ee 330 lecture 28 small-signal model extension applications of the small-signal model
TRANSCRIPT
![Page 1: EE 330 Lecture 28 Small-Signal Model Extension Applications of the Small-signal Model](https://reader035.vdocuments.mx/reader035/viewer/2022062309/5697bfa71a28abf838c98e4d/html5/thumbnails/1.jpg)
EE 330Lecture 28
Small-Signal Model Extension
Applications of the Small-signal Model
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32133
32122
32111
V,,VVfI
V,,VVfI
V,,VVfI
Nonlinear network characterized by 3 functions each functions of 3 variables
Consider 4-terminal networkI1
I2
I3 V1
V2
V3
4-TerminalDevice
Review from Last Lecture
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Consider now 3 functions, each a function of 3 variables
1 11 1 12 2 13 3y y y i v v v
Extending this approach to the two nonlinear functions I2 and I3
QVVj
321iij V
V,,VVfy
3232221212 vyyy vvi
3332321313 vyyy vvi
3132121111 vyyy vvi
This is a small-signal model of a 4-terminal network and it is linear9 small-signal parameters characterize the linear 4-terminal networkSmall-signal model parameters dependent upon Q-point !
where
Review from Last Lecture
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y11y12V2
V1
i1
y13V3
y22y21V1
V2
i2
y23V3
y33y31V1
V3
i3
y32V2
A small-signal equivalent circuit of a 4-terminal nonlinear network
QVVj
321iij V
V,,VVfy
Equivalent circuit is not uniqueEquivalent circuit is a three-port network
Review from Last Lecture
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Small-Signal Model
1 1 1 2 3
2 2 1 2 3
3 3 1 2 3
, ,
, ,
, ,
g
g
g
i V V V
i V V V
i V V V
I1
I2
I3 V1
V2
V3
4-TerminalDevice
3232221212 Vyyy VVi
3332321313 Vyyy VVi
3132121111 Vyyy VVi
QVVj
321iij V
V,,VVfy
3
Consider 3-terminal networkReview from Last Lecture
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Small-Signal Model
2122
2111
,
,
VVi
VVi
g
g
I1
I2
V1V2
3-TerminalDevice
2221212 VVi yy 2121111 VVi yy
QVVj
21iij V
,VVfy
y11 y22
y12V2
y21V1
V1 V2
i1 i2A Small Signal Equivalent Circuit
2Q
1Q
V
VV
Consider 3-terminal network
4 small-signal parameters characterize this 3-terminal (two-port) linear networkSmall signal parameters dependent upon Q-point
Review from Last Lecture
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Small-Signal Model
1 1 1 2 3
2 2 1 2 3
3 3 1 2 3
, ,
, ,
, ,
g
g
g
i V V V
i V V V
i V V V
I1
I2
I3 V1
V2
V3
4-TerminalDevice
3232221212 Vyyy VVi
3332321313 Vyyy VVi
3132121111 Vyyy VVi
QVVj
321iij V
V,,VVfy
2
Consider 2-terminal networkReview from Last Lecture
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Small-Signal Model
1 11 1yi V
Q
1 1
11
1 V V
f Vy
V
y11V1
i1
A Small Signal Equivalent Circuit
1QV V
Consider 2-terminal network
I1
V1
2-TerminalDevice
Review from Last Lecture
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Small Signal Model of MOSFET
1
GS T
DS
D OX GS T DS GS DS GS T
2
OX GS T DS GS T DS GS T
0 V V
VWI μC V V V V V V V V
L 2
WμC V V V V V V V V
2L
T
GI 0
3-terminal device
Large Signal Model
MOSFET is usually operated in saturation region in linear applications where a small-signal model is needed so will develop the small-signal model in the saturation region
ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
SaturationRegion
CutoffRegion
TriodeRegion
Review from Last Lecture
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Small Signal Model of MOSFET
