Lecture EE13
description
Transcript of Lecture EE13
Microelectronic circuits by Meiling CHEN
1
Lecture 13Lecture 13MOSFET Differential MOSFET Differential
Amplifiers Amplifiers
Microelectronic circuits by Meiling CHEN
2
topicstopics• Ideal characteristics of differential
amplifier– Input differential resistance– Input common-mode resistance– Differential voltage gain– CMRR
• Non-ideal characteristics of differential amplifier– Input offset voltage – Input biasing and offset current
• Differential Amplifier with active load• Frequency response
Microelectronic circuits by Meiling CHEN
3
Figure 7.1 The basic MOS differential-pair configuration.
MOS differential pair
Microelectronic circuits by Meiling CHEN
4
CSV
Figure 7.2 The MOS differential pair with a common-mode input voltage vCM.
Common mode operation
DDDDDD
tGSnD
GSCMs
DD
RIVvv
VVL
Wk
II
Vvv
III
21
2'
21
21
)(2
1
2
2
Q1 and Q2 in saturation mode
)(2
(min)
(max)
tGStCSssCM
DDDtCM
VVVVVv
RI
VVv
BJT’s differential pair VCM no bound
Make sure current source is working
tsCMSDDDD
tGSDS
VvvvRIV
Vvv
)(
GSSSCSCM
tSSCSCM
tsCMtGS
vVVv
VVVv
VvvVv
)(
Microelectronic circuits by Meiling CHEN
5
Exercise 7.1 kRmAIVVVmAL
WkVVV DtnSSDD 5.2,4.0,5.0,/4,5.1 2'
5.0816.0
15.22.05.1
816.0
)5.0(22.02
)(2
1
2
2'
tGSDS
DS
GS
GS
tGSnD
VVV
VkmV
VV
VmI
VVL
WkI
Saturation mode
5.011
1
D
tCMDtGD
tSGSD
tGSDS
CM
V
VVVVVV
VVVVV
VVV
VV
Saturation modeVVCM 5.1(max)
Microelectronic circuits by Meiling CHEN
6
Figure 7.3 (Continued)
48.0
VV
V
CM
CS
2.05.148.082.0
48.0
(min)
(min)
Microelectronic circuits by Meiling CHEN
7
Figure 7.5 The MOSFET differential pair for the purpose of deriving the transfer characteristics, iD1 and iD2 versus vid vG1 – vG2.
Large signal operation
22
'2
21
'1
)(2
1
)(2
1
tGSnD
tGSnD
VvL
Wki
VvL
Wki
2121 GGGSGSid vvvvv
2
'
'1
2
'
'1
2'2!
21
'21
21
2/1
22
1
2
21
2/1
22
1
2
2
12
2
1
LW
k
vvI
L
Wk
Ii
LW
k
vvI
L
Wk
Ii
vL
WkIii
Iii
vL
Wkii
n
ididnD
n
ididnD
idnDD
DD
idnDD
Microelectronic circuits by Meiling CHEN
8
Figure 7.6 Normalized plots of the currents in a MOSFET differential pair. Note that VOV is the overdrive voltage at which Q1 and Q2 operate when conducting drain currents equal to I/2.
Microelectronic circuits by Meiling CHEN
9
Figure 7.7 The linear range of operation of the MOS differential pair can be extended by operating the transistor at a higher value of VOV.
2
'
'1
21
2/1
22
1
2
LW
k
vvI
L
Wk
Ii
n
ididnD
More k is bigger more linear range of vid
Microelectronic circuits by Meiling CHEN
10
Figure 7.8 Small-signal analysis of the MOS differential amplifier: (a) The circuit with a common-mode voltage applied to set the dc bias voltage at the gates and with vid applied in a complementary (or balanced) manner. (b) The circuit prepared for small-signal analysis. (c) An alternative way of looking at the small-signal operation of the circuit.
