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Analog Integrated Circuits Fundamental Building Blocks

Faculty of Electronics Telecommunications and Information Technology

Fundamental Building Blocks

Differential amplifiers

Information Technology

Gabor Csipkes

Bases of Electronics Department

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

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?) 2

in inp CM

v V V v      

in inp inm inp inm

v V V V V       

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 3

2

in inm CM

v V V       2

inp inm CM

V V V     

In most cases VCM is the DC component

• f Vin → virtual ground.

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 load special 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

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 displacement relative 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

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

GS

V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 6 min

• V

 

1,2 1,2 min 1,2 1,2 min

NMOS: PMOS:

CMin DSat Th

• CMin

DD DSat Th

• V

V V V V V V V V       

   

1,2 1,2 1,2 1,2

NMOS: , PMOS: 0,

• ut

S DSat DD

• ut

S DSat

V V V V V V V    

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

• ut

V

inp

V

inm

V

   

1 1 2

2 2 || 2 2 ||

m in

• ut

DS D m in

• ut

g V V r R g V V r R           

• p

V

• m

V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 7

 

2

2 2 ||

DS D

r R  



 

1,2 1,2

2 || 2

• ut

m

m

• ut

DS D in R G

g V A r R V       

DC transfer function

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 V

• ut to Vin

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

1 2 1,2

2 2

GD

C C C C C C C C           

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 8

3 4 1,2

2 2

L DB L

C C C C C       

 

1 1 1 3

1 2 2 2 || ||

in

• ut

m in

• ut

DS D

sC V V g V V r R sC         

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

Differential amplifier with resistive load

 the small signal high frequency model

 



1,2 1 1,2 3,4 1

1 1 ( ) 1 || 1

zp m DS D

s C A A s g A s s s C C r R                      1

p

 

 

 

1,2 3,4 1

1 1 2 2 ||

p

• ut

DS D L

f R C C r R C g          

• ne pole and one right

half plane zero caused by the Miller effect

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 9

1 1,2 1

2 2

m zp m p L

g f C g GBW A f C              

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 ground Virtual ground

GS

V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 10 GS

V

min

• V

 

1,2 1,2 min 1,2 1,2 min

NMOS: PMOS:

CMin DSat Th

• CMin

DD DSat Th

• V

V V V V V V V V       

   

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

NMOS: , PMOS: ,

• ut

S DSat DD DSat

• ut

DSat S DSat

V V V V V V V V V     

Differential amplifier with current source load

 the small signal low frequency model

• ut

V

inp

V

inm

V

   

1 1 3 2

2 2 || 2 2 ||

m in

• ut

DS DS m in

• ut

g V V r r g V V r r           

• p

V

• m

V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 11

 

2 4

2 2 ||

DS DS

r r  



 

1,2 1,2 3,4

2 || 2

• ut

m

m

• ut

DS DS in R G

g V A r r V       

DC transfer function

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 V

• ut to Vin

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

1 2 1,2

2 2

GD

C C C C C C C C C C             

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 12

3 4 1,2 3,4 3,4

2 2

L DB DB GD L

C C C C C C C         

 

1 1 1 3 3

1 2 2 2 || ||

in

• ut

m in

• ut

DS DS

sC V V g V V r r sC         

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

Differential amplifier with current source load

 the small signal high frequency model

  

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

1 1 ( ) 1 || 1

zp m DS DS

s C A A s g A s s s C C r r                     

   

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

1 1 2 2 ||

p

• ut

DS DS L

f R C C r r C g          

• ne pole and one right

half plane zero caused by the Miller effect

1

p

 

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 13

1 1,2 1

2 2

m zp m p L

g f C g GBW A f C              

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 ground Virtual ground

GS

V

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 14 min

• V

 

1,2 1,2 min 1,2 1,2 min

NMOS: PMOS:

CMin DSat Th

• CMin

DD DSat Th

• V

V V V V V V V V       

   

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

NMOS: , PMOS: ,

• ut

S DSat DD DSat

• ut

DSat S DSat

V V V V V V V V V     

Differential amplifier with current mirror load

 the small signal low frequency model

MOS diode

V

1

2

in GS

V V    

From the schematic:

1 1 4 3 1 3

1 1

m GS G m DS DS

g V V g r r              

2 3 1 4 1 3

1 1 1 1 2

m m m m DS DS

g g g g r r A               

inp

V

inm

V

4 G

V

2 4 4

2

in GS GS G

V V V V        

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 15

1 3 2 2 4 4 2 4

1 1

DS DS m GS

• ut

m GS DS DS

g V V g V r r                 

2 4

1 1 2

DS DS

r r       

Eliminate VG4 and solve for V

• ut/Vin





1 2 4

||

m

• ut

m DS DS G R

A g r r    

1 2 3 4 1 2 3 4 m m m m DS DS DS DS

g g g g r r r r           

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

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 V

• ut to Vin

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

4 G

V

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 C C C C C C C C C C C C C                  

No half circuit analysis due to the current mirror that actively influences the signal !!

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 1 g V V     

 eliminate VG4 and solve for V

• ut/Vin → rigorous solution is rather complicated

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

   

1 4 3 3 5 4 1 4 1 3 2 4 4 4 2 5 4 2 4

1 1 2 2 1 1 2 2

m in in G m G

• ut

G DS DS m in in m G

• ut
• ut

G

• ut

DS DS

g V V V g sC sC V V sC V r r g V V g V V sC sC V sC V V r 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:

3 1 1 3 2

1 1 2 ( ) 1

m m

C C A s s g g A s as bs              

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 s A A s s s                            

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

1 1

1 2 2

m p

• ut

L L

g f GBW R C C         

• ne 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 1

p p

            

Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 19

3 1 2 3 1 3 3

; 2 2 2 2

m m p zp m zn

g g f f C C g f C             

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