

- 4 -

Basic Operational Transconductance Amplifier Topologies

SINGLE-ENDED

FULLY-DIFFERENTIAL

TAMU-ECEN-474 Jose Silva-Martinez_08

- 5 -

Fully-Differential Circuits

-vo1vin1

-

vo2vin2-+

+

In general:

Hence

ocodoooo

o

ocodoooo

o

vvvvvvv

vvvvvvv

222

222

21122

21211

ic

id

cccd

dcdd

oc

odvv

AAAA

vv

0Vidic

oddc

0Vicid

oddd v

vAvvA

Differential-mode output Common-mode output

0Vidic

occc

0Vicid

occd v

vAvvA


- 6 -

Fully-Differential Filters: Effects of current source inpedance and mismatches

-vo1vin1

-

vo2vin2-+

+

A very important parameter:dc

ddAACMRR

icm

sid

m

s

smm

mm

icm

sid

m

s

smm

mm

vgYv

gY

YggZggv

vgYv

gY

YggZggv

1121

22102

2221

12101

21

21

Example:

2IB

IBIB

v1 v2

v01v02

Z2Z1

M1 M2

Solving the circuit:

Ys is the admittance associated with the current source 2IB

212

12ii

iciiidvvvvvv

and w/


- 7 -

Fully-Differential Filters: Non-idealities

2IB

IBIB

v1 v2

v01v02

Z2Z1

M1 M2

Voltage gain: Note the effects of themismatches, especially in Adc and Acd

2

1

1

2

21

21

012

12

1

2

2

121

21

21

012

12

2

1

1

2

21

21

012

21

1

2

2

121

21

21

012

21

21

22

2212

2

2

mms

smm

mm

vii

oocc

mm

s

smm

mm

vii

oocd

mms

smm

mm

vii

oodc

mm

s

smm

mm

vii

oodd

gZ

gZY

Ygggg

vvvvA

gZ

gZYZZ

Ygggg

vvvvA

gZ

gZY

Ygggg

vvvvA

gZ

gZYZZ

Ygggg

vvvvA

id

ic

id

ic

22

11

2

11

1

1

ZgZgY

ZZg

AACMRR

m

ms

m

dc

dd


- 8 -

Fully-Differential Circuits

-vo1Z1vin1

ZF

-

vo2Z1vin2 ZF

-+

+

112

0201

ZZ

vvvvA f

inindd

Ideal voltage gain

Ideally even-order distortions are cancelled

Ideally common-mode signals are rejected

What sets the output common-mode of these circuits?Function of the amplifier output resistance

-vo1Z1vin1

ZF

-

vo2Z1vin2 ZF

-+

+

IB

Common-mode offsets can impact the

performance of the following stages

• Can exceed the common-mode input

range of preceeding stages

• With finite Acc can accumulate in a

multi-stage amplifier circuit


- 9 -

Fully-Differential Amplifiers: COMMON-MODE DC offset

If IB is positive transistors M3 eventually will be biased in triode region (small resistance)

dc gain reduces drastically

Linear range is further minimized

THD increases

The common-mode output impedance is the parallel of the equivalent output resistance (M1 and M3) and the parasitic capacitors.

For large dc gain, the output impedance at nodes v01 and v02 are further increased and IB produces a dc offset = RoutIB. Large common-mode offsets!

How can this issue be fixed?

2IB

IB+IBIB+IB

v1 v2

v01 v02

Z1 M1 M1 Z1

M3M3Vb


- 10 -

Fully-Differential Amplifiers: Characterization

Common-mode current offset of 0.01 mAper side is added on purpose

Tail current is 0.5 mA while the current sources on top are 0.26 mA!

Differential input voltage is set at 0


- 11 -

Fully-Differential Amplifiers: Characterization

Offset current is integrated, and output voltage moves upstairs and reach steady state when the current sources on top become equal to 0.25 mA!

Differential input voltage is set at 0


- 12 -

Fully-Differential Amplifiers: Common-mode Feedback

Gcmf=100 A/V.

If the current offset is 10 A, then the offset voltage needed for compensation is 100 mV.

Expected DC outputs after settling are 100 mV.

Adder

CM-Feedback


- 13 -

Fully-Differential Amplifiers: Common-mode Feedback

Gcmf=100 A/V.

If the current offset is 10 A, then the offset voltage needed for compensation is 100 mV.

Expected DC outputs after settling are 100 mV.

If necessary to reduce this 100mV offset further, then use a larger Gcmf

Agenda





14


- 15 -

A common mode feed-back circuit is a circuit sensing the common-mode voltage, comparing it with a proper reference, and feeding back the correcting common-mode signal (both nodes of the fully-differential circuit) with the purpose to cancel the output common-mode current component, and to fix the dc outputs to the desired level.