7-2.1 Small signal operation (differential gain)
idCMG
idCMG
vvv
vvv
2
12
1
2
1
21
21
2vvv
vvv
id
CM
Microelectronic circuits by Meiling CHEN
11
)//(
)//(2
1),//(
2
1
)//(2
)//(2
12
22
11
22
11
oDmid
ood
oDmid
ooDm
id
o
oDid
mo
oDid
mo
rRgv
vvA
rRgv
vrRg
v
v
rRv
gv
rRv
gv
DR
gsv gsmvgor
1ov
2idv
Doo
id
RrR
R
//21
Microelectronic circuits by Meiling CHEN
12
ro effects
idoDmooo
idoDmo
idoDmo
vrRgvvv
vrRgv
vrRgv
)//(
)2/)(//(
)2/)(//(
12
2
1
Microelectronic circuits by Meiling CHEN
13
2id
m
Vg
1oV
gsV
2idV
2idV
gsV
2
idm
Vg
1or DR DR 2or
2oV
Differential-mode equivalent circuit
)//(
)//(
)2/)(//(
)2/)(//(
12
12
2
1
oDmid
ood
idoDmooo
idoDmo
idoDmo
rRgv
vvA
vrRgvvv
vrRgv
vrRgv
Microelectronic circuits by Meiling CHEN
14
Common-mode gain et CMRR
SS
D
icm
o
icm
omSS
SSm
D
icm
o
icm
o
R
R
v
v
v
vgR
Rg
R
v
v
v
v
2/1
2/1
11
21
ssmcm
d
DmdssDcm
RgA
ACMRR
RgARRA
2
1,2/
21
21
(1) Half circuit of differential pair
(2) Full circuit
cm
d
Dmidoodicmoocm
A
ACMRR
RgvvvAvvvA /)(,0/)( 1212
mg
1 DR
1ov
ssR2
di
icmR2
icmv
di
Microelectronic circuits by Meiling CHEN
15
SSV
DDV DDV
fIRe
1DI
2DI
R
VVVI
IIIvv
VvL
WkI
GSSSDDD
refDDGSGS
tGSnD
1
2121
2' )(2
1
SSoo RrR
gsvgsmvg
or
1ov
R
gsvgsmvg
or
Microelectronic circuits by Meiling CHEN
16
Non zero common gain due to RD mismatch
D
Dssm
cm
d
Dmd
D
D
ss
D
ss
Dcm
icmss
Doo
icmss
DDo
icmss
Do
DD
R
RRg
A
ACMRR
RgA
R
R
R
R
R
RA
vR
Rvv
vR
RRv
vR
Rv
RRconsider
/2
22
2
2
2
12
2
1
21
mg
1 DR
1ov
ssR2
di
icmR2
icmv
di
SS
D
icm
o
icm
omSS
SSm
D
icm
o
icm
o
R
R
v
v
v
vgR
Rg
R
v
v
v
v
2/1
2/1
11
11
Microelectronic circuits by Meiling CHEN
17
Figure 7.11 Analysis of the MOS differential amplifier to determine the common-mode gain resulting from a mismatch in the gm values of Q1 and Q2.
Non zero common gain due to gm mismatch
21
21
22
21
11
21
2121
2
1
2
121
21
)(
)(
)(
)()(
mmm
ssmm
icmmd
ssmm
icmmd
ss
icmddicms
ss
sddssdds
m
m
d
dgsgs
mm
ggglet
Rgg
vgi
Rgg
vgi
R
viivv
R
viiRiiv
g
g
i
ivv
ggconsider
)(
)(2
2
tgsox
m
tgsox
d
VvL
WCg
VvL
WCi
Microelectronic circuits by Meiling CHEN
18
m
mssm
cm
d
Dmd
m
m
ss
Dcm
ssm
icmDmDdDdoo
ssm
icmmd
ssm
icmmd
g
gRg
A
ACMRR
RgA
g
g
R
RA
Rg
vRgRiRivv
Rg
vgi
Rg
vgi
/2
2
2
2
2
1212
22
11
Microelectronic circuits by Meiling CHEN
19
Figure 7.25 (a) The MOS differential pair with both inputs grounded. Owing to device and resistor mismatches, a finite dc output voltage VO results. (b) Application of a voltage equal to the input offset voltage VOS to the terminals with opposite polarity reduces VO to zero.