DQI
Og
OX GSQ T
WμC V V
Lmg
gOgmVGS
VGS
G D
S
Alternate equivalent expressions:
12 2
DQ OX GSQ T DSQ OX GSQ T
W WI =μC V V V μC V V
2L 2L
OX GSQ T
WμC V V
Lmg
OX DQ
W2μC I
Lmg
2DQ
m
GSQ T
Ig
V V
Review from Last Lecture
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Small Signal Model of BJT
3-terminal device
VCE
IC
Forward Active
Cutoff
Saturation
Usually operated in Forward Active Region when small-signal model is needed
1BE
t
V
V CE
C S E
AF
VI J A e
V
t
BE
V
V
ESB e
β
AJI
Forward Active Model:
Review from Last Lecture
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Small Signal Model of BJT
CQ
t
I
βVg
CQ
t
I
Vmg CQ
AF
I
VOg
21 22C BE CEy y i V V11 12B BE CEy y i V V
C m BE O CEg g i V V
B BEg
i V
gOgmVBE
VBEgπ
B
E
C
Review from Last Lecture
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Active Device Model Summary
Simplified
Simplified
MOStransistors
Diodes
Simplified
Simplified
Simplified
Bipolar Transistors
Element ss equivalent dc equivalnet
What are the simplified dc equivalent models?
Review from Last Lecture
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Active Device Model SummaryWhat are the simplified dc equivalent models?
Simplified
Simplified
Simplified
Simplified
Simplified
0.6V
dc equivalent
G D
S
VGSQ 2OXGSQ Tn
μC WV -V
2L
G D
S
VGSQ 2OXGSQ Tp
μC WV -V
2L
B C
E
BQβI0.6V
IBQ
B C
E
BQβI0.6V
IBQ
Review from Last Lecture
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Recall:
1. Linearize nonlinear devices (have small-signal model for key devices!)
2. Replace all devices with small-signal equivalent
3. Solve linear small-signal network
Alternative Approach to small-signal analysis of nonlinear networks
Remember that the small-signal model is operating point dependent!
Thus need Q-point to obtain values for small signal parameters
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Comparison of Gains for MOSFET and BJT Circuits
R
Q1
VIN(t)
VOUT
VCC
VEE
BJT MOSFET
R1
VIN(t)
VOUT
VDD
VSS
M1
DQ `1
VM
SS T
2I RA
V V CQ
VB
t
I RA
V
Verify the gain expression obtained for the BJT using a small signal analysis
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R
Q1
VIN(t)
VOUT
VCC
VEE
R
VIN
VOUT
RVIN
VOUT
Vbe gmVbegπ
OUT m BE
IN BE
= -g R
=
V V
V V
OUTV m
IN
A = -g RV
=V
CQIm
t
g =V
ICQV
t
RA -
V=
Note this is identical to what was obtained with the direct nonlinear analysis
Neglect λ effects to be consistent with earlier analysis
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M1
M2
VIN
VOUT
VDD
VSS
Example:
Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2
are operating in the saturation region and that λ=0
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M1
M2
VIN
VOUT
VDD
VSS
Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2
are operating in the saturation region and that λ=0
VIN
VOUT
M1 M2
Small-signal circuit
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M1
M2
VIN
VOUT
VDD
VSS
Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2
are operating in the saturation region and that λ=0
VIN
VOUT
M1 M2
Small-signal circuit
gmVGSVGS
G
S
D
Small-signal MOSFET model for λ=0
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Example: Determine the small signal voltage gain AV=VOUT/VIN. Assume M1 and M2
are operating in the saturation region and that λ=0
VIN
VOUT
M1 M2
Small-signal circuit
Small-signal circuit