What is a common-mode feed-back correction circuit ?


- 16 -

Fully-Differential Amplifiers: CMFB Principle

-vo1Z1vin1

ZF

-

vo2Z1vin2 ZF

-+

+

A common-mode feedback loop must be used: Circuit must operate on the common-mode signals only!

BASIC IDEA: CMFB is a circuit with very small impedance for the common-mode signals but transparent for the differential signals.

Use a common-mode detector (eliminates the effect of differential signals and detect common-mode signals)

Analyze the common-mode feedback loop: Large transconductance gain and enough phase margin

Minimum power consumption

2vvv 0201

cm

vo1 vo2vcm

Z Z

Simplest common-mode detector


- 17 -

CMFB Principles: Analysis of the loop for common-mode signals only

Analysis for common-mode noise; for instance noise due to power supplies:io1=io2=icm_noise

The two outputs can be connected together for the analysis of the CMFB loop!

mg

1Zcm

-

BASIC CONCEPTS:

The common-mode input noise is converted into a common-mode voltage (common-mode voltage noise) by the common-mode transconductance of the CMFB =1/Gm_fb.

common-mode voltage variations vcm_noise=icm_noise/Gm_fb !!

The larger Gm_fb the smaller the effects of the common-mode noise!

Gm_fb

vref

-

Gm_fb+

+

icm_noise vocm

Vref(define the common-mode level)

Effect of common-mode noise:

icm_noise

icm_noise

vcm_noise = icm_noise/Gm-fb


- 18 -

Fully-Differential Amplifiers: CMFB

CMFB Characteristics:

Transconductance gain=gm2/2 (no PMOS mirror in CMFB OTA)

dominant pole at the output

3 additional poles in the loop

Zcm reduces the OTA dc gain, affecting the differential gain

NOTE THAT Vcm IS FORCED TO BE AROUND THE GROUND LEVEL.

DC OFFSET VOLTAGE IS AROUND 2*Ioff/gm2

2IB

IBIB

v1 v2

v01v02

Z1 M1 M1 Z1

2IBM2 M2

GNDVcm

M3 M3

M3M3

CMFB

Zcm Zcm

Control


- 19 -

Fully-Differential Amplifiers: CMFB

CMFB Characteristics:

DC Transconductance gain=gm2/2

Loop gain (ignoring poles)

dominant pole at the output

3 additional poles in the loop

DC OFFSET IS AROUND 2Ioff/gm2

i3voc

m

2M10.5 Z1

2IBM2 M2

GNDVcm

M3 M3

2M3

CMFB

0.5Zcm

Loop

Zcurrent_source

2221

2121

33

2 ZgZgg

g mm

m

m


- 20 -

Fully-Differential Amplifiers: CMFB Principles

Common-mode stability: DC gain and most relevant poles

1 pole at vcm (1/RC)1 pole at M2 source (2gm2/C2)1 pole at gate of M3 (gm3/CP3)1 pole at the output (g01/C1)

dc gain = 0.5 gm2R012IB

IBIB

v1 v2

v01v02

Z1 M1 M1 Z1

2IBM2 M2

groundVcm

M3 M3

M3M3

CMFB

Zcm Zcm

GBW

First non-dominantpole

Dominant pole

Can be removed for CMFB analysis

Be sure phase margin > 45º


- 21 -

Fig. 3 Common-mode feedback basic circuit concept. (a) Basic common-mode detector, (b) A CMOS CMFB Implementation.

Notice that the resistors R reduce the differential gain!

. . .

Mp Mp Mp Mp

v02v01.v1

Mn Mn

Mcm Mcm

2IB

2IB

CL

CL

v2GND

.A

ACv1

2IB

v2

vC

R R

IB(vC)IB(vC)

(a) (b)

OPAMP CMFB

vC


- 22 -

Fully-Differential Amplifiers: Common-mode pulse

A pulsed current is added to the tail current (common-mode pulse)

This current must be absorbed by the CMFB

Differential feedback does not reduce common-mode offsets and noise.

Differential Time Constant=5K*10P=50nsecs


- 23 -

Fully-Differential Amplifiers with CMFBDifferential input signals only

Single-ended outputs

Seems to be that the system is working fine, isn’t it?

