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ECEN 326
Electronic Circuits
Introduction
Dr. Aydın Ilker Karsılayan
Texas A&M University
Department of Electrical and Computer Engineering
NPN & NMOSNPN & NMOS DC
E
I IC
I
B
E
C
B
VCE ≥ VCE,sat ⇒ ACTIVE
VBE = 0.7 V
IC = βIB
IE = IC + IB
G
S
D
B
IDIG
VDS ≥ Vov ⇒ ACTIVE
Vov = VGS − Vtn
IG = 0
ID =k′n
2
W
LV2
ov
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 1
PNP & PMOSPNP & PMOS DC
IE
IC
IB
C
E
B
VEC ≥ VEC,sat ⇒ ACTIVE
VEB = 0.7 V
IC = βIB
IE = IC + IB
G
D
S
BID
IG
VSD ≥ Vov ⇒ ACTIVE
Vov = VSG − |Vtp|IG = 0
ID =k′p
2
W
LV2
ov
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 2
NPN & NMOSNPN & NMOS Small-signal T model, ro = ∞
e ie
ie
E
α
C
r
roBre =
VT
IE=
α
gm≈
1
gm
gm =IC
VT
gm
1 is
is
G
S
ro
D
gm = k′n
W
LVov =
√√√√√√2k′n
W
LID
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 3
PNP & PMOSPNP & PMOS Small-signal T model, ro = ∞
eα
E
B
C
i
re iero
re =VT
IE=
α
gm≈
1
gm
gm =IC
VT
G
S
gm
1
is
isro
D
gm = k′p
W
LVov =
√√√√√√2k′p
W
LID
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 4
BJT Node ResistancesBJT Node Resistances AC, ro = ∞
RC
RE
Rbase Rbase = (β + 1)(re + RE)
RE
RB
Rcollector
Rcollector = ∞
RB
RC
Remitter
Remitter = re +RB
β + 1
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 5
BJT AmplifiersBJT Amplifiers AC, ro = ∞
vo
RC
vi
vo
RE
vi
RC
RB
vo
vi
vo
RC
RE
vi
vo
vi=
−αRC
re
vo
vi=
RE
re + RE
vo
vi=
αRC
Remitter
vo
vi=
−αRC
re + RE
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 6
MOS Node ResistancesMOS Node Resistances AC, ro = ∞
RD
RS
RgateRgate = ∞
RS
RG
Rdrain
Rdrain = ∞
RG
RD
Rsource
Rsource =1
gm
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 7
MOS AmplifiersMOS Amplifiers AC, ro = ∞
vo
RD
vi
vo
RS
vi
vo
RD
RG
vi
vo
RD
RS
vi
vo
vi=
−RD
1
gm
vo
vi=
RS
1
gm+ RS
vo
vi=
RD
Rsource
vo
vi=
−RD
1
gm+ RS
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 8
NPNNPN Small-signal π model
b
gm vbe
i
rπ vbe ro
ie
Cc
E
iB
Early Effect → ro
gm =IC
VTro =
VA
IC
rπ =β
gmVT =
kT
q
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 9
PNPPNP Small-signal π model
π veb gm
ib
r
e
C
i
o
E
ic
r
B
veb
Early Effect → ro
gm =IC
VTro =
VA
IC
rπ =β
gmVT =
kT
q
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 10
NMOSNMOS Small-signal π model
rogs gm vgs vgmb vbsv
D
bs
B
S
G
Channel Length Modulation → roBody Effect (Vt=Vt0+γ
[√|−2φF+VSB|−
√|−2φF|
]) → gmb
gm =
√√√√√√2k′n
W
LID ro =
1
λnID
gmb = χgm k′n = µnCox
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 11
PMOSPMOS Small-signal π model
vsg rogm vsg g
D
vsbmb vsb
S
GB
Channel Length Modulation → roBody Effect (Vt=Vt0+γ
[√|−2φF+VSB|−
√|−2φF|
]) → gmb
gm =
√√√√√√2k′p
W
LID ro =
1
λpID
gmb = χgm k′p = µpCox
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 12
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers
Network
Two−portvi vo
⇓
RnviRivi voviGm