VGS1 gm1VGS1VIN
VOUT
VGS2 gm2VGS2
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Example:
Small-signal circuit
VGS1 gm1VGS1VIN
VOUT
VGS2 gm2VGS2
Analysis:
By KCL
1 1 2 2m GS m GSg gV V
but
1GS INV V
2GS OUT-V V
thus:
1
2
OUT m
V
IN m
gA
g VV
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Example:
Small-signal circuit
VGS1 gm1VGS1VIN
VOUT
VGS2 gm2VGS2
Analysis:
1
2
OUT m
V
IN m
gA
g VV
1
1 1 2
2 12
2
2
2
D OX
V
D OX
WI C
L W LA
W LWI C
L
Recall: 1
1
2m D OX
Wg I C
L
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Example:
Small-signal circuit
VGS1 gm1VGS1VIN
VOUT
VGS2 gm2VGS2
Analysis:1
2
OUT m
V
IN m
gA
g VV
1 2
2 1
V
W LA
W LRecall:
If L1=L2, obtain
1 2 1
2 1 2
V
W L WA
W L W
The width and length ratios can be accurately set when designed in a standard CMOS process
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R1
VIN(t)
VOUT
VDD
VSS
M1
OUT DD DV =V -I R
2OX
DQ SS T
μ C WI V V
2L 2
OX
D IN SS T
μC WI V -V -V
2L
2TSSOX
DQ VV2L
WC μI
Graphical Analysis and Interpretation Consider Again
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
R1
VIN(t)
VOUT
VDD
VSS
M1
OUT DD DV =V -I R
2OX
DQ SS T
μ C WI V V
2L
Graphical Analysis and Interpretation Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
Load Line
Device Model at Operating Point
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
Load LineQ-Point
R1
VIN(t)
VOUT
VDD
VSS
M1
OUT DD DV =V -I R
2OX
DQ SS T
μ C WI V V
2L
2OX
D IN SS T
μC WI V -V -V
2L
2TSSOX
DQ VV2L
WC μI
Graphical Analysis and Interpretation
VGSQ=-VSS
Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
Load LineQ-Point
R1
VIN(t)
VOUT
VDD
VSS
M1
Graphical Analysis and Interpretation
VGSQ=-VSS
Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
Saturation region
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
Load LineQ-Point
R1
VIN(t)
VOUT
VDD
VSS
M1
Graphical Analysis and Interpretation
VGSQ=-VSS
Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
Saturation region
•Linear signal swing region smaller than saturation region
•Modest nonlinear distortion provided saturation region operation maintained
•Symmetric swing about Q-point
•Signal swing can be maximized by judicious location of Q-point
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
Load LineQ-Point
R1
VIN(t)
VOUT
VDD
VSS
M1
Graphical Analysis and Interpretation
VGSQ=-VSS
Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
Saturation region
Very limited signal swing with non-optimal Q-point location
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ID
VDS
VGS1
VGS6
VGS5
VGS4
VGS3
VGS2
Load LineQ-Point
R1
VIN(t)
VOUT
VDD
VSS
M1
Graphical Analysis and Interpretation
VGSQ=-VSS
Device Model (family of curves) 2
1 OX
DQ GS T DS
μ C WI V -V V
2L
Saturation region
•Signal swing can be maximized by judicious location of Q-point
•Often selected to be at middle of load line in saturation region
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Small-Signal MOSFET Model Extension
Existing model does not depend upon the bulk voltage !
Observe that changing the bulk voltage will change the electric field in the channel region !
VBS
VGS
VDS
IDIG
IB
(VBS small)
E
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Further Model ExtensionsExisting model does not depend upon the bulk voltage !
Observe that changing the bulk voltage will change the electric field in the channel region !
