Lecture 19 Bipolar Junction Transistors (BJT): Part 3...

ECE 3040 - Dr. Alan Doolittle Georgia Tech

Lecture 19

Bipolar Junction Transistors (BJT): Part 3

Ebers Moll Large Signal BJT Model, Using CVD model to solve for DC bias point

Reading:

Pierret 11.1


IE IC

IB

Collector

Base

Emitter

αFIF

IF

−= 10

TEB

VV

FF eII

DiodesIdeal

Development of the Large Signal Model of a BJT (Ebers-Moll Model) PNP in Active Mode

Emitter

Base

Collector

Forward Biased - BE

Reverse Biased - BC

Accelerated by the

Electric Field

IR=IRO~0

IE IC IB

Collector

Base

Emitter IF IR

Note: Green arrows indicate directions and magnitude of hole motion.


Development of the Large Signal Model of a BJT (Ebers-Moll Model) PNP in Inverse Active Mode

Emitter

Base

Collector

Reverse Biased - BE

Forward Biased - BC

Accelerated by the Electric Field

In Inverse Active bias mode, the transistor still “sort of” works (may attenuate instead of amplify) but works poorly because the doping order of emitter, base and collector are reversed.

IE IC

IB

Collector

Base

Emitter

αRIR

IF=IFO~0 IR

−= 10

TCB

VV

RR eII

DiodesIdeal

IE IC IB

Collector

Base

Emitter IF IR

Note: Green arrows indicate directions and magnitude of hole motion.


Note: A=αRIRo= αFIFo

IE IC

IB

Collector

Base

Emitter

αFIF αRIR

IF IR

−=

−= 11 00

TCB

TEB

VV

RRV

V

FF eIIandeII

DiodesIdeal

−−

−=

−−

−=

11

11

00

00

TCB

TEB

TCB

TEB

VV

RV

V

FFC

VV

RRV

V

FE

eIeII

eIeII

α

α

Development of the Large Signal Model of a BJT (Ebers-Moll Model) Full Ebers Moll Model of a PNP


Development of the Large Signal Model of a BJT (Ebers-Moll Model)

IE IC

IB

Collector

Base

Emitter

αFIF αRIR

IF IR

−=

−= 11 00

TBC

TBE

VV

RRV

V

FF eIIandeII

DiodesIdeal

−−

−=

−−

−=

11

11

00

00

TBC

TBE

TBC

TBB

VV

RV

V

FFC

VV

RRV

V

FE

eIeII

eIeII

α

α

Full Ebers Moll Model of a NPN


Using the Ebers-Moll model requires mathematical complexity (and much pain). Thus, we have an approximate solution

method* that allows a quick solution.

*I refer to as the “CVD/Beta Analysis”. This is just my term, not a universal name.


Quick Solution using a CVD/Beta Approach

Consider the following pnp BJT circuit with a common emitter current gain, βDC=180.7. Find Ib, Ic, and Ie assuming a turn on voltage of 0.7V.

0=-4V+IB(12000)+VEB+IE(15000) 4V=IB(12000)+0.7V+IC(1/αDC)(15000)

4V=IB(12000)+0.7V+[βDCIB][(1+βDC)/ βDC](15000) 3.3V=IB[(12000)+(1+180.7)(15000)]

IB= 1.2uA IC=180.7IB=218uA IE=(181.7/180.7)IC=219uA

CBoEdcC III +=α

CEoBdcC III += β

Neglect Leakage currents

R1(Ib)

R3(Ie)

Ie

Ib

Ic

CBE III +=



Compare our results using the CVD/Beta model to the full Ebers-Moll solution used in PSPICE...

Actual Vbe=0.662V not 0.7V as assumed

Actual Ibase=1.05uA not 1.2uA as calculated

Only 1% error in the

collector and emitter

currents

Current into various nodes Voltage at various nodes


IV curve looks like a diode

Real shows variation due to “base width modulation” dependent on the applied VCB

After the base-collector junction is reverse biased (starts collecting), IE~=IC

Real IV is limited by breakdown of the base-collector junction

Development of the Large Signal Model of a BJT (Ebers-Moll Model) Common Base

Input

IE and VEB

Output

IC and (-VCB)

Input Output


IV curve looks like a diode but has a DC shift associated with the reverse biased base-collector junction current

After the base-collector junction is reverse biased (starts collecting), IC=βIB


Input

IB and VEB

Output

IC and VEC

Real IV is limited by breakdown of the base-

collector junction

Real shows finite slope due to “base width modulation” dependent on the applied VCB

Input

Output

Common Emitter


−−

−=

−−

−=

11

11

0

0

TCB

TEB

TCB

TEB

VV

RV

V

C

VV

VV

FE

eIeAI

eAeII

−

+−

−

=

−

−

−

+=

1sinh

cosh1

sinh

1

1sinh

11sinh

cosh

TCB

TEB

TCB

TEB

VV

B

B

B

BoBCo

C

CVV

B

B

BoBC

VV

B

B

BoBVV

B

B

B

BoBEo

E

EE

e

LW

LW

LpD

nLD

qAe

LWL

pDqAI

e

LWL

pDqAe

LW

LW

LpD

nLDqAI

IF0

IR0

A

A

*



−−

−=

−−

−=

11

11

0

0

TCB

TEB

TCB

TEB

VV

RV

V

C

VV

VV

FE

eIeAI

eAeII

When VCB=0,

gaincurrentbasecommonIIbut

IIeIIandeII

ThusseeAI

but

eAIandeII

DCFEFC

EFCV

V

FFCV

V

FE

F

VV

CV

V

FE

TEB

TEB

TEB

TEB

ααα

αα

=→=

==

−=

−=

>

−=

−=

,

11

,*)(

,

11

00

0

0

VEB

IB

IC

IE

Looks like a diode


The collector current is the fraction of the emitter current “collected”


−−

−=

−−

−=

11

11

0

0

TCB

TEB

TCB

TEB

VV

RV

V

C

VV

VV

FE

eIeAI

eAeII

When VEB=0,

DCRCRE

VV

RCV

V

RRE

R

VV

RCV

V

E

IIbut

eIIandeII

ThusseeAI

but

eIIandeAI

TCB

TCB

TCB

TCB

ααα

α

≠→=

−−=

−−=

>

−−=

−−=

,

11

,*)(

,

11

00

0

0VCB

IB

IC

IE

Looks like a diode

In Inverse Active mode, the emitter current is the fraction of the collector current “collected”


Lecture 19 Bipolar Junction Transistors (BJT): Part 3...

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Transcript of Lecture 19 Bipolar Junction Transistors (BJT): Part 3...