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FET Amplifier Circuits Analysis- FET amplifier parameter gm- CS amplifiers- CS with RS amplifiers- SF amplifiers- Bootstrap amplifier- CG amplifiers
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EE2603-02 Electronic Circuit Analysis
1
2. FET Amplifier Circuits Analysis
• FET amplifier parameter gm • CS amplifiers • CS with RS amplifiers • SF amplifiers • Bootstrap amplifier • CG amplifiers
EE2603-02 Electronic Circuit Analysis
EE2603-02 2
Types of FET amplifiers (MOSFET)
(a) Common Source (CS) High AV and high Ri Voltage amplifications
VDD
RD
RL
CS
Ri C1C2
vi RGRS
vo
(b) Common Source (CS) with RS Low AV and high Ri Stability applications
VDD
RD
RL
Ri C1C2
vi RGRS
vo
(c) Source Follower (SF) Very low Ro and high Ri Buffer applications
VDD
RL
Ri
C1
C2
vi RGRS
vo
(d) Common Gate (CG) Very low Ri and high AV
High Frequency applications
VDD
RD
RLRi
C1CG
viRGRS
vo
C2
EE2603-02 Electronic Circuit Analysis
FET amplifier parameter gm
3
VDD
RD
RGRS
ID
IDRS
+
-
-+VGS
IG=0IDSS VP gm
nscalculatiocircuitequivalentFETforVV
1VI2
gFind
)3(Vgetand)1(inISubstituteandISolveIinequationquadraticgetandabove)2(inR,V,IgivenSubstitute
)2(VRI
1IVV
1II
)circuittheingivenarecomponentsall(RR
RVVWhere
)1()biasdividervoltage(RIVVor)biasself(RIV
P
GS
P
DSSm
GSDD
DSPDSS
2
P
SDDSS
2
P
GSDSSD
21
1DDG
SDGGSSDGS
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−=
−−−−
−−−−⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
+=
−−−−=−=
MOSFET-self-bias amplifier
EE2603-02 Electronic Circuit Analysis
FET amplifier parameter gm
4
RS
R2
RD
VDD
VGS
ID
+
-
+-
R1
VG
+
-IDRS
IDSS VP gm
MOSFET-voltage divider-bias amplifier
nscalculatiocircuitequivalentFETforVV
1VI2
gFind
)3(Vgetand)1(inISubstituteandISolveIinequationquadraticgetandabove)2(inR,V,IgivenSubstitute
)2(V
RIV1I
VV
1II
)circuittheingivenarecomponentsall(RR
RVVWhere
)1()biasdividervoltage(RIVV
P
GS
P
DSSm
GSDD
DSPDSS
2
P
SDGDSS
2
P
GSDSSD
21
1DDG
SDGGS
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−=
−−−−
−−−−⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
+=
−−−−=
EE2603-02 Electronic Circuit Analysis
EE2603-02 5
VDD
RD
RG RS=2.4k
ID
IDSS=8mAVP=8V
gm=?Example: Find gm of the given MOSFET amplifier
( )
( )
( ) ( )
mSVV
VIg
neglectedVVbeyondVVButVkmAorVkmAV
orI
IIIII
IIVVII
IRIVbutkRmAIVV
P
GS
P
DSSm
PGS
GS
D
DDDDD
DD
P
GSDSSD
DSDGSSDSSp
94.0825.41
8821
281.15
1.154.229.625.44.277.1
29.677.152.11
04.264.4652.11
6.147421534.46