Settling time


- 24 -

Fully-Differential Amplifiers with CMFBDifferential input signals + common-mode pulses

Single-ended outputs


- 25 -

Fully-Differential Amplifiers with CMFBDifferential input signals + common-mode pulses

Common-mode output

True pulse response of the CMFBEvidently PM<45 degreesGBW ~ 1/0.8us=1.2 MHzDC-CMFB resistance ~ 10mV/Ioffset


- 26 -

Fully-Differential Filters: Adding buffers to handle the resistive CM-detector

The stability conditions are exactly the same for OTA’s and OPAMP’s:1 pole at vcm (1/RC)1 pole at M2 source (2gm2/C2)1 pole at gate of M3 (gm3/CP3)1 pole at the output (g01/C1)1 pole at buffer outputIn OPAMP’s you can use resistors as common-mode detector due to the presence of the output buffersdc gain = 0.5gm2R01

2IB

IBIBv01v02

Z1

M1 M1

Z1

2IBM2 M2

groundVcm

M3 M3

M3M3

CMFB

Zcm Zcm

GBW

First non-dominantpole

Dominant pole

Isolated Common-Mode Sensing

• Source-Followers isolate the loading of the common-mode sensor resistors

• Need to have a replica source follower to set the appropriate reference level for the CMFB amplifier

27

[Gray]

Two Differential Pair CM Sensor

28

CMocm

mDCCMcmc

mcmf

CMocmACCMDCCMcms

VVggVV

gG

VVgIIII

5

2,

2

220,,

[Gray]

M2 M2 M2 M2

M5

Agenda





29


- 30 -

2 IB

IB+icmfb

GND

VC

IB

IB

IBIB

GND

IB

VC

CMFB is required for Differential Structures

CMFB Requirements: Fixes the OTA output (low offset) ==> High dc loop gainReduction of common-mode noise==> Large Bandwidth

CMFB CMFB

Rg1g

Gm

mm

R Rmm gG

GND

CMFBicmfb = gcmfb(v01+v02-Vref)

IB+icmfbIB+icmfb


- 31 -

IB

VB1

IBIB

VREFIB

Common-mode loop gain = AV Gmp RL4 poles in the CMFB loop. Loop stability requires AV Gmp / CL < p2 @ VC, p3 @ VB1, p4 @ VD

IB

IBIB

IB

VB2

VDD

VSS

VC

Efficient CMFB for Differential Pair Based OTAs

+-AV

VD


- 32 -

IB

IBIB

IB

CMFB

IB

IBIB

IB

VDD

VSS

IB

GND

M1 M1R1 R1

M1

Efficient CMFB for Pseudo-Differential OTAs

common-mode detector

Agenda





33


- 34 -

Filter is based on Biquadratic Cells:Biquad Realization in Gm-C topology

vi-

vi+

vo-

vo++ -

- +

+ -

- +

+ -

- +

+ -

- +

gm1 gm2 gm1

2C2

2C2

2C1

2C1

gm1

f0 (MHz) Gm1 (mA/V) Gm2 (mA/V)

Biquad 1 537.6 5.4 9.6Biquad 2 793.2 5.4 5.07


- 35 -

Time Domain characterization of the CMFBCommon-mode characterization using common-mode current pulsesOne CMFB circuit per pole

•Pulse response of the CMFB

•Phase margin is better than 45 degrees

CMFB

icm

icm

vi-

vi+

vo-

vo++ -

- +

+ -

- +

+ -

- +

+ -

- +

CMFB


- 36 -

OTA based on complementary differential pairs

-v1 v1v0 -v0

VCP

VCN

CLCL

M1 M1

M3 M3

M4 M4

M2 M2

VDD

VSS

Efficient OTA based on linear complementary differential pairs

Linear circuit due to source degeneration M3 and M4

Suitable for fast applications

11 22

2

31

1

Mm

m

Mm

mm Rg

gRggG


- 37 -

Optimized Class AB Common-mode Feedback

• Most important non-dominant pole at B

v03 v04-v1 v1v01 v02

VREF

Previous OTA CMFB Next OTA

A A'B

C

M1M3

M6

M5E'

E

• Class AB error amplifier is used• 4 non-dominant poles at A~E• 2 LHP zeros at A and C (Helpful in BW extension)


- 38 -

Analysis of Class AB Common-mode Feedback

CMFB can be simplified taking advantage of circuit’s symmetry

Class AB CMFB Analysis

39

103

6

5

5

56

6

1

1

1

103

6

5

5

111

21

21

1

1

1

111

21

m

EB

L

L

Lm

m

m

mm

C

m

C

m

A

m

gs

m

EB

L

L

Lm

m

m

VCMFB

gsC

gsC

gsC

ggg

g

ggsCgsC

gsCg

sC

gsC

gsC

gsC

ggg

g

A

• 2 pole-zero pairs (A and C) are very close to each other

• Allows for stable CMFB


- 40 -

Remarks• DC operating points for high impedances are difficult to fix

• Fully differential amplifiers with high output impedance nodes must use common-mode feedback circuits .

• Common mode circuits can fix the DC operating points as well as minimize the common mode output components.

• Low voltage constraints impose optimal bias conditions at both the input and output ports of an amplifier.

• Common mode circuits for LV should be used both at the input and output

Next Time

• Output Stages

41

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

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