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Department of Electronic EngineeringNational Taipei University of Technology

/135

• PN BJT

•• BJT ( )

••

(CE) (CB) (CC)

••

2 Department of Electronic Engineering, NTUT

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PN BJT

3

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PN

• PN

• PN

PN

Cathode Anodepn

0t = 1t t= t = ∞pn pn pn

(Depletion region)

E

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PN

•

•

1F

T

V

Vtot SI I e

−

=

+− FV

pn2 pn

S iA n D p

DDI Aqn

N L N L

= +

26 mV@ 300 T

kTV T K

q= =≃

F TV V>F

T

V

Vtot SI I e

≃

F TV V<< tot SI I−≃

−+ RV

pn

DI

DV

D

T

V

VSI e

≃

SI−

I/V

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(Reverse Breakdown)

• PN IS

PN

• ( )

• PN(Zener effect) (Avalanche effect)

DI

DVBDV

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•

( 1V/µm)

n

−+ RV

pn E•

PN

3 ~ 8 V

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( )

• PN

•(impact ionization)

−+ RV

pn E• ()

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( )

•

( )

0 1s 2s 3s 4st

BEV

0 1s 2s 3s 4st

BE BE bev V v= +

BEV bev ( ) BEv ( + )

beV phasor ( )

0 1s 2s 3s 4st

bev

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•

•

•VCCS

VCVS CCVS

+-

+

-

v1 v = mv1+- v = gi1

i1

VCCS CCCS

+

-v1 i = gv1

i1

i = bi1

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(VCCS)

•

• VCCS RL RL vout

+

−inv

1 1i kv=

1kv1i LR

L mkR V

mV

t tinv outv

+

−1v

+

−inv

+

−1v

+

−outv

VCVS

1out L L inv kv R kR v= − = − kRL 1 VCCS

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• VCCS rin

+

−inv 1kv1i LR

+

−outv

+

−1vinr

1 1

1

out L LL

in in

v kv R kv RkR

v v v

− −= = = −

kRL 1 VCCS

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BJT

• (bipolar-junction transistor, BJT) 1945Shockley Brattain Bardeen

• (BJT )

VBE ( ) VCE

e− (−IE )

Collector

Base

Emitter

(C)

(B)

(E)

+

−0.8 VBEV =

−

+1 VCEV =

+−

+

−

−+

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BJT I/V

• IC VBE

• IC VCE

+

−BEV

CI+

−CEV

+

−BEV

CI+

−CEV

2B

T

V

VSI e

1B

T

V

VSI e

CEV

CI

1BE BV V=

2BE BV V=

BEV

CI

BE

T

V

VC SI I e= ⋅

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BJT VCCS

• BJT exponential VCCS

CBV+

−

+−BEV

CEV

+

−

(C)

(B)

(E)

Collector

Base

Emitter

BEV

+

−

BE

T

V

VsI e

(C)(B)

(E)

BE

T

V

VC sI I e=

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( ) (I)

BEV BEV BEV BEV

CEVCEV

CEV CEV

CI

BE

T

V

VC SI I e= ⋅

CI

VBE

IC

(VBE=0 V)

VCE

(VCE>VBE)IC

(VCE=0 V)

VCE

VBE

(VCE=VBE)IC

VCE VBE

(VCE<VBE)IC

VCE

IC

CI

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( ) (II)

BEV+

−CEV

+

−

VCE

VCE

IC

VBE1

VBE2

VBE3

BEV

CEV

BE

T

V

VC SI I e= ⋅

BEV

CEV

CEV

BEV

BJT

IC VCE

VBE

BEV+

−

CEV

+

−

BE

T

V

VSI e⋅

IC

VCECEV

+

−

BJT

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• VOUT165 10 ASI −= ⋅

1.69 mABE

T

V

VC SI I e= ⋅ =

( )33 V 3 V 1.69 10 1000 1.31 VCE C LV I R −= − = − ⋅ ⋅ =

1.31 VOUTV =

750 mV

3 V

+

−

+

−CILR

OUTV

+

−

1 kΩ

Q:

VBE IC

3 V 2.155 VOUT C LV I R= − =

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C BI Iβ=

1 11

BE

T

V

VE C B C SI I I I I e

ββ β

+= + = + = ⋅

BE

T

V

VC SI I e= ⋅

1 BE

T

V

VB SI I e

β= ⋅

1C E EI I Iβ α

β= =

+

β IC IE

+

−BEV

CEV+

−

CI

BI

EI

IE IC

IB IC

C BI Iβ=

IB IE

( )1E BI Iβ= +

β

IB IC

β

( β

)VCCS

( )expC S BE TI I V V= ⋅

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• BJT VBE

750 mV β

50~200 IB IE

1.685 mABE

T

V

VC SI I e= ⋅ =

200 50C B CI I I< <

8.43 A 33.7 ABIµ µ< <

1.005 1.02C E CI I I< <

1.693 mA 1.719 mAEI< <

165 10 ASI −= ⋅

50 200 1.05 1.002β α< < ⇒ < <

VBE( VCCS )

+

−BEV

BE

T

V

VSI e

BE

T

V

VSIe

β

CB

E

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− BJT RC

• VBE = 800 mV β=100BJT BJT

RC

X+

−BEV

CICR500 Ω

+2 VCCV =

−

( ) VXV

( ) CR Ω

2.0

1.424

0.800

500 1041

175 10 ASI −= ⋅

1.153 mABE

T

V

VC SI I e= ⋅ = 1

11.53 µABE

T

V

VB SI I e

β= ⋅ =

11.165 mA

BE

T

V

VE SI I e

ββ+= ⋅ =

1.424 VCC C C X XV R I V V= + ⇒ =

1.424 VCE X BEV V V= = >

800 mVCE XV V= = 1041 CC XC C

C

V VR R

I

−= ⇒ = Ω

RC

VBE IC

(VCE VBE )

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•

10 VCCV =

2 kCR = Ω

220 kBR = Ω

CI

BI

4 VBBV =

+

−

CEV+

−BEV

4 0.715 µA

220kBB BE

BB

V VI

R

− −= = =

200 15 µA 3 mAC BI Iβ= = × =

200β =

( )1 3.015 mAE BI Iβ= + =

10 3 mA 2 k 4 VCE CC C CV V I R= − = − × Ω =

0.015 0.7 3 4 12 mWT B BE C CE C CEP I V I V I V= + = × + × =≃

(mA)Ci

,C satI

,CE satV

(V)CEv0 2 4 6 8 10

1

2

3

4

5

6

(Cut-off)

Q-point

5 µABi =

10 µA

15 µABQI =

20 µA

25 µA

30 µA

CE CC C CV V I R= − CC CEC

C

V VI

R

−=

y x

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gm (I)

• +

• VBE ( )

•

+

−

BEV∆

CI∆+

CEV

−

0BEas VC C

BE BE

I dI

V dV

∆ →∆ =∆

Cm

BE

dIg

dV=

BE

T

V

VC SI I e= ⋅ 1BE BE

T T

V V

V VC Cm S S

BE BE T T

dI Idg I e I e

dV dV V V

= = ⋅ = ⋅ =

gm

gm IC !!

