ECEN474/704: (Analog) VLSI Circuit Design Fall spalermo/ecen474/lecture10_ee474_simple... · PDF file 2018. 3. 6. · Announcements & Agenda • Simple OTA Parameters • OTA w/ Cascode

Sam Palermo Analog & Mixed-Signal Center

Texas A&M University

Lecture 10: Simple OTA

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

Announcements

• HW2 is due today

• No class on Thursday Mar 8

2

Announcements & Agenda

• Simple OTA Parameters • OTA w/ Cascode Load & Tail Current

Source

• References • Razavi Chapters 4, 6, 9.8-9.11 • Sedra/Smith Section 9.5.5

3

OpAmps and OTAs

• High voltage gain • High input impedance • Voltage source output

(low impedance) 4

OpAmp OTA

• High “voltage” gain • High input impedance • Current source output

(high impedance)

Operational Transconductance Amplifier

• Important Parameters • Differential Gain • Gain-Bandwidth Product • Common-Mode Input Range • Common-Mode Gain • Common-Mode Rejection

Ratio (CMRR) • Power-Supply Rejection Ratio

(PSRR) • Slew Rate

5

M1 M2Vi+ Vi-

VDD

VSS

Rbias

Itail

M5 M6

M3 M4

CL

Vo

OTA Differential Gain

6

M1 M2Vi+ Vi-

VDD

VSS

Rbias

Itail

M5 M6

M3 M4

CL

Vo

 

idoutmo

mmmm

id outm

m

mid outmo

id i

id i

vrgv gggg

vrg g gvrgv

vVvV

1

6521

6 5

1 2

and design By 22

2 and

2 Let

 

  

  

 

  

 

26

1 1

oo

m outm

id

o DM gg

grg v vA

 

TAMU-ELEN-474 2009 Jose Silva-Martinez

- 7 -

Frequency Response

id1

IB

M1 M1

v1

id2

iout id1

0.5gmvd RXCX

Vx

    gdndbndgpdbpgspX

mpmpPX

d XX

Xm X

CCCfactormillerCCC

ggrrR

V CSR RgV



 



12

/1/1|||| 1

5.0

001



Magnitude

gmRX

1/RXCX

VX

Consider node VX

v2

2 dv

2 dv

TAMU-ELEN-474 2009 Jose Silva-Martinez

- 8 -

Low Frequency Response

0.5gmvd 1/gmp’CX

Vx



gmR0

gmpvx

CO

Vo

-0.5gmvd

Ro

Vout

OPONO RRR 

id1

MP

id1

IB

M1 M1

v1

id2

iout VX

MP’

 

odmo

mp x

ompx d

mo d

mo

Rvgv

g R

RgRvgRvgv





  

  

 

  

1 222

dv 2 dv

TAMU-ELEN-474 2009 Jose Silva-Martinez

- 9 -

Frequency Response

0.5gmvd 1/gmp’CX

Vx



gmR0

1/R0C0

gmpvx

CO

Vo

-0.5gmvd

Ro

Vout

AV1

AV2

OPONO RRR 

id1

MP

id1

IB

M1 M1

v1

id2

iout VX

MP’

   





   









   

  

   





   





 

   

  

 

  

 

    





   





   

  

   

  

mp

x

mp

x

oo

d omo

mp

xoo

d omo

oo

omp

mp

x

mpd m

oo

od mo

g Cs

g Cs

CsR vRgv

g CsCsR

vRgv

CsR Rg

g Cs

gvg CsR

Rvgv

1

2

1 1

2

1

11 1

1 2

11

1

212 2 dv

2 dv

OTA Gain-Bandwidth Product (GBW)

10

M

m pm

L

oo po

pmpo

oo

m DM

C g

C gg

gg gA

526

26

1

 



 





,

node mirror"" theat and nodeoutput theat

poles 2 have willcircuit The

L

m

L

oo

oo

m poDMdBDM C

g C

gg gg

gAAGBW 126 26

1 3 



  

   

  

 

 

dominates and spaced widely are poles the Assuming po

OTA Common-Mode Input Range

11

• Common-mode input range set by transistor saturation conditions • Low-end set by tail current source

saturation 1

14

14 2

Tn

oxn

tail

oxn

tail SSGSDSATSSicm V

L WC

I

L WC

IVVVVV  

• High-end set by differential pair saturation

15

5

151 TnTp

oxp

tail DDTGSDDTocmicm VV

L WC

IVVVVVVV     





   





 

15

5

1

14

2 TnTp

oxp

tail DDicmTn

oxn

tail

oxn

tail SS VV

L WC

IVVV

L WC

I

L WC

IV    





  





 

OTA Common-Mode Gain

12

• Ideally, common-mode perturbations are suppressed by the differential amplifier, i.e. Acm = 0

• Finite common-mode gain exists due to amplifier asymmetries and finite tail current source impedance

• Note transistor numbers are different from previous slides, as I borrow figures from Sedra/Smith text

[Sedra]

OTA Common-Mode Gain

13

[Sedra]

• Modeling the input transistors as a transconductance current source with a parallel output resistance

   

icm

m oSS

oSS icms v

g rR

rR vv 

 

1 1

1

12

2

SSicm

o mcm

SS

icm o

Rv iG

R vi

2 1

2





OTA Common-Mode Gain

14

[Sedra]

 

  2222

1111

22

22

2 1

oSSmoSSo

oSSmoSSo

SSicm

o mcm

rRgrRR

rRgrRR

Rv iG







 

  

 

 

  

 

3 3144

3 313

1

1

m ooicmmcmm

m ooicmmcmg

g rRvGgi

g rRvGv

OTA Common-Mode Gain

15

KCL at vo

Since Ro2>>ro4 and Ro1>>ro3 and gm3=gm4

[Sedra]  

  

 

3 3144

1

m ooicmmcmm g

rRvGgi

 

  

  

  

 



3 314

24

22 4

11 2

0

m oom

SS

oo icmo

o

o

o

o icmmcm

g rRg

R Rr

vv

r v

R vivG

SSm CM

omSS

o

icm

o CM

Rg A

rgR r

v vA

3

33

4

2 1

1 1

2



 

OTA Common-Mode Gain & Rejection Ration (CMRR)

16

• To improve (lower) common-mode gain, we need a high tail current impedance

cm

dm

A ACMRR 10log20

462 1

omCM

o cm rgv

vA 

• An amplifier figure-of-merit is the common-mode rejection ratio (CMRR)

 46 26

1 1010 2log20log20 om

oo

m

cm

dm rg gg

g A ACMRR 



  

 



OTA Power-Supply Rejection Ration (PSRR)

17

  

   

 

  

   

 





SSo

dm 10

DDo

dm 10

vv Alog20PSRR

vv A

log20PSRR

42

1

42

1

1