0644.4676.54.3876.5648
4.28648
84.2
181
4.24.2,8,8
22
222
=⎟⎠
⎞⎜⎝
⎛−
−−
−
×−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−=∴
∴−=−=
−=×−−=×−=∴
=±
=−±−−
=
=+−⇒−+=
+−=⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=∴
−=−===−=
EE2603-02 Electronic Circuit Analysis
6
Example: Find gm of the given FET amplifier
( )
( )
( ) ( )( )
mS025.189.31
882
VV
1VI2
g
V9.3VisanswerCorrectneglectedisitV8VbeyondisV37.15VBut
V37.15k4.2mA8.695.0orV9.3k4.2mA04.295.0V
mA8.6ormA04.252.11
41.2796.5052.11
1845259796.50I
01.80I96.50I76.5I96.42I76.51.80I8
I4.295.08648
8I4.295.0
18VV
1II
V95.0k2000k100
k10020whereV
I4.295.0RIVVbutk4.2R,mA8I,V8V
P
GS
P
DSSm
GS
PGS
GS
D
D2DD
2DD
2D
2D
2
P
GSDSSD
G
DSDGGSSDSSp
=⎟⎠
⎞⎜⎝
⎛−
−−
−
×−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−=∴
−=
∴−=−=
−=×−−=×−=∴
=±
=−±−−
=
=+−⇒−+=
+−−=⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=∴
=+
×=
−=−===−=
RS=2.4kWR2=
100kW
RD=4.7kW
VDD=20V
VGS
ID
+-
R1=2MW
VG
+
-
IDSS=8mA
VP=-8V
EE2603-02 Electronic Circuit Analysis
CS amplifier analysis
7 Rin = RG
( ))R//R(g
vR//Rvg
vvA LDm
gs
LDgsm
in
ov −=
×−==
Ri
viRG
vo
Rin
Ro
vin
iin
iL
ig=0 DG
S
gmvgs
RL
vgs
RD
Ro = RD
MOSFET-self-bias CS amplifier MOSFET-voltage divider-bias CS amplifier
RS
RG
RD
RL
VDD
CS
ViVo
RS
R2
RD
RL
VDD
CS
R1
ViVo
EE2603-02 Electronic Circuit Analysis
CS with RS amplifier analysis
8
Ri
viRG
vo
Rin
Ro
vin
iin
iL
ig=0 DG
S
gmvgs
RL
vgs
RD
RS
Rin = RG Ro = RD
( )
{ }SmS
LD
SmLDm
Sgsmgs
LDgsm
ino
v
Rg1ifR
)R//R(Rg1
)R//R(gRvgv
R//RvgvvA
<<−
≈
+
−=
+
×−==
approximate
JFET-self-bias CSwithRS amplifier MOSFET-voltage divider-bias CS withRS amplifier
RS
RG
RD
RL
VDD
ViVo
RS
R2
RD
RL
VDD
R1
ViVo
EE2603-02 Electronic Circuit Analysis
SF amplifier analysis
9
( )( ) ( )
( )LSm
LSmLSm
LSgsmgs
LSgsm
ino
v
R//Rg1if1R//Rg1)R//R(g
R//RvgvR//Rvg
vvA
<<⇒≈
+=
+
×==
Ri
viRG vo
Rin Ro
vin
iin ig=0 DG
S
gmvgs
RL
vgs
RS( )( ) ( )mSgsmgsS
RSRSSogsmRSgsRSg/1//Rvg/v//R
I/V//RRvgIandvV==
=⇒==
MOSFET-v.divider-bias SF amplifier
RS
RG
RL
VDD
Vo
Vi
JFET-self-bias SF amplifier
Rin = RG Ro = RS//1/gm
R2 RS
R1
RL
VDD
Vi
Vo
EE2603-02 Electronic Circuit Analysis
EE2603-02 10
( )
( )
( ) ( )
mSVV
VIg
neglectedVVbeyondVVButVkmAorVkmAV
orI
IIIII
IIVVII
IRIVbutkRmAIVV
P
GS
P
DSSm
PGS
GS
D
DDDDD
DD
P
GSDSSD
DSDGSSDSSp
94.0825.41
8821
281.15
1.154.229.625.44.277.1
29.677.152.11
04.264.4652.11
6.147421534.46
0644.4676.54.3876.5648
4.28648
84.2
181
4.24.2,8,8
22
222
=⎟⎠
⎞⎜⎝
⎛−
−−
−
×−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−=∴
