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Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Differential amplifiers Information Technology Gabor Csipkes Bases of Electronics Department

Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

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Page 1: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Analog Integrated CircuitsFundamental Building Blocks

Faculty of Electronics Telecommunications and Information Technology

Fundamental Building BlocksDifferential amplifiers

Information Technology

Gabor CsipkesBases of Electronics Department

Page 2: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Outline

differential and common mode signals – voltage balancing and virtual ground

a differential amplifier with resistive load

input and output voltage range input and output voltage range

the half circuit concept

small signal and low frequency model

small signal and high frequency model

frequency response

the differential amplifier with current source load

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 2

the differential amplifier with current mirror load

Page 3: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential and common mode signals

differential voltage (vin) → floating voltage between two ground referenced nodes

common mode voltage (VCM) → the component common to both Vinp and Vinm (average?)

2in

inp CMvV V

v

in inp inm

inp inm

v V VV V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 3

2in

inm CMvV V

2

inp inmCM

V VV

In most cases VCM is the DC component of Vin → virtual ground.

Page 4: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifiers

two common source amplifiers balanced around gound or virtual ground

input signal → differential and common mode components

the output can be either differential (symmetrical/balanced) or referenced to ground → special case: differential amplifier with current mirror loadspecial case: differential amplifier with current mirror load

operation often described through the equivalent half circuit (exceptions!!) → the circuit must be symmetrical

The load can be any type discussed for the elementary common source amplifiers

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 4

equivalent half circuits

Page 5: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Virtual ground

What is virtual ground? → playground balance/scale example

This point is not moving relative to ground in spite of the non-zero displacement but its

position is not zero → virtual ground

positive displacement

negative displacementrelative position to

ground not zero

position is not zero → virtual ground

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 5

the displacements are measured relative to the virtual ground instead of the proper ground

in terms of variations the virtual ground is no different from proper ground

in a circuit any potential not changing with the signal is virtual ground

Page 6: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with resistive load

common source amplifier with resistive load as half circuit

bipolar version can also be used if the technology allows bipolar transistors

differential input and differential output

input common mode (VCMin) range and output voltage swing are both important

Virtual ground

Virtual ground

GSV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 6

minoV

1,2 1,2 min

1,2 1,2 min

NMOS:

PMOS:CMin DSat Th o

CMin DD DSat Th o

V V V V

V V V V V

1,2 1,2

1,2 1,2

NMOS: ,

PMOS: 0,out S DSat DD

out S DSat

V V V V

V V V

Page 7: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with resistive load

the small signal low frequency model – the large signal behavior given by the DC transfer function: only qualitative description here

outVinpV

inmV

1

1

2

02 2 ||

02 2 ||

m in out

DS D

m in out

g V Vr R

g V Vr R

opVomV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 7

22 2 ||DS Dr R

1,2

0 1,22 ||2

outm

moutDS D

inRG

gVA r RV

DC transfer function

Page 8: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with resistive load

the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances

calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin

the differential input source resistance is neglected the differential input source resistance is neglected

1 2 1,2

2 2GDC C C

C C C C C

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 8

3 4 1,22 2L DB LC C C C C

1 1

13

12 2 2 || ||

in out m in out

DS D

sC V V g V V

r RsC

The analysis of one half circuit is sufficient → KCL at the output:

Page 9: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with resistive load

the small signal high frequency model

1,200

1

1,2 3,4 1

11( )

1 || 1

zpm

DS D

sC AA sg

A s ss C C r R

1p

1,2 3,4 1

1 12 2 ||p

out DS D L

fR C C r R C

g

one pole and one right half plane zero caused by

the Miller effect

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 9

1

1,2

10

2

2

mzp

mp

L

gfC

gGBW A fC

Page 10: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current source load

common source amplifier with current source load as half circuit

bipolar version can also be used if the technology allows bipolar transistors

differential input and differential output, similar to the resistive load configuration

input common mode (VCMin) range and output voltage swing are both important

Virtual groundVirtual

ground

GSV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 10

GSV

minoV

1,2 1,2 min

1,2 1,2 min

NMOS:

PMOS:CMin DSat Th o

CMin DD DSat Th o

V V V V

V V V V V

1,2 1,2 3,4

3,4 1,2 1,2

NMOS: ,

PMOS: ,out S DSat DD DSat

out DSat S DSat

V V V V V

V V V V

Page 11: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current source load

the small signal low frequency model

outVinpV inmV

1

1 3

2

02 2 ||

02 2 ||

m in out

DS DS

m in out

g V Vr r

g V Vr r

opVomV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 11

2 42 2 ||DS DSr r

1,2

0 1,2 3,42 ||2

outm

moutDS DS

inRG

gVA r rV

DC transfer function

Page 12: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current source load

the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances

calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin

the differential input source resistance is neglected the differential input source resistance is neglected