IC = 1mA VT = 26mV 110.0385 0.0385 S 38.5 mS

26 mg −= = Ω = =Ω

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gm (II)

• gm=dIC/dVBE IC-VBE

IC0 VBE0

• IC-VCE IC1

IC2

mg V∆

BEV0BEV

0CI

CI

V∆

2BE BV V V= + ∆

2BE BV V=

1BE BV V=1BE BV V V= + ∆

CI

2CI

1CI

2mg V∆

1mg V∆

CEV

VBE0 ±∆VIC0 ±gm∆V

gm= IC0/VT gm IC0 IC0

( )

VBE ∆V IC2 IC1

IC gm2> gm1

m C BEg dI dV=

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BJT

• BJT

+

−

BEV∆

+CEV

−

BI∆

EI∆

CI∆

rπrπ E

CB

vπ

−

+mg vπrπ

mr gπ β=

BE BE beV V v∆ = ++

−

B B bI I i∆ = +

BEV∆+

−

BE

T

V

VSI e

∆

C C cI I i∆ = +b ci i β=

+CEV

−

!

CB

E

bev−

+c m bei g v=

bi

ib B-E

b c m bei i g vβ β= =

be

b m

vr

i gπβ= =

BJT

m C Tg I V=

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• v1 Q1

(a) (b) 1 mV C B?

165 10 ASI −= ⋅ 100β =

1

3.75 C

mT

Ig

V= =

Ω

6.92 mABE

T

V

VC SI I e= =

800 mVBEV =

375 m

rgπβ= = Ω

+

−1v

+ci

−

bi

rπ vπ mg vπ

1v vπ =

1

1 mV0.267 mA

3.75 c m mi g v g vπ= = = =Ω

1 1 mV26.7 µA=

375 c

b

v ii

rπ β= = =

Ω

+

−1v

+1.8 V−

CI

−

+800 mV

(1)

(2) gm rπ

(3)

VBE IC

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v.s.

•

+

−1v

+

CR−rπ vπ mg vπ

+

−outv

+

−1v

+3.6 VCCV =

−200 CR = Ω

−

+800 mV

+

−OUT OUT outv V v= +3.6 6.92 mA 200 2.216 VCV = − × Ω = (>VBE, )

1out m C m Cv g v R g R vπ= − = −

1

outv m C

vA g R

v= = −

1

3.75 mg =Ω 200 CR = Ω 53.4vA = −

RC

BJT

800 mVBEV = 6.92 mABE

T

V

VC SI I e= =

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(Early Effect)

• (VA )

BJT IC VBE VCE

( ) VBE IC VCE IC

1BE

T

V

V CEC S

A

VI I e

V

+

≃

1 11

BE BE

T T

V V

V VC CE CS S

CE CE A A A o

I d V II e I e

V dV V V V r

∂ = + = ⋅ = ∂ ≃

CI

BE

T

V

VSIe

β

w/ Early Effect

w/o Early Effect

CEV

1BE

T

V

VS CE

A

I Ve

Vβ

+

BJTro

CI

CEVAV−

CdICEdV

1

or

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1BE BE

T T

V V

V VCE ce ceC C c S C S

A A

V v vI I i I e I I e

V V

+∆ = + = + = +

BE

T

V

V cec S

A

vi I e

V=

BE

T

ce A Ao V

c CVS

v V Vr

i II e

= = ≃

+

−BEV

C C cI I i∆ = +

CE CE ceV V v∆ = +

rπ

+

−vπ mg vπ or

B C

E

Early effect BJT

BJT (gm, vπ, ro)

mr gπ β=m C Tg I V=

o A Cr V I=IC

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• BJT IC = 1 mA β = 100 VA=15 V

+

−BEV

CI∆

V∆rπ

+

−

vπ mg vπ or

B C

E

1

26 C

mT

Ig

V= =

Ω

2600 m

rgπβ= = Ω

15 kAo

C

Vr

I= = Ω

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PNP

• PNP NPN

BEV+

−CEV

+

−BI

EI

CI

EB

T

V

VC sI I e=

EB

T

V

VsB

II e

β= 1 EB

T

V

VE sI I e

ββ+=

1EB

T

V

V ECC s

A

VI I e

V

= +

+

−vπ mg vπ orrπ

cibi

ei

B C

E

+

−vπ mg vπ orrπ

cibi

ei

B C

Enpn

( )

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BJT

• BJT B-C 2 VA

+

−Xv

Xi

rπ

+

−vπ mg vπ

Xm X

vg v i

r ππ

+ =

1mg rπ β= >> 1

1 1X T

X m m C

v V

i g r g Iπ−= =

+≃

BC diode

IC=1 mA ?

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(I) –

+

−INv

CR

CCV

+

−OUTv

+

−inv rπ

+

−vπ mg vπ or CR

+

−outv

+

−INv

CR

CCV

+

−OUTv

+

−inv

rπ−

+vπ mg vπ or

CR+

−outv

+

−inv rπ

+

−vπ mg vπ or CR

+

−outv

VCCS

NPN

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(II) –

−

+INv

CR

CCV

+

−OUTv

−

+inv rπ

−

+vπ mg vπ or

CR+

−outv

+

−inv rπ

+

−vπ mg vπ or CR

+

−outv

+

−INv

1CR

CCV

+

−OUTv

2CR

1Q

2Q

−

+inv 1rπ

−

+1vπ 1 1mg vπ 1or

1CR

+

−outv

2rπ−

+2vπ 2 2mg vπ 2or

2CR

35 Department of Electronic Engineering, NTUT

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• MOSFET

MOSFET IV

( ) ( )2 212 2

2D n ox GS TH DS DS n GS TH DS DS

WI C V V V V K V V V V

Lµ = − ⋅ − = − ⋅ −

( ) ( ) ( ) ( )2 211 1

2D n ox GS TH DS n GS TH DS

WI C V V V K V V V

Lµ λ λ= − + = − +

,DS sat GS THv v V= −Di

0GSv

DSv

1GSv

2GSv

3GSv

4GSv

5GSv

2GS THv V−

( ) ( )2

2 1D n GS TH DSi K v V vλ= − +

(Triode Region)

(Saturated Region)

+

−GSV

D

G

S

+

−DSV

DI

DSV( )1

2DS

D n GS TH

VR

I K V V= =

−

36 Department of Electronic Engineering, NTUT

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MOSFET

•

•

•

( ) ( ) 22

2D n D

m GS TH n ox GS TH n ox DGS GS TH

I K W W W Ig V V C V V C I

V L L L V Vµ µ∂= = − = − = =

∂ −

( ) ( )2 21

2D n ox GS TH n GS TH

WI C V V K V V

Lµ= − = − gm ID !!

( ) ( ) ( )2 2 11D

n GS TH DS n GS TH DDS DS o

I dK V V V K V V I

V dV rλ λ λ∂ = − + = − = =

∂

MOSro

CI

CEV1AV λ− = −

DdIDSdV

1

or

( ) ( )21D n GS TH DSI K V V Vλ= − +

1o

D

rIλ

=

+

−gsv

DG

S

m gsg vor

BJT !

