ece 2c, notes set 3: small-signal models of active … notes, m. rodwell, copyrighted 2009 ece 2c,...
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class notes, M. Rodwell, copyrighted 2009
ECE 2C, notes set 3: Small-Signal Models of Active Devices
Mark Rodwell
University of California, Santa Barbara
rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax
class notes, M. Rodwell, copyrighted 2009
Goals of this note set:
devicesnonlinear of models signal-smalllinear make toHow
elementscircuit nonlinear Linear vs.
?network output) (input,port - twoa isWhat
class notes, M. Rodwell, copyrighted 2009
2-Port Descriptions ( 3-Wire Network or Device)
subcircuita element, passivea or,a transist :containmight Box
s.t variableindependen theof functions as writtenbe thencan
,variables*dependent * the, variables tworemaining The
.*st variableindependen* theasset be can variablesAny two
freedom. of degrees 2 are There
. and , , , variables therelate sticscharacteri terminalThe 2121 IIVV
class notes, M. Rodwell, copyrighted 2009
Two-Port Parameters: Represent Device or Network
devices. active modelingon is focusour now But,
network.any represent port to- twoa usecan We
class notes, M. Rodwell, copyrighted 2009
Transistors are Nonlinear Elements
*signals small* assume weifeasy made is Analysis
difficult. very theforeis analysiscircuit sistor Exact tran
apply.not doesion superposit of principle The
. voltagesapplied theof functionsnonlinear are currents Transistor
ID
VDS
increasingVGS
)1())(2/( 2
, DSthgsggoxD VVVLWcI
class notes, M. Rodwell, copyrighted 2009
A Nonlinear Two-Port
currents. signal AC and voltagessignal AC
plus
currents bias DC and voltagesbias DC
of sumsoften are currents and voltages thecircuits,tor In transis
voltages. theof functionsnolinear are currents The
always).not (but small often very are signals AC the...and
class notes, M. Rodwell, copyrighted 2009
Nonlinear Two-Port Characteristics
...
22
...22
21
21
2
22
2
2
2
2
22
1
1
2
2
2
2
2
21
1
22
21
21
1
22
2
2
2
1
22
1
1
2
1
2
2
2
11
1
11
VVVV
IV
V
IV
V
IV
V
IV
V
II
VVVV
IV
V
IV
V
IV
V
IV
V
II
series...Taylor a Write
seriesTaylor in the sorder term-first but the allneglect can wecase, In this
smaller.even are and , , then small, are and ifBut
d.complicate very still is This
21
2
2
2
121 VVVVVV
class notes, M. Rodwell, copyrighted 2009
Assuming Small Signals (Derivatives)
...
...
2
2
21
1
22
2
2
11
1
11
VV
IV
V
II
VV
IV
V
II
instead. and writesmall very are and If 2121 VVVV
small. are and if sorder term-higher eneglect thcan We 21 VV
class notes, M. Rodwell, copyrighted 2009
Small-Signal 2-Port Admittance Parameters
2221212
2121111
VYVYI
VYVYI
shown)not (..areimplicit as taken are currents & voltagesDC
Where
2
222
1
221
2
112
1
111
V
IY
V
IY
V
IY
V
IY
class notes, M. Rodwell, copyrighted 2009
Admittance Parameters
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
jV
jV
jYjY
jYjY
jI
jI
etc. , Re)( , Re)(
:ndescriptio domain-Frequency
1111
tjtj eItieVtv
implicit. as takenis bias DC
voltages.of functions as writtenare Currents
class notes, M. Rodwell, copyrighted 2009
Side Point: Impedance Parameters
currents. of functions as writtenare Voltages
2
1
2221
1211
2
1
I
I
ZZ
ZZ
V
V
matrix. Y theof inverse theismatrix ZThe
class notes, M. Rodwell, copyrighted 2009