VBS
VGS
VDS
IDIG
IB
(VBS small)
E
Changing the bulk voltage will change the thickness of the inversion layer
Changing the bulk voltage will change the threshold voltage of the device
BST0T VVV
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VT
VT0
VBS
~ -5V
BST0T VVV
Typical Effects of Bulk on Threshold Voltage for n-channel Device
1-20.4V 0.6V
Bulk-Diffusion Generally Reverse Biased (VBS< 0 or at least less than 0.3V) for n-channel Shift in threshold voltage with bulk voltage can be substantialOften VBS=0
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T T0 BSV V V
Typical Effects of Bulk on Threshold Voltage for p-channel Device
1-20.4V 0.6V
Bulk-Diffusion Generally Reverse Biased (VBS > 0 or at least greater than -0.3V) for n-channel
VT
VT0
VBS
Same functional form as for n-channel devices but VT0 is now negative and the magnitude of VT still increases with the magnitude of the reverse bias
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Model Extension Summary
1
GS T
DS
D OX GS T DS GS DS GS T
2
OX GS T DS GS T DS GS T
0 V V
VWI μC V V V V V V V V
L 2
WμC V V V V V V V V
2L
T
BST0T VVV
Model Parameters : {μ,COX,VT0,φ,γ,λ}
Design Parameters : {W,L} but only one degree of freedom W/L
0I
0I
B
G
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Small-Signal Model Extension
1
GS T
DS
D OX GS T DS GS DS GS T
2
OX GS T DS GS T DS GS T
0 V V
VWI μC V V V V V V V V
L 2
WμC V V V V V V V V
2L
T
BST0T VVV
000
QQQ VVGS
G13
VVDS
G12
VVGS
G11 V
Iy
V
Iy
V
Iy
000
QQQ VVGS
B33
VVDS
B32
VVGS
B31 V
Iy
V
Iy
V
Iy
Q Q Q
D D D
21 12 13
GS DS GSV V V V V V
I I Iy y y
V V Vm o mbg g g
GI =0
BI =0
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DS2
TGSOXD VVV2L
WμCI 1
BST0T VVV
11
OX GS T DS OX EBQ
W WμC 2 V V V μC V
2L LQQ
D
m
V VGS V V
Ig
V
2
OX GS T DQ
WμC 2 V V λ λI
2LQQ
D
o
V VDS V V
Ig
V
1
OX GS T DS
WμC 2 V V 1+λV
2LQ Q
D T
mb
BS BSV V V V
I Vg
V V
1
21
1 12 Q
Q Q
D T
mb BSV V
BS BSV V V V
I Vg V
V V
OX EBQ OX EBQ
W WμC V μC V
L L
2m
BSQ
g-V
mbg
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Small Signal Model Summary
OX
m EBQ
μC Wg V
L
DQo λIg
BSQ
mmbV
gg
2
G
S
Vgs
Vbs
Vds
id
ig
ibB
D
Small Signal
Network
dsobsmbgsmd
b
g
vgvgvgi
i
i
0
0
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Relative Magnitude of Small Signal MOS Parameters
OX
m EBQ
μC Wg V
L
o DQg λI 5E-7
2mb m m
BSQ
g g .26gV
d m gs mb bs o dsi g v g v g v
DQOX
m IL
WC2μg
DQ
m
EBQ
2Ig
V
Consider:
3 alternate equivalent expressions for gm
If μCOX=100μA/V2 , λ=.01V-1, γ = 0.4V0.5, VEBQ=1V, W/L=1, VBSQ=0V
-4
22OX
DQ EBQ
μC W 10 WI V 1V =5E-5
2L 2L
OX
m EBQ
μC Wg V 1E-4
L
0 m mbg <<g ,g
mb mg < g
In this example
This relationship is common
In many circuits, VBS=0 as well
![Page 41: EE 330 Lecture 28 Small-Signal Model Extension Applications of the Small-signal Model](https://reader035.vdocuments.mx/reader035/viewer/2022062309/5697bfa71a28abf838c98e4d/html5/thumbnails/41.jpg)
Large and Small Signal Model Summary
dsobsmbgsmd
b
g
vgvgvgi
i
i
0
0
1
GS T
DS
D OX GS T DS GS DS GS T
2
OX GS T DS GS T DS GS T
0 V V
VWI μC V V V V V V V V
L 2
WμC V V V V V V V V
2L
T
BST0T VVV
Large Signal Model Small Signal Model
OX
m EBQ
μC Wg V
L
DQo λIg
BSQ
mmbV
gg
2
where
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End of Lecture 28