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BJT

38

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•

•

−

+inv out inv v=

sR

+

−

( )

−

+inv

Lout in

s L

Rv v

R R=

+

sR

+

−LR

vin

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/

•

−

+thv

ocv

thR

+

−ocv

+

−−

+thv

sR

LR

+outv

−LR +

outv

−

th outR R=

outR

th inR R=

inR

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• 1010-mV 200Ω 8Ω

(a) 2 kΩ 500Ω

(b) 10Ω 2Ω

10vA =10 mV

+

−mv

200 Ω

8 Ω

200 Ω 8 Ω

outRinR

inin m

in s

Rv v

R R=

+2 k 0.91in in mR v v= Ω ⇒ =

500 0.71in in mR v v= Ω ⇒ =

Lout amp

L o

Rv v

R R=

+ 2 0.8o out ampR v v= Ω ⇒ =

10 0.44o out ampR v v= Ω ⇒ =

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••

•

xv

+

−

inR

xi xi

outR

xv

+

−

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• (a) a-b

(b) Rth

v

+−

b

a

V

+

−v

Rth

vV2i1

i−i1

6 Ω4 Ωi1 +

−

i

a

b

3 Ω

16v i=( )1 1 16 2 4i i i i= + −

1 0.5 , 3i i v i= =

( )3 th

vR

i= = Ω

+−a

b(a)

6 Ω

V2i1

i14 Ω

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• B ( )

+

−xv rπ+

−vπ mg vπ or

CRxi

xin

x

vR r

i π= = T

m C

Vr

g Iπβ β= =

1. β ( IC IB

)

2. (CE ) RC

( BJT )

BB

inv

CR

CCV

outv

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• C ( )

rπ+

−vπ mg vπ or

invoutR

outR

0vπ = 0mg vπ = out oR r=

(CE )

CC

outv

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• E ( Early Effect)

rπ+

−vπ mg vπ

xv

v

rπ

π

inv

outR

xi

CCV

xv vπ = −

m x

vg v i

rπ

ππ

+ = −

1 11

xout

x mm

vR

i ggrπ

= =+≃

1 m

mm

gr g

g rππ

ββ

= → = <<

CE ( vbe )

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• E AC rπ• E AC ro

• B AC 1/gm

m

rgπβ=

AC

Ao

C

Vr

I=

AC

1 T

m C

V

g I=

AV = ∞

AC

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(I)

• (B-E B-C ) BJT VCCS

• BJT gm rπ ro

IC

•

( )

T

m C

Vr

g Iπβ β= = A

oC

Vr

I=C

mT

Ig

V=

rπ = ∞1A

oD D

Vr

I Iλ= =2 D

mGS TH

Ig

V V=

−

BJT

MOSFET

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(II)

•

β

VBE

IC IB ( β)IB RB

VBE

BR CR

CCV

1R CR

2R

CCV

1R CR

2RERREV

−

+

CCV

BR CR

CCV

VBE IC

()

R1 R2

RE

BJT(thermal

runaway)

RB

BJT

BJT

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( )

+

− inv

1CR

CCV

1CICBV

+−BEV

2CI−

+

outv

−

+

()

()

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• BJT

BR CR

CCV

BI

CI

X

Y

B B BE CCR I V V+ = CC BEB

B

V VI

R

−= CC BEC B

B

V VI I

Rβ β −= =

CC BECE CC C C CC C

B

V VV V I R V R

Rβ −= − = −

RB RC VCE

RB RC

( )CC BECE CC C C CC C BE

B

V VV V I R V R V

Rβ −= − = − >

+

−BEV

(1)

(2)

VBE VBE 700 mV 800 mV( 800 mV) VBE

IC=ISexp(VBE/VT) VBE VBE IC=ISexp(VBE/VT) VCC−IBRB

VBE

52 Department of Electronic Engineering, NTUT

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• BJT

BR CR

BI

CI

X

Y

2.5 VCCV =

100 kΩ 0.5 kΩ

1710 ASI −= 100β =

17 µACC BEB

B

V VI

R

−= ≃

1.675 V CE CC C C BEV V I R V= − = >

( ) 800 mVBEV =

17 µA 100 1.7 mACI = × =

IC VBE ln 852 mVCBE T

S

IV V

I= =

16.5 µACC BEB

B

V VI

R

−= =

17 µA 100 1.65 mACI = × =VBE

VBE 850 mVIC

1.65 mAIB (VCC−VBE)

VBE VCC

IB IC

(1)

VBE IB IC

(2)

52 mV?

ln 851.2 mVCBE T

S

IV V

I= =

( )

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− BJT VBE

• ( IB )

1R CR

CCV

CI

XY

2R

2

1 2BE X CC

RV V V

R R= =

+

BE

T

V

VC SI I e=

IC VBE VBE R1 R2

1R CR

CI

X

Y

2.5 VCCV =

17 kΩ 5 kΩ

2R8 kΩ100β =

1710 ASI −=

231 µABE

T

V

VC SI I e= =2

1 2

800 mVX CC

RV V

R R= =

+2.31 µABI =

11 2

100 µA 43CCB

VI I

R R= =

+≃ (IB )

1.345 VCE CC C C BEV V I R V= − = > ( )

1I

IB IC/β β

IB IB I1

R1 VBE

IC

1I

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IB

1R

2R

CCV

CR

CIY

X

1R

2R

thR

thV

XCI

CCV

CR

BI

1R

+

−

2RCCV+

−

+

−

2

1 2th CC

RV V

R R=

+

1 2||thR R R=

X th B thV V I R= −th B th

T

V I R

VC SI I e

−

=

1ln C

B th TS th

II V V

I R

= − ⋅

VBE ln CBE T B C BE B C

S

IV V I I V I I

I= → → → → → →⋯

R1 R2 IB VX IB

IC

R1 R2 I1>10IB

1I

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• R1 R2 VBE

β ( R1 R2 IB )

VBE

R2 1% VX 1%exp(0.01VBE/VT)=1.36 1%

36%

1R

2R

CR

CIY

X

EI

ERP

CCV

1

1 2

1E P E CC BE C

E

RI V R V V I

R R R

= = − +

≃

VX RE

VBE

( β >> 1)

•

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•

(1) I1 >> IB β (I1 10IB ) ( )

(2) VRE (~100 mV) VX VBE ( RE )

(3) RC RC BJT

1R

2R

CR

CIYX

BI

ER

P

CCV

1I1 BI I>>

+

−REV

RC BJT

VRE VX VBE

I1 IB 10 β

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•gm=1/(52Ω)

RC 3 kΩ

1

52 C

mT

Ig

V= =

Ω0.5 mACI =

778 mVBEV =

200 mVRE E CV R I =≃ 400 ER = Ω

2

1 2

978 mVX BE E C CC

RV V R I V

R R= + = =

+

5 µABI =

11 2

10 50 µACCB

VI I

R R= > =

+ 1 2

2.5 V50 k

50 µAR R+ = = Ω

1 30.45 kR = Ω 2 19.55 kR = Ω

CC C C XV R I V− > 1.522 VC CR I < 3.044 kCR < Ω

175 10 ASI −= ×

100β =

1R

2R

CR

CIY

X

EI

ERP

2.5 VCCV =

VX

1I

BJT

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• 500 mVREV =1 100 BI I≥

500 mV 0.5 mA 1 kER = = Ω

2

1 2

1.278 VX BE E C CC

RV V R I V

R R+ = =

+≃

1 2

100CCB

VI

R R≥

+ 1 2 5 kR R+ ≤ Ω

1 1.45 kR = Ω 2 3.55 kR = Ω

1.044 kCC XC

C

V VR

I

−< = ΩVRE

VX RC BJTRC I1 IB

R1 R2 R1 R2

175 10 ASI −= ×

100β =

1R

2R

CR

CIYX

EI

ERP

2.5 VCCV =1

52 C

mT

Ig

V= =

Ω0.5 mACI =

778 mVBEV =5 µABI =

BJT

RC 1 kΩ

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( )