1 2 1,2

2 2GDC C C

C C C C C C C

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 12

3 4 1,2 3,4 3,42 2L DB DB GD LC C C C C C C

1 1

1 33

12 2 2 || ||

in out m in out

DS DS

sC V V g V V

r rsC

The analysis of one half circuit is sufficient → KCL at the output:

Page 13: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current source load

the small signal high frequency model

1,200

1

1,2 3,4 1,2 3,4

11( )

1 || 1

zpm

DS DS

sC AA sg

A s ss C C r r

1,2 3,4 1,2 3,4

1 12 2 ||p

out DS DS L

fR C C r r C

g

one pole and one right half plane zero caused by

the Miller effect

1p

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 13

1

1,2

10

2

2

mzp

mp

L

gfC

gGBW A fC

Page 14: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

no equivalent half circuit due to the current mirror load

differential input and single ended output

input common mode (VCMin) range and output voltage swing are both important

Virtual groundVirtual

ground

GSV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 14

minoV

1,2 1,2 min

1,2 1,2 min

NMOS:

PMOS:CMin DSat Th o

CMin DD DSat Th o

V V V V

V V V V V

1,2 1,2 3,4

3,4 1,2 1,2

NMOS: ,

PMOS: ,out S DSat DD DSat

out DSat S DSat

V V V V V

V V V V

Page 15: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

the small signal low frequency model

MOS diode

V1 2

inGS

VV

From the schematic:

1 1 4 31 3

1 1 0m GS G mDS DS

g V V gr r

2 3 1 41 3

0

1 1

1 12

m m m mDS DS

g g g gr r

A

inpVinmV

4GV2

4 4

2in

GS

GS G

VV

V V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 15

1 3

2 2 4 42 4

1 1 0

DS DS

m GS out m GSDS DS

g V V g Vr r

2 4

1 12DS DSr r

Eliminate VG4 and solve for Vout/Vin

0 1 2 4||m out

m DS DSG R

A g r r

1 2

3 4

1 2

3 4

m m

m m

DS DS

DS DS

g gg gr rr r

Page 16: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

the DC transfer function → single ended output

the slope in the linear region is A0 → the same order of magnitude as the gain of the configuration with current source load

the unloaded DC output voltage defined by the diode in the current mirror → V -V the unloaded DC output voltage defined by the diode in the current mirror → VDD-VSG3

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 16

Page 17: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances

calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin

the differential input source resistance is neglected the differential input source resistance is neglected

4GV

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 17

1 2 1,2

3 1 3 3 4

4 2 4

5 4

GD

DB DB GS GS

L DB DB L

GD

C C CC C C C CC C C C CC C

No half circuit analysis due to the current mirror that actively

influences the signal !!

Page 18: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

analysis of A(s) → consider the circuit as a whole and add capacitances to the small signal low frequency model

Kirchhoff's current law at the output and at the gate of M4

1 1g V V

eliminate VG4 and solve for Vout/Vin → rigorous solution is rather complicated

the demonstration shows that C has little influence on A(s) → it can be neglected

14 3 3 5 4 1 4

1 3

24 4 4 2 5 4

2 4

1 12 2

1 12 2

m in inG m G out G

DS DS

m in inm G out out G out

DS DS

g V VV g sC sC V V sC Vr r

g V Vg V V sC sC V sC V Vr r

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 18

the demonstration shows that C5 has little influence on A(s) → it can be neglected

A(s) will have the form:31

01 3

2

1 12

( )1

m m

CCA s sg g

A sas bs

Page 19: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Differential amplifier with current mirror load

the small signal high frequency model → use the dominant pole approximation on A(s)

0 1 1( )

1 1

zp zn

s sAA s

s s

where a and b are coefficients dependent on the small signal parameters

11

12 2

mp

out L L

gf GBWR C C

one pole and one right half plane zero caused by the Miller effect + a pole-left half plane

zero pair introduced by the mirror load

1 2

1 1p p

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 19

3 12

3 1

3

3

;2 222

m mp zp

mzn

g gf fC C

gfC

Page 20: Analog Integrated Circuits Fundamental Building Blocks · 2018-10-29 · Analog Integrated Circuits Fundamental Building Blocks Faculty of Electronics Telecommunications and Information

Bibliography

P.E. Allen, D.R. Holberg, CMOS Analog Circuit Design, Oxford University Press, 2002

B. Razavi, Design of Analog CMOS Integrated Circuits, McGraw-Hill, 2002

D. Johns, K. Martin, Analog Integrated Circuit Design, Wiley, 1996

P.R.Gray, P.J.Hurst, S.H.Lewis, R.G, Meyer, Analysis and Design of Analog Integrated Circuits, Wiley,2009

R.J. Baker, CMOS Circuit Design, Layout and Simulation, 3rd edition, IEEE Press, 2010

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 20