General Comment About 2-Port Parameters
models. signal-smallansistor explain tr way tonatural a
provide they because parametersport -2 introduced have We
years.Senior or Junior theuntilleft becan this:My view
.parametersport -2about discuss tomoremuch is There
class notes, M. Rodwell, copyrighted 2009
Small-Signal Equivalent-Circuit
2
1
2221
1211
2
1
V
V
YY
YY
I
I
)()( )( :partsimaginary and real havemight and
frequency with might vary )( assumed have wefar, So
.generatorscurrent controlled twoand sadmittance twoas
parameters-Yfour thengrepresenti now are We
jjBjGjY
jY
class notes, M. Rodwell, copyrighted 2009
Small-Signal Equivalent-Circuit
.negligibleusually is ports),-2other not (but storsFor transi
uctance transcondreverse ctancetranscondu
econductancoutput econductancinput
:notation thechanged also have that weNote
)( parts.imaginary no have and
frequency,ith not vary w do parameters-Y that thesuppose Now
1221
2211
r
out
inr
in
outm
out
outout
in
inin
g
V
IgG
V
IgG
V
IGG
V
IGG
GjY
class notes, M. Rodwell, copyrighted 2009
Small-Signal Equivalent-Circuit: Neglecting Gr.
ctancetranscondu
econductancoutput econductancinput
in
outm
out
outout
in
inin
V
Ig
V
IG
V
IG
model.circuit equivalentfrequency -lowr transisto typicala is This
class notes, M. Rodwell, copyrighted 2009
Recall MOSFET Characteristics: Mobility-Limited Case
:current limitedmobility
Id
VgsVth
mobility-limited
velocity-limited
voltage,knee thenlarger tha voltagesdrainfor Applies
ID
VDS
increasingVGS
)1())(2/( 2
, DSthgsggoxD VVVLWcI
class notes, M. Rodwell, copyrighted 2009
Recall MOSFET Characteristics: Velocity-Limited Case
))(1(, VVVVvWcI thgsDSsatgoxvD
Id
VgsVth
mobility-limited
velocity-limited
ID
VDS
increasingVGS
voltage,knee thenlarger tha voltagesdrainfor Applies
current limitedvelocity
/gsatLvV
class notes, M. Rodwell, copyrighted 2009
FET Small-Signal Model: Mobility-Limited
.1 asroughly varies that Note
using are wemodels theofaccuracy the within to
1
1
eConductancOutput
))(/()1)()(/(
ctanceTranscondu
)1())(2/(
Current Drain
2
,
Dds
D
DS
D
DS
D
ds
ds
thgsggoxDSthgsggox
GS
Dm
DSthgsggoxD
/IR
I
V
I
V
I
RG
VVLWcVVVLWcV
Ig
VVVLWcI
RDS
gmVGS
VGS
D
S
G
class notes, M. Rodwell, copyrighted 2009
FET Small-Signal Model: Velocity-Limited
1
1
eConductancOutput
)1(
ctanceTranscondu
))(1(
Current Drain
,
D
DS
D
DS
D
ds
ds
gsatoxDSgsatox
GS
Dm
thgsDSgsatoxvD
I
V
I
V
I
RG
WvcVWvcV
Ig
VVVVWvcI
RDS
gmVGS
VGS
D
S
G
class notes, M. Rodwell, copyrighted 2009
Transconductance vs Vgs
gthgsgox
GS
Dm
gthgsgoxD
LVVWcV
Ig
LVVWcI
/)(
2/)(
limitedmobility
2
,
satgox
GS
Dm
thgssatgoxvD
vWcV
Ig
VVVvWcI
)(
limitedvelocity
,
Id
VgsVth
V
gm
VgsVth
V
mobility-limited velocity-limited
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 250 nm NMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 250 nm NMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 250 nm PMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 250 nm PMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 45 nm NMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 45 nm NMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 45 nm PMOS Characteristics
class notes, M. Rodwell, copyrighted 2009
Rough Estimate: 45 nm PMOS Characteristics
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