ecen474/704: (analog) vlsi circuit design fall...
TRANSCRIPT
Sam PalermoAnalog & 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
idoutm
m
midoutmo
idi
idi
vrgvgggg
vrgggvrgv
vVvV
1
6521
65
12
and design By 22
2 and
2Let
26
11
oo
moutm
id
oDM gg
grgvvA
TAMU-ELEN-474 2009 Jose Silva-Martinez
- 7 -
Frequency Response
id1
IB
M1 M1
v1
id2
ioutid1
0.5gmvd RXCX
Vx
gdndbndgpdbpgspX
mpmpPX
dXX
XmX
CCCfactormillerCCC
ggrrR
VCSRRgV
12
/1/1||||1
5.0
001
Magnitude
gmRX
1/RXCX
VX
Consider node VX
v2
2dv
2dv
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
ioutVX
MP’
odmo
mpx
ompxd
mod
mo
Rvgv
gR
RgRvgRvgv
1222
dv2dv
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
ioutVX
MP’
mp
x
mp
x
oo
domo
mp
xoo
domo
oo
omp
mp
x
mpdm
oo
odmo
gCs
gCs
CsRvRgv
gCsCsR
vRgv
CsRRg
gCs
gvgCsR
Rvgv
1
2
11
2
1
111
12
11
1
2122dv
2dv
OTA Gain-Bandwidth Product (GBW)
10
M
mpm
L
oopo
pmpo
oo
mDM
Cg
Cgg
gggA
526
26
1
,
node mirror"" theat and nodeoutput theat
poles 2 have willcircuit The
L
m
L
oo
oo
mpoDMdBDM C
gC
gggg
gAAGBW 126
26
13
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
saturation1
14
142
Tn
oxn
tail
oxn
tailSSGSDSATSSicm V
LWC
I
LWC
IVVVVV
• High-end set by differential pair saturation
15
5
151 TnTp
oxp
tailDDTGSDDTocmicm VV
LWC
IVVVVVVV
15
5
1
14
2TnTp
oxp
tailDDicmTn
oxn
tail
oxn
tailSS VV
LWC
IVVV
LWC
I
LWC
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 transconductancecurrent source with a parallel output resistance
icm
moSS
oSSicms v
grR
rRvv
11
1
12
2
SSicm
omcm
SS
icmo
RviG
Rvi
21
2
OTA Common-Mode Gain
14
[Sedra]
2222
1111
22
22
21
oSSmoSSo
oSSmoSSo
SSicm
omcm
rRgrRR
rRgrRR
RviG
33144
3313
1
1
mooicmmcmm
mooicmmcmg
grRvGgi
grRvGv
OTA Common-Mode Gain
15
KCL at vo
Since Ro2>>ro4 and Ro1>>ro3 and gm3=gm4
[Sedra]
33144
1
mooicmmcmm g
rRvGgi
3314
24
224
112
0
moom
SS
ooicmo
o
o
o
oicmmcm
grRg
RRr
vv
rv
RvivG
SSmCM
omSS
o
icm
oCM
RgA
rgRr
vvA
3
33
4
21
11
2
OTA Common-Mode Gain & Rejection Ration (CMRR)
16
• To improve (lower) common-mode gain, we need a high tail current impedance
cm
dm
AACMRR 10log20
4621
omCM
ocm rgv
vA
• An amplifier figure-of-merit is the common-mode rejection ratio (CMRR)
4626
11010 2log20log20 om
oo
m
cm
dm rggg
gAACMRR
OTA Power-Supply Rejection Ration (PSRR)
17
SSo
dm10
DDo
dm10
vvAlog20PSRR
vvA
log20PSRR
42
1
42
1
1
oo
m
vdd
oo
mdm
gggPSRR
A
gggA
[Razavi]
OTA Slew Rate
18
[Razavi]
OTA Slew Rate
19
L
SS
CI Rate Slew
[Razavi]
Simple OTA Summary
20
M1 M2Vi+ Vi-
VDD
VSS
Rbias
Itail
M5 M6
M3 M4
CL
Vo
L
tail
L
TAILn
L
m
gs
mg
M
mp
L
oo
pn
TAIL
n
oo
moutmv
pnTAIL
ooout
TAILnmm
CISR
C
ILWKP
CGGBW
Cg
CgC
gg
LW
IKP
gggRGA
Iggg
ILWKPgG
Rate Slew
PoleDominant -Non
PoleDominant
Gain DC
eConductancOutput
ctanceTranscondu
p1
1
6
62
62
1
62
1
62
11
2
2
2
1
6
1
2
612
11382
382
m
m
min
mmon
gg
gkTv
ggkTi
Voltage NoiseInput
Current NoiseOutput
OTA w/ Cascode Load and Tail Current Source
21
19
9
1
146
464921
4649
464649
1
2
21
281081082p1
21810810821
22
Range Mode-CommonInput 2CMRR
21
where2
1Gain Mode-Common
Rate Slew
11 PoleDominant
Gain DC
TnTp
oxp
tailDDicmTn
oxn
tail
oxn
tail
oxn
tailSS
oommom
oommCM
oomooSSSSm
CM
L
tail
L
m
Lo
om
LoLoomooo
omoomooomDM
VV
LWC
IVVV
LWC
I
LWC
I
LWC
IV
rrggrgrrgg
A
rrgrrRRg
A
CISR
Cg
CrrgGBW
CrCrrgrrr
rgrrgrrrgA
M1 M2Vi+ Vi-
VDD
VSS
Rbias
CL
M7
M8
M9 M10
M3
M4
M5 M6
VBN
VBP
Next Time
• Noise
22