Input offset voltage
2121
21
21
.3
.2
.1
2
2
1
1
tt
LW
LW
DD
VVQQ
RR
Microelectronic circuits by Meiling CHEN
20
))(2
(
))(2
)((
)(
)(
2
2
)2
(2
)2
(2
2
2
22
12
2
1
2
1
21
D
DOVos
D
DtGS
D
D
tGSLWC
tGSLWC
Dm
D
Dm
O
d
Oos
DDDO
DDDDD
DDDDD
DDD
DDD
DD
R
RVV
R
RVV
R
R
VV
VV
Rg
RI
Rg
V
A
VV
RI
VVV
RR
IVV
RR
IVV
RRR
RRR
RRconsider
ox
ox
))/(
)/()(
2(
)/(2
)/(
2
)/(
)/(
22
)/(
)/(
22
)(2
1)(
)(2
1)(
2
1
2
1
21
LW
LWVV
LW
LWII
LW
LWIII
LW
LWIII
L
W
L
W
L
WL
W
L
W
L
W
QQconsider
OVos
oVV
Microelectronic circuits by Meiling CHEN
21tos
OV
t
tGS
t
tGSn
tGS
ttGSn
tGS
ttGSn
tGS
ttGSn
ttGSn
ttt
ttt
tt
VV
V
VI
VV
VII
IVV
L
Wk
VV
VVV
L
WkI
VV
VVV
L
WkI
VV
VVV
L
Wk
VVV
L
WkI
VVV
VVV
VVconsider
2
2
2
2
2)(
2
1
)1()(2
1
)1()(2
1
])(2
1[)(2
1)
2(
2
12
2
2'
2'12
2'1
22'2'1
2
1
21
222 )())/(
)/(
2()
2( t
OV
D
DOVos V
LW
LWV
R
RVV
Microelectronic circuits by Meiling CHEN
22
Differential amplifier with active load
1. Differential gain 2. Common-mode gain et CMRR
Active load
Microelectronic circuits by Meiling CHEN
23
Microelectronic circuits by Meiling CHEN
24
Differential-mode equivalent circuit with active load
2idV
2id
m
Vg 1or
mo gr
1//3
4gsmVg 4or 2or
oV
)2
( idm
Vg
2idV
2idV
2id
m
Vg 1or
mo gr
1//3
4gsmVg 4or 2or
oV
)2
( idm
Vg
2idV
1Q 4Q 2Q
3Q
42 // ooo rrR
om
d
ooo
oomid
oovv
m
id
od
v
m
vm
moo
vmgs
oogsv
mo
rg
A
rrrwhen
rrgv
rrg
v
vA
gg
grrgv
rrvgv
idid
ididid
id
2
)//()//)((
1)
1////(
)//)((
42
424222
223124
4242
)//( oDmd rRgA Passive load
active load
SSoo RrR Passive load
active load
Microelectronic circuits by Meiling CHEN
25
Common-mode equivalent circuit with active load
iCMViCMV
di
di
mg
11or
mo gr
1//3
4gsVoV
4gsmVg
ssR2 1i
2i
4or 2or
di
mg
1
ssR22i
)( oss rR
iCMViCMViCMViCMV
di
di
mg
11or
mo gr
1//3
4gsVoV
4gsmVg
ssR2 1i
2i
4or 2or
di
mg
1
ssR22i
)( oss rR
1i
SSicm
SSicm
mogs
gsmoo
Riv
Riv
griv
ivgrv
2
2
)1
//(
)(
2
1
414
244
moSS
o
icm
ocm
SS
icm
mo
SS
icmmoo
mo
SS
icmgs
SS
icmgsmoo
grR
r
v
vA
R
v
gr
R
vgrv
gr
R
vv
R
vvgrv
3
4
34
34
44
1
1
2
]2
)1
//(2
[
)1
//(2
)2
(
Microelectronic circuits by Meiling CHEN
26
Figure 7.29 Determining the short-circuit transconductance Gm ; io/vid of the active-loaded MOS differential pair.
1. Find the transconductance Gm
Microelectronic circuits by Meiling CHEN
27
mm
idmo
mmmmm
idm
id
m
mmo
idmgmo
id
m
mg
moo
oom
idmg
gG
vgi
ggggg
vg
v
g
ggi
vgvgi
v
g
gv
grr
rrg
vgv
2143
23
41
234
3
13
331
133
13
,
)2
()2
)((
)2
(
)2
(
)/1(,
)////1
)(2
(
Microelectronic circuits by Meiling CHEN
28
2. Find the output resistance Ro
3. Find the differential gain
42
4244
22
22
12222
2
//
22
2
1
)/1)(1(
/
oox
xo
o
x
o
x
o
x
o
xx
oo
om
momoo
ox
rri
vR
r
v
R
v
r
vi
r
viii
rR
rg
grgrR
Rvi
om
d
ooo
oomomid
od
rg
A
rrrwhen
rrgRGv
vA
2
)//(
42
42
Microelectronic circuits by Meiling CHEN
29
Figure 7.31 Analysis of the active-loaded MOS differential amplifier to determine its common-mode gain.
Common-mode gain et CMRR
Microelectronic circuits by Meiling CHEN
30ssmom
mmooo
ssmoomcm
d
ssmcm
ooom
om
o
ssicm
ocm
oom
moo
om
mgm
om
g
ssomssooo
ss
icm
RgrgCMRR
ggrrrlet
RgrrgA
ACMRR
RgA
rrrg
rg
r
Rv
vA
rirg
igriiv
rg
igvgi
rg
iv
RrgRrRR
R
vii
342
342
3
4333
33
4
4233
14424
33
14344
33
13
21
21
,
]2)][//([
2
1
,1
12
1
])//1
([)(
)//1
(
)//1
(
22
2