• IC

BR CR

CCV

BI

X

Y

CI

X Y B BV V R I= −

RC

B CI I<< B CY CC C C B B BE BE

R IV V R I R I V V

β= − = + = + CC BE

CB

C

V VI

RR

β

−=+

VBE IC ln CBE T

S

IV V

I=

RC

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• IC

2 kCR = Ω

800 mVBEV =

ln 807.6 mVCBE T

S

IV V

I= =

154.5 mVB BR I = 0.955 VY B B BEV R I V= + ≃

ln 791 mVCBE T

S

IV V

I= =

81 mVB BR I = 0.881 VYV ≃

100β =

175 10 ASI −= ×

1 kCR = Ω10 kBR = Ω

2.5 VCCV =

BI

X

Y

CI

1.545 mACC BEC

BC

V VI

RR

β

−= =+

800 mVBEV = 0.81 mACC BEC

BC

V VI

RR

β

−= =+

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(1) VBE ( VBE )

(2) RC β

•

CC BEC

C

V VI

R

−≃

Y CC C C BEV V R I V= − ≃

( )CC BEV V−

BR β

10C BR R β=1.1CC BE

CC

V VI

R

−= ln CBE T

S

IV V

I=

1.1CC BE

CC

V VR

I

−=10

CB

RR

β=

CC BEC

BC

V VI

RR

β

−=+

1.8 VCCV =1

13 mg =Ω

BR CR

CCV

BI

X

Y

CI

175 10 ASI −= ×

100β =

1

13 C

mT

Ig

V= =

Ω 2 mACI = 754 mVBEV =

475 1.1

CC BEC

C

V VR

I

− Ω≃ ≃ 4.75 k10

CB

RR

β= = Ω 95 mVB BI R =

754 mV 95 mV 849 mVCV = + =

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BJT

• / 6

+

−inv

outv

outvoutv

+

−inv

+

−inv

B-EVCCS

CE CB CC

base ( )

CE

CC

CB

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(Common-Emitter Topology)

• B C E

+

−inv

outv

CCV

CR inv

rπ

+

−vπ mg vπ CR

outv

out

C

v

R−

Early Effect ( ro)

out m Cv g v Rπ= − outv m C

in

vA g R

v= = −inv vπ =

(1)

(2) gm IC

Cm

T

Ig

V= C C RC

vT T

I R VA

V V= =

RC CC BEV V V≤ −

CCv

T

VA

V≤

BJT

CC BEv

T

V VA

V

−<

(3) RC RC RC

BJT

RC VCC

VCC BJTVCC

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800 mV

1.8 VCCV =

CRpp2 mV

t

pp77 mV

800 mV

t

• RC 1 kΩ 21.7v m CA g R= − −≃

1 mWC CCP I V= =

0.556 mACI =

CC C C BEV I R V− = 800 mVBEV ≃

1.798 kCC BEC

C

V VR

I

−≤ = Ω

39v m CA g R= − −≃

0.02173mg =

VCC 38.46CC BEv

T

V VA

V

−< =

1 mW

2 mW

2 mWC CCP I V= = 1.1111 mACI = 0.04273mg = 900 CC BEC

C

V VR

I

−≤ = Ω 38.45v m CA g R= − −≃

• RC 1 kΩ 0.4 mA 27.66Cv m C C

T

IA g R R

V= − = − −≃

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CE

•

rπ

+

−vπ mg vπ CR

Xi

Xv

Xi

rπ

+

−vπ mg vπ CRXv

+

−

+

−

X Tin

X m C

v VR r

i g Iπββ= = = =

IC (IB )

0vπ =

Xout C

X

vR R

i= =

•

outv m C

in

RA g R

Rβ= − = − CE I/O

Early Effect

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CE

• RC ( VCC

BJT )

• CE IC=1 mA RC 1 kΩ β=100 VA=10 V ?

inv

rπ

+

−vπ mg vπ or CR

outv

( )||v m C oA g R r= −

inR rπ=

||out C oR R r=

1 26 m C Tg I V= = Ω

10 ko A Cr V I= = Ω( )|| 35v m C oA g R r= − ≃

2.6 kin mR r gπ β= = = Ω

|| 0.91 kout C oR R r= = Ω

VAV = ∞ 38vA ≃

RC

CR = ∞ Ω 384vA ≃

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CE

• RC

•

•

• CE VCC = 3 V VA = 5 V ? VCC 10 V ?

CR → ∞ v m oA g r= − (intrinsic gain)( )

Cm

T

Ig

V= A

oC

Vr

I= A

vT

VA

V=

intrinsic gainVA 5 V

intrinsic gain 200

CC BEv

T

V VA

V

−<VCC BJT

VCC

_384.6v VCC V

A =

192.3v VAA =

_10353.8v VCC V

A =

max84.6vA =

192.3v VAA = max

192.3vA =

69 Department of Electronic Engineering, NTUT

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CE

••

CCV

CR

OUTv

V∆

ER

+

−

+

−

0ER = mV g V∆ → ∆

0ER ≠ m smallV g V∆ → ∆RE

( CE )

( )1in ER r Rπ β= + +

+

−inv rπ

+

−vπ mg vπ

outv

CR

ER

RE m E

vv g v R

rπ

ππ

= +

11in RE m E m E

vv v v v g v R v g R

r rπ

π π π ππ π

= + = + + = + +

1

1111

mg rout m C m C C

vin m E

Em Em

v g R g R RA

v g R Rg R gr

π

π

>>− −= = = −+ ++ +

≃

( CE ) 1 m Eg R+

bev

REv

vbe ( CE ) ic ib

( CE )( )in mR r gπ β> =

+

−REv

C

E

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CE

•

•

Xv i rπ π=

RE ( ) ( )1X m X Xi g r i iπ β+ = + ( )1X X E Xv r i R iπ β= + + ( )1Xin E

X

vR r R

i π β= = + +

+

−Xv rπ

+

−vπ mg vπ CR

outv

ER+REv−

P

+

−Xv rπ

+vπ

Xi

inR

( )1 ERβ+

−

rπ ib

RE ib+βib

ib (1+β)RE

emitter ground base (1+β)

+

− Xvrπ+

−vπ mg vπ CR

Xi

ER+REv−

0vπ =0in m E

vv v g v R

rπ

π ππ

= = + +

0vπ = 0mg vπ =

Xout C

X

vR R

i= =

Xi

Early Effect

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• CE

•BR

rπ

( )1 ERβ+

A

gm1m Eg R >>

out A out

in in A

v v v

v v v=

( )( )

1

1EA

in E B

r Rv

v r R Rπ

π

ββ

+ +=

+ + +

( )( ) ( )

1

1 1E m C

E B E

r R g r R

r R R r Rπ π

π π

ββ β

+ + −= ⋅+ + + + +

11

Cv

BE

m

RA

RR

g β

−

+ ++

≃

( )1in B ER R r Rπ β= + + +

out CR R=

1

1

m Eg Rm C C

vm E E

g R RA

g R R

>>−= −+

≃

( )( )

1

1 11

Eout m C

in E Bm E

r Rv g R

v r R Rg R

r

π

π

π

ββ

+ + −= ⋅+ + +

+ +

( )1C

E B

R

r R Rπ

ββ

−=+ + +

CR

outv

ER

invBR

A

CCV

1BR

β+

1

mg

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( )

