Post on 19-Jan-2017
transcript
Microelectronic circuits by Meiling CHEN
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Lecture 13Lecture 13MOSFET Differential MOSFET Differential
Amplifiers Amplifiers
Microelectronic circuits by Meiling CHEN
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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
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Figure 7.1 The basic MOS differential-pair configuration.
MOS differential pair
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CSV
Figure 7.2 The MOS differential pair with a common-mode input voltage vCM.
Common mode operation
DDDDDD
tGSnD
GSCMs
DD
RIVvv
VVLWkII
Vvv
III
21
2'
21
21
)(21
2
2
Q1 and Q2 in saturation mode
)(2
(min)
(max)
tGStCSssCM
DDDtCM
VVVVVv
RIVVv
BJT’s differential pair VCM no bound
Make sure current source is working
tsCMSDDDD
tGSDS
VvvvRIVVvv
)(
GSSSCSCM
tSSCSCM
tsCMtGS
vVVvVVVvVvvVv
)(
Microelectronic circuits by Meiling CHEN
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Exercise 7.1 kRmAIVVVmALWkVVV DtnSSDD 5.2,4.0,5.0,/4,5.1 2'
5.0816.015.22.05.1
816.0
)5.0(22.02
)(21
2
2'
tGSDS
DS
GS
GS
tGSnD
VVVVkmV
VV
VmI
VVLWkI
Saturation mode5.011
1
D
tCMDtGD
tSGSD
tGSDS
CM
VVVVVVV
VVVVVVVV
VV
Saturation mode VVCM 5.1(max)
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Figure 7.3 (Continued)
48.0
VV
V
CM
CS
2.05.148.082.0
48.0
(min)
(min)
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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
)(21
)(21
tGSnD
tGSnD
VvLWki
VvLWki
2121 GGGSGSid vvvvv
2
'
'1
2
'
'1
2'2!
21
'21
21
2/122
12
21
2/122
12
212
21
LWk
vvILWkIi
LWk
vvILWkIi
vLWkIii
Iii
vLWkii
n
ididnD
n
ididnD
idnDD
DD
idnDD
Microelectronic circuits by Meiling CHEN
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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.
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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
2/122
12
LWk
vvILWkIi
n
ididnD
More k is bigger more linear range of vid
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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
2121
2
1
21
21
2vvv
vvv
id
CM
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)//(
)//(21),//(
21
)//(2
)//(2
12
22
11
22
11
oDmid
ood
oDmid
ooDm
id
o
oDid
mo
oDid
mo
rRgv
vvA
rRgvvrRg
vv
rRvgv
rRvgv
DR
gsv gsmvgor
1ov
2idv
Doo
id
RrRR
//21
Microelectronic circuits by Meiling CHEN
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ro effects
idoDmooo
idoDmo
idoDmo
vrRgvvvvrRgvvrRgv
)//()2/)(//()2/)(//(
12
2
1
Microelectronic circuits by Meiling CHEN
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2id
mVg
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
vrRgvvvvrRgvvrRgv
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Common-mode gain et CMRR
SS
D
icm
o
icm
omSS
SSm
D
icm
o
icm
o
RR
vv
vvgR
RgR
vv
vv
2/1
2/1
11
21
ssmcm
d
DmdssDcm
RgAACMRR
RgARRA
21,2/
21
21
(1) Half circuit of differential pair
(2) Full circuit
cm
d
Dmidoodicmoocm
AACMRR
RgvvvAvvvA /)(,0/)( 1212
mg1 DR
1ov
ssR2
di
icmR2
icmv
di
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SSV
DDV DDV
fIRe
1DI
2DI
RVVVI
IIIvv
VvLWkI
GSSSDDD
refDDGSGS
tGSnD
1
2121
2' )(21
SSoo RrR
gsvgsmvg
or
1ov
R
gsvgsmvgor
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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
RRRg
AACMRR
RgARR
RR
RRA
vRRvv
vR
RRv
vRRv
RRconsider
/2
22
2
2
2
12
2
1
21
mg1 DR
1ov
ssR2
di
icmR2
icmv
di
SS
D
icm
o
icm
omSS
SSm
D
icm
o
icm
o
RR
vv
vvgR
RgR
vv
vv
2/1
2/1
11
11
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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