∴−=−=
−=×−−=×−=∴
=±
=−±−−
=
=+−⇒−+=
+−=⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=∴
−=−===−=
Example: .amplifierSFfolowingtheofvvA,
ivR,RFind
in
ov
in
inino ==
VDD
RS=2.4k
IDSS=8mAVP=8V
RL=2.4k
Vin
Vo
Ro
Rin
RG=1M
( ) Ω==== k74.0k06.1//k4.2k94.01//k4.2g/1//RR mSo
( ) 53.013.213.1
)k4.2//k4.2(94.01)k4.2//k4.2(94.0
R//Rg1)R//R(g
vvA
LSm
LSm
in
ov ==
+=
+==
Ω== 1M R R Gin
EE2603-02 Electronic Circuit Analysis
EE2603-02 11
Bootstrap Amplifier analysis Miller’s Theorem
alminteroutputatcetanresisA11
ZV
V1Z
VVZV
IVZ
V
2112
222
2M
⇐−
=
−=
−
×==
ZVVIand
ZVVI 12
221
1−
=−
=
cetanresisInputA1
Z
VV1Z
VVZV
IVZ
V1
2
211
11
1M
⇐−
=−
=
−
×==
12
V VVAWhere =
ZI1 I2
V1 V2
I1 I2
V1 V2ZM2ZM1
Rin
EE2603-02 Electronic Circuit Analysis
EE2603-02 12
RL
RS2
RG
RD
VDD
Rin
RS1
Vo
Vo2
Vo1
Vin
Miller’s Theorem applied to Bootstrap amplifier
Rin
Miller’s resistor RG is connected between Vin and Vo2
ZI1 I2
V1 V2
I1 I2
V1 V2ZM2ZM1
RL
RS2
RM1
RD
VDD
Rin
RS1
Vo
Vo2
Vo1
Vin
RM2
V
G1Min A1
RRR
−==
V
G2M3S
A11
RRR
−==
EE2603-02 Electronic Circuit Analysis
EE2603-02 13
Example: .amplifierCSBootstrapfolowingtheofRFind in
RLRG
RD
VDD
Rin 1.2kW
Vo3
Vo1
Vin
300kW
RS2
1kW RS1
Vo2
1. Find gm
2. Find Vo1/Vin=AV1
( )( ) ( )( ) 3990
72834881
22241121241
21
211 .
.
.)k.(mS.
)k.(mS.RRVgV
RVgvvA
SSgsmgs
Sgsm
in
ov ==
+=
++==
3. Find Rin = RM1
)VtofromVconnectedR(k.k
AR
RR oinGV
GMin 1
11 499
39901300
1Ω=
−
Ω=
−==
( )
( )
( ) ( )
mS..VV
VI
g
neglectedVVbeyondisV.VButV.kmA.orV.k.V
.or...
I
IIIII
II
VV
II
IRIVbutkR,mAI,VV
P
GS
P
DSSm
PGS
GS
D
DDDDD
DD
P
GSDSSD
DSDGSSDSSp
2418053
1882
12
8920
92019200531053
945200532891724
521125657624
0642416648
8648
8181
1188
22
222
1
=⎟⎠
⎞⎜⎝
⎛−
−−
−
×−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−=∴
∴−=−=
−=×−−=×−=∴
=±
=−±−−
=
=+−⇒−+=
+−=⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=∴
×−=−===−=
RLRG
RD
Rin 1.2kW
Vo3
Vo1
Vgs
300kW
RS2
1kW RS1Vgs
Vin gmVgs
EE2603-02 Electronic Circuit Analysis
CG Amplifier
14
R2 RS
R1
RD
RL
VDD
C1
VO
Rin
Vin
RSRG
RD
RL
VDD
C1
VO
Rin
Vin
MOSFET-voltage divider-bias CG amplifier MOSFET-self-bias CG amplifier
EE2603-02 Electronic Circuit Analysis
EE2603-02 15
gmvgsvgs
+
-
G D
S
vin+
-Rin
vo
+
-
Gate capacitor
shortRG RL
IRS
⎟⎠⎞⎜
⎝⎛=
⎟⎠
⎞⎜⎝
⎛−
−=⎟
⎠⎞
⎜⎝⎛=
−=−=
mS
gsmgs
SinSin
gsmgsin
g1//R
vgv//RI
V//RR
vgIandvV
( )( )
( )⇐=−
×−==∴
−=×−=
LDmgs
gsm
ino
V
gsinLDgsmo
R//Rgv
RL//RDvgVVA
vVbutR//RvgV
CG amplifier analysis
RSRG
RD
RL
VDD
C1
VO
Rin
Vin