CCV

CR

outv

ER

inv

2rπ

CCV

CCV

CR

outv

ER

inv

2rπ

•

2||ER rπ2

1||

Cv

Em

RA

R rg π

= −+

CCV

CR

outv

ER

inv

CCV

CCV

CR

outv

ER

inv2rπ 2||

1C

v

Em

R rA

Rg

π= −+

2||CR rπ

( )( )1 ||in ER r R rπ πβ= + +

out CR R=

( )1in ER r Rπ β= + +

2||out CR R rπ=

( )1 ERβ+

( ) ( )21 ||ER rπβ+

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•C1

1C

v

Em

RA

Rg

= −+

( )1in ER r Rπ β= + +

out CR R=

CR

outv

ER

inv

biasI

CCV

1CC1 AC

CR

outv

CCV

invBR

1I

1R

2R 1C

CR

BR1R

outv

inv

2R

( ) 21in BR R r Rπ β= + + +

1||out CR R R=

1

2

||1

1

Cv

B

m

R RA

RR

g β

= −+ +

+

• I/O (C1

)

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• 1 kΩ 2 mV 1mA CE 40 mV ( RE = 4/gm β = 100)

1 kBR = Ω

1

26 mg =Ω

40 mV20

2 mVvA = =4

104 Em

Rg

= = Ω

12.8 k

1B

C v Em

RR A R

g β

= ⋅ + + Ω + ≃

11

Cv

BE

m

RA

RR

g β

−

+ ++

≃

75 Department of Electronic Engineering, NTUT

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• ro Early Effect

ro

( BJT ) BJT

( )||x Ev i R rπ π= −

( )ro x m ov i g v rπ= −

( ) ( ) ( )|| ||x x m o x m x E o x Ev i g v r v i g i R r r i R rπ π π π= − − = + +

( ) ( ) ( )( )1 || || 1 ||out m E o E o m o ER g R r r R r r g r R rπ π π= + + = + +

( ) ( )|| 1 ||out o m o E o m ER r g r R r r g R rπ π+ + ≃ ≃1m og r >>

( )1 ||m Eg R rπ+

rπ

+

−vπ mg vπ

xi

ER

xv

P

xior

+

−

out o ER r R= +:

ix RE||rπ vπ 0outR

ER

inv or

ER rπ>> [ ]1out o m oR r g r rπ β+≃ ≃

ER rπ<< ( )1out o m ER r g R+≃

76 Department of Electronic Engineering, NTUT

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• 1 mA 20 kΩ BJT β =100VA=10 V

• (C1 )

10 kAo

C

Vr

I= = Ω ER rπ<< ( )1 2m Eg R+ =

126 E

m

Rg

= = Ω

2.6 k Em

r Rgπβ= = Ω >>

outR

1R

2R 1CbV+

−

1I

outR

2R

1R

( ) 1 1 2 1|| 1 || ||out out o mR R R r g R r Rπ= = +

( )1out o m ER r g R+≃

outR

1bV+

−

2bV+

−

outR

2or

( )1 1 2 11 ||out o m oR r g r rπ= +

Cascode

77 Department of Electronic Engineering, NTUT

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CE (I)

• 100 Ω CE

2.5 VCCV =

100 kΩ 1 kΩBR CR

XOUTv

100 2.5 V 2.5 mV

100 k 100 XVΩ= ⋅

Ω + Ω≃

RB VX ?

(1) RB

(2)

2.5 VCCV =

100 kΩ 1 kΩBR CR

XOUTv1C

C1 ACDC

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CE (II)

CCV

BR CR

XOUTv

1CY

1inR rπ=

CR

BR

CCV

BR CR

YX BR

CRX

+

−

outv

inv

( ) ( )

outRCR

BR

CC BEC

B

V VI

Rβ −=

CC BEY CC C BE

B

V VV V R V

Rβ −= − >

2 ||in BR r Rπ=

, , m og r rπ

BJT

v m CA g R= −

( )||v m C oA g R r= −

out CR R=

||out C oR R r=

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CE (III)

• 8 Ω

2.5 VCCV =

100 kΩ 1 kΩBR CR

X OUTv1C

2.5 VCCV =

100 kΩ 1 kΩBR CR

X1C2C

8 spR = Ω8 spR = Ω

(AC 8 DC1 )

VCE BJTheavy saturation

AC DC

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CE (IV)

•2.5 VCCV =

100 kΩ 1 kΩBR CR

X1C2C

BR

CR+

−

outv

inv 100 kΩ

1 kΩ 8 spR = Ω

VC 1.5 V

175 10 ASI −= ×

1.5 VCV = 2.5 1.5 1 VRCV = − =1 V

1 mA1 kCI = =

Ω

ln 796 mVCBE T

S

IV V

I= =

17 µACC BEB

B

V VI

R

−= = 58.8C

B

I

Iβ = =

( )|| 0.31v m C spA g R R= =

CECE

CE (buffer)

8 spR = Ω

, , m og r rπ

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CCV

1R CR

X1C

2R+

−inv

2R+

−inv

1R

CR

outv

1 2|| ||inR r R Rπ=

||out o CR r R=

( )||v m C oA g R r= −

CCV

1R CR

X1C

2R+

−inv

ER

2R+

−inv 1R

CR

outv

ER

CCV

1R CR

X1C

2R+

−inv

ER 2C

( )1C

vm E

RA

g R

−=+

( ) 1 21 || ||in ER r R R Rπ β= + +

out CR R=

v m CA g R= −

1 2|| ||inR r R Rπ=

out CR R=

Bypass AC RE

AC

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• IC=1 mA RE VRE =400 mV20 2 kΩ

2.5 VCCV =

1R CR

X1C

2R+

−inv

ER 2C

1 mAC EI I= ≃ 400 ER = Ω1

26 mg =Ω

20v m CA g R= = 512 CR = Ω

400 mV ln 400 mV 736 mV 1.14 VCX RE BE T

S

IV V V V

I= + = + = + =165 10 ASI −= ×

100β =

400 mVREV =

1 µACB

II

β= =

1 2

10CCB

VI

R R>

+ 1 2 25 kR R+ < Ω

2

1 2

1.14 VX CC

RV V

R R= =

+ 2 11.4 kR = Ω1 13.6 kR = Ω

1 2|| || 1.85 kinR r R Rπ= = Ω

RE R1 R2

1 2

5CCB

VI

R R>

+ 1 2 50 kR R+ < Ω2 22.4 kR = Ω1 27.2 kR = Ω

1 2|| || 2.14 kinR r R Rπ= = Ω

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CCV

1R CR

sR

1C 2R+

−inv

ER

2CLR

outv

+

−inv

sR

1 2||R RER

||C LR R

outvX

( )( )

1 2

1 2

|| || 1

|| || 1EX

in E s

R R r Rv

v R R r R Rπ

π

ββ

+ + =+ + +

( )( )

1 2

1 2

|| || 1 ||1|| || 1

Eout out C LX

in in X E sE

m

R R r Rv v R Rv

v v v R R r R R Rg

π

π

ββ

+ + = =+ + + +

R1 R2

DC AC

( )

DCAC

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(Common-Base Topology)

• E C B

CCV

CR

+

− inv

+−bV

OUTv rπ+

−vπ mg vπ CR

outv

+

−inv

v m CA g R= CE CB

RCout

mC

vg v

R π− = outin

m C

vv v

g Rπ = − = − outm C

in

vg R

v=

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• CB IC=0.2 mA600 mV

• VB

1.8 VCCV =

CR

+inv

BV

outv

600 mV

600 mV ln 600 mV 1.354 VCB BE T

S

Iv V V

I= + = + =

RC1.8 V 1.354 V 0.446 V− =

17.2Cv m C C

T

IA g R R

V= = =

175 10 ASI −= ×100β =

Vb

+

−inv 600 mV

outv

CR

1.8 VCCV =

1R

2R

BI1I

100β =175 10 ASI −= ×1

1 2

10 20 µA CCB

VI I

R R+≃ ≃ ≃

1 2 90 kR R+ = Ω 2

1 2

1.354 VB CC

RV V

R R=

+≃

2 67.7 kR = Ω1 22.3 kR = Ω

0.2 mACI = 0.2 100 mA 2 µABI = =

β

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•

CCV

CR

inR 1in

m

Rg

=

VA=∞ CBIC=1 mA 26

Ω (CE β/gm)