gggletRgg
vgi
Rggvgi
Rviivv
RviiRiiv
gg
iivv
ggconsider
)(
)(2
2
tgsox
m
tgsox
d
VvLWCg
VvLWCi
Microelectronic circuits by Meiling CHEN
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m
mssm
cm
d
Dmd
m
m
ss
Dcm
ssm
icmDmDdDdoo
ssm
icmmd
ssm
icmmd
ggRg
AACMRR
RgAgg
RRA
RgvRgRiRivv
Rgvgi
Rgvgi
/2
2
2
2
2
1212
22
11
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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
VVQQQQRR
Microelectronic circuits by Meiling CHEN
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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
RRVV
RRVV
RR
VVVV
Rg
RI
RgV
AVV
RIVVV
RRIVV
RRIVV
RRR
RRR
RRconsider
ox
ox
))/()/()(
2(
)/(2)/(
2
)/()/(
22
)/()/(
22
)(21)(
)(21)(
2
1
2
1
21
LWLWVV
LWLWII
LWLWIII
LWLWIII
LW
LW
LW
LW
LW
LW
QQconsider
OVos
oVV
Microelectronic circuits by Meiling CHEN
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OV
t
tGS
t
tGSn
tGS
ttGSn
tGS
ttGSn
tGS
ttGSn
ttGSn
ttt
ttt
tt
VVV
VIVV
VII
IVVLWk
VVVVV
LWkI
VVVVV
LWkI
VVVVV
LWkVVV
LWkI
VVV
VVV
VVconsider
22
22
2)(
21
)1()(21
)1()(21
])(2
1[)(21)
2(
21
2
2
2'
2'12
2'1
22'2'1
2
1
21
222 )())/()/(
2()
2( t
OV
D
DOVos V
LWLWV
RRVV
Microelectronic circuits by Meiling CHEN
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Differential amplifier with active load
1. Differential gain 2. Common-mode gain et CMRR
Active load
Microelectronic circuits by Meiling CHEN
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Microelectronic circuits by Meiling CHEN
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Differential-mode equivalent circuit with active load
2idV
2id
mV
g 1orm
o gr 1//3
4gsmVg 4or 2or
oV
)2
( idm
Vg
2idV
2idV
2id
mV
g 1orm
o gr 1//3
4gsmVg 4or 2or
oV
)2
( idm
Vg
2idV
1Q 4Q 2Q
3Q
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om
d
ooo
oomid
oovv
m
id
od
v
m
vm
moo
vmgs
oogsv
mo
rgA
rrrwhen
rrgv
rrgvvA
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
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Common-mode equivalent circuit with active load
iCMV iCMV
di
di
mg1
1orm
o gr 1//3
4gsVoV
4gsmVg
ssR2 1i
2i
4or 2or
di
mg1
ssR22i
)( oss rR
iCMV iCMViCMV iCMV
di
di
mg1
1orm
o gr 1//3
4gsVoV
4gsmVg
ssR2 1i
2i
4or 2or
di
mg1
ssR22i
)( oss rR
1i
SSicm
SSicm
mogs
gsmoo
RivRiv
griv
ivgrv
22
)1//(
)(
2
1
414
244
moSS
o
icm
ocm
SS
icm
mo
SS
icmmoo
mo
SS
icmgs
SS
icmgsmoo
grRr
vvA
Rv
gr
Rvgrv
gr
Rvv
Rvvgrv
3
4
34
34
44
11
2
]2
)1//(2
[
)1//(2
)2
(
Microelectronic circuits by Meiling CHEN
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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
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mm
idmo
mmmmm
idm
id
m
mmo
idmgmo
id
m
mg
moo
oom
idmg
gGvgi
ggggg
vgvgggi
vgvgi
vggv
grr
rrg
vgv
2143
23
41
234
3
13
331
133
13
,
)2
()2
)((
)2
(
)2
(
)/1(,
)////1)(2
(
Microelectronic circuits by Meiling CHEN
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2. Find the output resistance Ro
3. Find the differential gain
42
4244
22
22
12222
2
//
22
21
)/1)(1(/
oox
xo
o
x
o
x
o
x
o
xx
oo
om
momoo
ox
rrivR
rv
Rv
rvi
rviii
rRrg
grgrRRvi
om
d
ooo
oomomid
od
rgA
rrrwhen
rrgRGvvA
2
)//(
42
42
Microelectronic circuits by Meiling CHEN
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Figure 7.31 Analysis of the active-loaded MOS differential amplifier to determine its common-mode gain.
Common-mode gain et CMRR
30ssmom
mmooo
ssmoomcm
d
ssmcm
ooom
om
o
ssicm
ocm
oom
moo
om
mgm
om
g
ssomssooo
ss
icm
RgrgCMRRggrrrlet
RgrrgAACMRR
RgA
rrrgrg
rRv
vA
rirg
igriiv
rg
igvgi
rg
iv
RrgRrRRRvii
342
342
3
4333
33
4
4233
14424
33
14344
33
13
21
21
,
]2)][//([
21
,112
1
])//1([)(
)//1(
)//1(
222