vo
vi= GmRn
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 13
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers Gm & Rn
RnviRi voviGm iscvi
Gm =isc
vi
∣∣∣∣∣∣∣∣vo=0
RnviRi viGm vo
io
Rn =vo
io
∣∣∣∣∣∣∣∣vi=0
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 14
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers Multistage
vi
vov3v2v1 vN−1
#1 #2 #3 #N
viii
Ri
#1 #3 #N#2
io vo
Ro
#1 #2 #3 #N
vo
vi=
v1
vi
v2
v1· · ·
vo
vN−1Ri =
vi
iiRo =
vo
io
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 15
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers Multistage
vi
vov3v2v1 vN−1
#1 #2 #3 #N
Rn1
vi isc1
#1 #2 #3 #N
#1 #2 #3 #N
Gm1 =isc1
vi
v1
vi= Gm1Rn1
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 16
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers Multistage
vi
vov3v2v1 vN−1
#1 #2 #3 #N
isc2v1
Rn2
#N
#N
#2 #3
#2 #3
Gm2 =isc2
v1
v2
v1= Gm2Rn2
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 17
Two-Port Modeling of AmplifiersTwo-Port Modeling of Amplifiers Multistage
vi
vov3v2v1 vN−1
#1 #2 #3 #N
RnN
iscNvN−1
#N
#N
GmN =iscN
vN−1
vo
vN−1= GmNRnN
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 18
BJT Node ResistancesBJT Node Resistances AC
RC
RE
Rbase Rbase = rπ + (β + 1)RE
ro +RC
β + 1
ro + RC + RE
RE
RB
Rcollector
Rcollector = g′mroRx + ro + Rx
g′m = gm
rπ
rπ + RB, Rx = RE‖(rπ + RB)
RB
RC
Remitter
Remitter = (rπ + RB)‖
1
g′m
‖ro
1 +
RC
ro
g′m = gm
rπ
rπ + RB
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 19
BJT AmplifiersBJT Amplifiers AC
Calculation of Gm and Rn is not necessary if ro is grounded,
since it can be combined with either RE or RC.
vo
RC
vi
vo
RE
vi
vo
vi= −α
RC‖ro
re
vo
vi=
RE‖ro
re + (RE‖ro)
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 20
BJT AmplifiersBJT Amplifiers AC
RC
RB
vo
vi
vo
RC
RE
vi
Gm = g′m +
1
ro
g′m = gm
rπ
rπ + RB
Rn = RC‖ro
vo
vi= GmRn
Gm = −gm
1 −RE
βro
1 + gmRE
1 +1
β+
1
gmro
≈ −gm
1 + gmRE
Rn = RC‖ [gmro(RE‖rπ) + ro + (RE‖rπ)]
vo
vi= GmRn
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 21
MOS Node ResistancesMOS Node Resistances AC
RD
RS
Rgate Rgate = ∞
RS
RG
Rdrain
Rdrain = g′mroRS + ro + RS
g′m = gm + gmb
RG
RD
Rsource
Rsource =
1
g′m
‖ro
1 +
RD
ro
g′m = gm + gmb
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 22
MOS AmplifiersMOS Amplifiers AC
Calculation of Gm and Rn is not necessary if ro is grounded,
since it can be combined with either RD or RS.
vo
RD
vi
vo
RS
vi
vo
vi= −
RD‖ro1
gm
vo
vi=
RS‖ro‖1
gmb1
gm+
RS‖ro‖1
gmb
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 23
MOS AmplifiersMOS Amplifiers AC
vo
RD
RG
vi
vo
RD
RS
vi
Gm = g′m +
1
ro
g′m = gm + gmb
Rn = RD‖ro
vo
vi= GmRn
Gm = −gm
1 + g′mRS +
RS
ro
g′m = gm + gmb
Rn = RD‖(g′mroRS + ro + RS)
vo
vi= GmRn
ECEN 326 Electronic Circuits - Aydın I. Karsılayan - Introduction 24
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