CCV

CR

BV

XI

+

−XV V∆

1Xin

X m m

V VR

I g V g

∆ ∆= = =∆ ∆

•

CR

outRor 1outR

1 || ||out out C o CR R R r R= =

1out oR r=

out CR R=

CB Rin Rout

outv m out

in

RA g R

R= =

1 || ||out out C o CR R R r R= =

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CB

CR

CCV

+

−inv

sR

1

mg

outv

X

X

1

mg

sR

+

−inv

11

1 1m

X in inm s

sm

gv v v

g RRg

= =++

outm C

X

vg R

v= CB

11out m C C

in m ss

m

v g R R

v g R Rg

= =+ +

CE ( Rs

)

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• CB 50 Ω RF50Ω CB 50Ω

( )

CR

CCV

CR

CCV

BV

outv

50 sR = Ω

outv

BV

+

−inv

150 in

m

Rg

= = Ω

0.52 mAC m TI g V= =

11 2

Cv

sm

RA

Rg

= =+

CB 50

1in

in

sm

vi

Rg

=+ 1

C inout

sm

R vv

Rg

=+

0.5C sR R≤

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CB

CCV

CRoutv

BRor

ER

BV

+

−inv

ER

orCR

1outR 2outR

150 in

m

Rg

= = Ω

0BR =

( ) ( )1 1 || ||out m E o ER g R r r R rπ π= + +

( ) ( ) || 1 || ||out C m E o ER R g R r r R rπ π= + +

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RB ro

rπ+

−vπ mg vπ CR

outvBR

ER+inv

−

P

outm

C

vg v

Rπ = − out

m C

vv

g Rπ = −

RBout out

m C C

v v v

r g r R Rπ

π π β= − = −

( ) ( )out outP B B

C C

v vv R r R r

R Rπ πβ β−= − + = +

P KCL P inm

E

v v vg v

r Rπ

ππ

−+ =

( )1

outB in

out Cm

m C E

vR r v

v Rg

r g R R

π

π

β+ −

−+ ⋅ = ( )

( )11

1

out C C

Bin E BE

m

v R RRv R R r R

gπ

ββ

β

=+ + + + +

+

≃

CERB RB

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RB

CCV

CR

+

−inv

ER

outvBR

CB Stage

rπ

+

−vπ mg vπ CR

outvBR

+

−Xv

Xi

XB

rv v

r Rπ

ππ

= −+

KCL m X

vg v i

rπ

ππ

+ = −

1m X X

B

rg v i

r r Rπ

π π

−+ = − +

1

1 1X B B

X m

v r R R

i gπ

β β+= ++ +≃

RB=0,Rin=1/gm

BR

ER

AV = ∞AV = ∞

1

1B

m

R

g β+

+

( )1 Er Rπ β+ +

emitter base RB (1+β) Emitterdegeneration base emitter RE (1+β)

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CR

CCV

BR

outv

CR

outv

CCV

1

1

1B

m

R

g β+

+

XReqR

XR

1

1

1B

eqm

RR

g β= +

+

2 2 1

1 1 1 1

1 1 1eq B

Xm m m

R RR

g g gβ β β

= + = + + + + +

• RX

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CB (I)

•

CCV

CR

OUTv

+

−inv

1C+

−BV

CCV

CR

OUTv

+

−inv

1C+

−BV

CCV

CR

outv

+

− inv

1C+

−BV

1

mg

ERER

emitter DC path emitter DC pathAC

RE emitter DC path

1||in E

m

R Rg

=

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CB (II)

CCV

CR

outv

+

−inv

1C+

−BV X

inRER

sR

1||in E

m

R Rg

=

Rin

( )

1||

11 1 1||

EX in m

in in s m E sE s

m

Rv R g

v R R g R RR Rg

= = =+ + ++

outm C

X

vg R

v=

( )1

1 1out

m Cin m E s

vg R

v g R R=

+ +

CCV

CR

outv

+

− inv1C

+

−bV

inRER

sRini

1i

2i

iin i1 RE(shunt ) i2 RC

RE

RC RE

RE 1/gm i2

1E

m

Rg

>>C E TI R V>>

RE RE VT

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CB (III) - Vb

• CECE CB bypass

AC CE bypass( common AC

)

CCV

CR

ER

1R

2R

1C

inv

1I

CCV

CR

ER

thR

+

−thV

CCV

CR

ER

1R

2R

BC

β I1>> IB2

1 2b CC

RV V

R R+≃

Base

1 2||thR R R=

bypass CB base ACground

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• CB 10 50 Ω

1E mR g>> 500 ER = Ω

1 50 in mR g = Ω≃ 0.52 mA, 899 mVC BEI V= =

bypass (AC )

500 CR = Ω10v m CA g R= =

RE 0.52 mA 500 260 mVE E C E TI R I R V= × Ω = >>≃

1.16 Vb E E BEV I R V= + =

R1 R2 10 52 µABI =

1

1 2

1.16 Vb CC

RV V

R R=

+≃

1 2

52 µACCV

R R=

+1 25.8 kR = Ω

2 22.3 kR = Ω

2.5 VCCV =

CR

ER

1R

2R

BC

OUTv

1Cinv

100β =

165 10 ASI −= ×

AV = ∞

900 MHzC1 CB

1

11

20mg

j Cω=

1

20 2071 pF

2 900 MHzm mg g

Cω π

= = =⋅

11 1

1 20m

B

g

j Cβ ω=

+

0.7 pFBC =

( 10 )

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(Common Collector Topology)

• B E C

CCV

ER

INV

OUTV1BEV

2BEV

1INV

1OUTV

1IN INV V+ ∆

1OUT OUTV V+ ∆

∆VOUT > ∆VIN VBE2 < VBE1

IE

IERE=VOUT

∆VOUT ∆VIN

1

rπ

+

−vπ mg vπ

ER

inv+

−

outv

outm

E

v vg v

r Rπ

ππ

+ =1

out

E

r vv

Rπ

π β=

+

in outv v vπ= +

11 1

11

out E

inE

E m

v Rrv R

R gπ

β

=+ +

+

≃

1

Early Effect

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CC

• CC

CCV

inv+

−

ER

CCV CCV

thR

inv+

− inv+

−out inv v=

ER

1th

m

Rg

=

outv

th inv v=

1in

m

Rg

=

CC Rth=1/gm

CC(CE CB

)

outv

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•

•

CCV

INv

OUTv

1I

1vA ≃

VBE out in BEv v V= −

VBE vOUT vIN

CCV

ERinv+

−

outv

sRsR

CCV

thR

th inv v=+

−

1

1s

m

R

g β+

+

ER

11

out E

sinE

m

v RRv R

gβ

=+ +

+

outv

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CC

rπ

+

−vπ mg vπ

ER

Xv+

−

Xi

inR

0CR →

CCV

ER

CCV

inRER

Xi v vπ π=

iX gmvπ RE ( )X m Ei g v Rπ+

( ) ( )X X m E X X m Ev v i g v R i r i g v Rπ π π π= + + = + +

( )1XE

X

vr R

i π β= + +Follower RE

buffer ( )

