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