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• CE 20 1 kΩ

(a) 8Ω ?(b) CC ? CC 5 mA

β=100 VA follower

CCV

1 kΩ CR8 spR = Ω

1C

1inRinv+

−1I

CCV

( )20 ||8 0.159v CA R= ⋅ Ω = ( )1 2 1 1058 in spR r Rπ β= + + = Ω

( )1||20 10.28C in

vC

R RA

R= ⋅ =

CCV

1 kΩ

inv+

−

CR

1C

8 spR = Ω

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CCV

sR

ER

outR

sR

CCV

1

1s

m

R

g β+

+

ER

1||

1s

out Em

RR R

g β

= + +

Followerdriver follower

( ) ( )ER

inv+

−inv+

−

CCV

sR

ER

or

sR

ER or||

1||

1

E ov

sE o

m

R rA

RR r

gβ

=+ +

+

( ) ( )1 ||in E oR r R rπ β= + +

1|| ||

1s

out E om

RR R r

gβ

= + +

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CC

CCV

ER

X

OUTv

1R

2R

1C

inv

−

+

inv

−

+

1C

CCV

BRBI

XY OUTv

ER

R1 R2 IB

β

VCC C VCC BJT

RB RE

β

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• RB=10 kΩ RE=1 kΩ VCC=2.5 V

KVL B CBE E C CC

R IV R I V

β+ + =

800 mVBEV ≃ 1.545 mACI =

ln 748 mVCBE T

S

IV V

I= = 1.593 mACI =

159 mVB BI R =1.593 VC EI R = C E B BI R I R>>inv

−

+

1C

CCV

BRBI

XY OUTv

ER

165 10 ASI −= ×100β =

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(I)

• 10 kΩ 10 mV0.1 W 8Ω

12 V

2 2, ,0.1 W 8L L rms L L rmsP i R i= = ⋅ = ⋅

, 0.112 AL rmsi =

, ,2 0.158 AL peak L rmsi i= =

, , 0.158 8 1.26 Vo peak L peak Lv i R= ⋅ = × ≃

1.26126

0.01vA = =

inv

−

+

10 ksR = Ω CC

8 LR = Ω

outv

Li126vA =

1. 8Ω CE2. 126 CC3. 10 kΩ CB

CE CC CB

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(II)

•

inv

−

+

10 ksR = Ω CC

8 LR = Ω

outv

1vA 2vA 3vA

1.CE CE CC

2.CC

3.CE CE

2.CE CE

3.

1.CE CE CB

1.CE CE CC

2.CC

3.CC

1 2 3v v v vA A A A= ⋅ ⋅

CC +CE +CC

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• 8Ω CC ( )

Li

CC

8 LR = Ω

ov

4ER

4BV

4BI3ov

4inR 12 VCCV =

(III) –

, 0.158 AL peaki = , 1.26 Vo peakv =

4 50β =

4

12 620

0.3CC CEQ

EEQ

V VR

I

− −= = = Ω

500.3 0.294 A

1 51CQ EQI Iβ

β= = ⋅ =

+

0.294 A11.3

26 mVC

mT

Ig

V= = = 4.42

m

rgπβ= = Ω

( )( )( )( )

( )( )

1 || 51 20 || 80.985

1 || 4.42 51 20 || 8E L

vE L

R RA

r R Rπ

ββ

+ ⋅= = =

+ + + ⋅

1.26 V vo3

1.28 V

0.158 A

0.158 A

Ci

CQ EQI I≃

CEvCEQV 12 VCCV =

1.26 V1.26 V

0.3 AEQI =

6 VCEV =

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(IV) –

• 10 kΩ CC

6 V, 1 mACEQ CQV I= =

1 2|| 100 kR R = Ω

1

12 66 k

0.001CC CE

EE

V VR

I

− −= = = Ω

10.0385

26 C

mT

Ig

V= = =

Ω2.6 k

m

rgπβ= = Ω

( )1 2|| || 1 85.9 kin ER R R r Rπ β= + + = Ω ( )

( )1

0.8921

Einv

in s E

RRA

R R r Rπ

ββ

+= =

+ + + 8.92 mVov =

1 155 kR = Ω 2 282 kR = Ω

+inv

−

sR

10 kΩ

12 VCCV =

1R

2R

1 100β =1ov

1ER

( ) ( )1 1 2 1 1 1|| || 1in ER R R r Rπ β= + +

CEv12 VCCV =CEQV

Ci

CQ EQI I≃

Rs 10

1 mACQI =

6 VCEV =

608.6 kΩ

10 mVinv =

( )

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(V) –

2 328.8, 5v vA A= =

3 4 4 4 6 0.7 6.7 VC B E BEV V V V= = + = + =

4

0.2945.88 mA

50BI = = 33 313 mA, 0.5C

C mT

II g

V= =≃

3 200 m

rgπβ= = Ω

( ) ( )( )

4 4 4 41 ||

4.42 51 20 ||8 296

in E LR r R Rπ β= + +

= + = Ω

( )( )

3 3 43

3 3 3

||5

1C in

vE

R RA

r Rπ

ββ

= =+ + 3 27.3 ER Ω≃

, , , ,126 0.892 0.985v v in v gain v o v gainA A A A A= = ⋅ ⋅ = ⋅ ⋅

, 144v gainA ≃

VBE4

33

3 3

12 6.7296 CC C

CRC RC

V VR

I I

− −= Ω = = 3 18.9 mARCI =

( ) ( )3 5 6 3 3 3|| || 1 50 k || 200 101 27.3 2.8 kin ER R R r Rπ β= + + = Ω + ⋅ Ω ≃

5 6|| 50 kR R = Ω ( ) 5 69.9 kR = Ω 6 176 kR = Ω

12 VCCV =

5R

6R

3R

4R

3CR

3ER

2CR

2ER

3inR2inR

1ov2ov

3 4C BV V=3 100β =2 100β =

22

12 61.2 k

5CC C

CCQ

V VR

I

− −= = = Ω 22

2

0.52 kT

CQ

Vr

Iπβ= = Ω

( )( )

2 2 32

2 2 2

||28.8

1C in

vE

R RA

r Rπ

ββ

= =+ + 2 23.7 ER Ω≃ 5 6|| 50 kR R = Ω ( ) 3 181 kR = Ω

4 69.1 kR = Ω

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(VI) –

•

• ( )headroom

•• decouple

181 kΩ

23.7 Ω

1.2 kΩ

69.9 kΩ

176 kΩ

296 Ω

20 Ω 8 Ω27.3 Ω

155 kΩ

282 kΩ

69.1 kΩ6 kΩ

12 VCCV =

10 kΩ

−

+sv

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(I)

PSRR

DDV

SSV

INv +

INv − −

+

OUTv

offsetCMRR

( )SR

0

(dB)

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(II)

• OPA (DVCVS)

• OPA A OPAvo

+

−

1v

2vov

+

−

− −

1v2v

( )1 2 oA v v v− =−

−A → ∞

1 2 0v v− =

1 2v v=

( )1 2ov A v v= −

v1 = v2 (virtual short)(v1=0)

(v2≈0)(virtual ground virtual earth)

non-inverting input

inverting input

+

++

+

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(I)

•

•

IvOv

1R

2R

−

+

2

1

Ov

I

v RA

v R= = −

0a bv v= =

1 2 1Ii i v R= =

av

0bv =

IvOv

1R

2R

−

+1i

2iZin

22 2

1O I

Rv i R v

R= − = −

2

1

1Ov

I

v RA

v R= = +

Ov−

+Iv

1R

2R

Ov−

+Iv

1R

2R

1i

2iav

a Iv v=

1 2 1ai i v R= = −Zin

( ) 22 1 2

1

1O I

Rv i R R v

R

= − + = +

KCL KVL ( )

v i i v

R2 5 kΩ 25 kΩR1

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(II)

• (level shifting)

IvOv

1R

2R

−

+

IvOv

1R

2R

−

+

−

+BIASV

2 2

1 1

1O I BIAS

R Rv v V

R R

= − + +

Ov−

+Iv

1R

2R

2 2

1 1

1O I BIAS

R Rv v V

R R

= + −

2R

1R

IvOv

+

−

−

+BIASV

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( )

•

•

IvOv

1 1 kR = Ω

2 10 kR = Ω

−

+

2

1O I

Rv v

R= −

IvOv

1 1 kR = Ω

2 10 kR = Ω

−

+

IvOv

1 1 kR = Ω

2 10 kR = Ω

−

+

−

+BIASV

2 2

1 1

1O I BIAS

R Rv v V

R R

= − + +

+VCC

−−−−VSS

100 mV1 V−

OPAOK

+VCC

GND

1 V−100 mV

OPA0 V

100 mV 1 V 2.475 V= − +

Level shiftingAC

VCC/2

+VCC

GND225 mV

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(III)

• /

1v

Ov

1R fR

−

+

2v

nv

2R

nR

1 21 2

f f fO n

n

R R Rv v v v

R R R

= − + + +

⋯

1 2f nR R R R= = = =⋯

( )1 2O nv v v v= − + + +⋯

−

+1v

2v

bR

aR

aR

bR

Ov

( )1 2b

Oa

Rv v v

R= −

( v2=0 v1 vo1 v1=0 v2

vo2 vo= vo1 +vo2 )

v i i v

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(IV)

•

−

+

1v2v

aR

aR3v

4vaR

aR

bR

bR

ov

( )1 2 3 4b

Oa

Rv v v v v

R= + − −

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(V)

•

•

0

ivov

R

C

−

+

( )0 0ov =

KCL 0i ov dvC

R dt+ =

0

1 t

o iv v dtRC

= − ∫

iVoV

R

1sC

−+

1 1o i i

sCV V VR sRC

= − = −

ivov

C

R

−

+

( )1o i i

RV V sRC V

sC

= − = −

v i i v

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(Voltage Follower)

• ( )

• (heavy load)

Iv Ov−

+

1Ov

I

vA

v= ≃

Iv

100 ksR = Ω

1 kLR = Ω+

−Ov+

−

Source Load

1k0.01

100k+1kO Iv v= ≃

Iv

100 ksR = Ω

1 kLR = Ω+

−

Ov+

−

Source Load

Buffer

O Iv v≃

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• ZL

+

−

SV

1R

OV

ILZ

1SI V R=

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• general

INv +

INv −

2R

1R

3R

4R

Ov−

+

BIASV

( )( )

( )( )

4 1 2 3 1 22

1 3 4 1 1 3 4O IN IN BIAS

R R R R R RRv v v V

R R R R R R R+ −

+ += − +

+ +

INv +4

3 4IN

Rv

R R ++4 2

3 4 1

1 IN

R Rv

R R R +

+ +

INv −2

1IN

Rv

R −−

3

3 4BIAS

RV

R R+BIASV 3 2

3 4 1

1 BIAS

R RV

R R R

+ +

31

2 4

RR KR R= =

1 1

1 IN

Kv

K K ++

+

2

1IN

Rv

R −−

( ) ( )11 1

1 1 BIASK VK

+ +

( )2

1O IN IN BIAS

Rv v v V

R + −= − +

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( )

( )2 41 2

3

21O BIAS

G

R Rv v v V

R R

= + − +

2v

1v

2R

4R

GROv

−

+ BIASV

+

− 4R

3R

3R2R

−

+ 1v

211

G

Rv

R

+

2v

221

G

Rv

R

+

3

3 4BIAS

RV

R R+BIASV 3 4

3 4 3

1 BIAS

R RV

R R R

+ +

21

G

Rv

R

−

22

G

Rv

R

−

2 21 21

G G

R Rv v

R R

− + +

2 22 11

G G

R Rv v

R R

− + +

4

3

R

R

× − +

4 4

3 4 3

1R R

R R R

× ⋅ + + +

( )2 41 2

3

21 BIAS

G

R Rv v V

R R

= + − +

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OPA

• OPA ( )1

oAA s

sτ=

+

12c cfω π

τ= =

fall-off rate:−6 dB/oct

f (Hz)fc fT

Gain (dB)

f (Hz)

Phase (deg.)

0

90−

oA

oAτ OPA ( )1 τ−

cf 3 dB

Tf 0 dB (1)OPA fT OPA (GBW)

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(Gain-Bandwidth Product)

•• OPA

• =

12c cfω π

τ= =

( )1

o

c

AA s

s

ω

=+

( )2

1

o

c

AA jω

ωω

=

+

( ) 1TA jω =

2

1 To

c

Aωω

+ =

2

1T

c

ωω

>>

To

c

Aωω≃

T o cAω ω=

3 dB

( )x x Tf A j fω⋅ =

OPA fx

( ) Tx

x

fA j

fω =

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OPA (I)

• (AOL)

OPA

•

Bipolar OPA Ri 150 kΩFETs (Mega ) OPA

•

Bipolar OPA 100Ω

OPA OPA1 kΩ 100 kΩ 10 kΩOPA

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OPA (II)

• (Input offset voltage,VOS VIO)

OPA 0 VAC

(VIO)

• (Input offset current,IOS IIO)

0OPA

BJT

1 1O f BV R I=IB1 (IB2=0)

2 2 21

1 fO B

RV I R

R

= − +

1 2 1 2 21

1 fO O O B f B

RV V V I R I R

R

= + = − +

IB1 = IB2

IB2 (IB1=0)

2BI

1BI

fR

1R

OV

SV

2R −+

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OPA (III)

• (VIN)

OPA ( )offset offset OPA

• (Vopp)

DC 0 V OPA

2 1iV V V− ≤ ≤

iV1V

2V−

oV

1oV

2oV−

Vi

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OPA (IV)

• Slew Rate (SR)

OPA (OPA

) SR OPA step(unit gain) zero crossing

• SR sino mv V tω=

cosom

dvV t

dtω ω=

0, ,2 ,

om

t

dvV

dt ω π π

ω=

=⋯

mSR V ω≥ mVSR

ω≥

SR OPA

OPA

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OPA (V)

• (Common-mode rejection ratio, CMRR)

OPA ( )

CMRR (dB)

CMRR 80 dB CMRR

• (Power supply sensitivity,∆VIO/∆VGG)

∆VGG ∆VIO

•

OPA

• Ci

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OPA (VI)

• (Full power response)

OPA

• (Gain-Bandwidth Product)

17 OPA

OPA

75 kHz

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OPA (VII)

• (Rise time, tr)

OPA OPA 10% 90%

• (Power supply voltage)

• (Power supply current)

• ( )

•( )

0.35r ct f× ≅

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• OPA

• datasheetAC

• 100

• Slew Rate

• OPAOPA datasheet

• bypassDC 1 MHz 1 µF

(10MHz MHz)0.1 µF

OPA

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•

• ( )gm rπ

ro

• BJTCE CB CB

CC CE CB CC

• OPA

135 Department of Electronic Engineering, NTUT